BaoCaoDATN_HoangThanhTung

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1 | Sinh vin thc hin : Hong Thanh Tng in T 1-K54

LI NI U

Ngy nay, nh c s tin b vt bc trong khoa hc v k thut, cc cng

ngh mng khng dy ngy nay ang c pht trin mnh m v c nhiu ng

dng thit thc trong cuc sng. Vi kh nng c ng cao, thun tin trong s

dng, cc cng ngh ny ang dn dn thay th cc cng ngh mng c dy truyn

thng. Song cng do s di chuyn ca cc thit b di ng trong mng lm cho topo

mng lun thay i, cng vi l t l li cao v gii hn v bng thng, nng

lng so vi mng c dy, nn cc giao thc nh tuyn trong mng khng dy tr

nn phc tp hn. M hnh m ha ngun phn tn trong mng cm bin khng dy

l mt ch mi vi kh nng gim dung lng tn hiu ti ngun bng cch khai

thc s tng quan gia cc ngun vi nhau, cho nn lm gim khi lng tnh ton

cng nh nng lng tiu th. n ny c thc hin nhm mc ch tm hiu

su hn v m ha ngun phn tn s dng m LDPC trong mng cm bin khng

dy.

Trong qu trnh thc hin n, em gp rt nhiu kh khn. Tuy nhin

c s gip tn tnh ca thy gio Nguyn Trung Dng, cng bn trong nhm

cng nh cc bn trong phng lab em hon thnh n ny.

Mc d c gng ht sc nhng n chc chn khng trnh khi nhiu

thu st, v th em rt mong nhn c s gp t cc thy, c gio v cc bn

hon thin hn.

Em xin gi li cm n chn thnh n:

- Thy gio Nguyn Trung Dng

- Cc bn trong phng lab WSN

- Cng ton th gia nh, bn b h tr cho em.

H Ni, ngy 20/05/2014

Sinh vin thc hin

Hong Thanh Tng T01-K54

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TM TT N

M ha ngun phn tn trong mng cm bin khng dy s dng LDPC:

Cng ngh mng cm bin khng dy WSN ang ngy cng pht trin v c

nhiu ng dng thc t. n c thc hin s tng hp cc kin thc c bn v

mng cm bin khng dy, tm hiu su hn v m ha ngun phn tn da trn s

tng quan ca cc ngun: cc loi m ha ngun phn tn, v c th l m ha

ngun phn tn s dng syndrome. Mc tiu ca n l tm ra cch tt nht cho

vic nn v m ha d liu c truyn trn mng cm bin khng dy. iu ny

rt c quan tm v vic nn s gip nghin cu nhng yu cu cht ch cho vic

truyn trn mi cm bin. M LDPC l m c s dng trong n lm gim s

lng bt ca d liu ngun truyn i, gim t l li bt v gim nng lng tiu th.

Hiu qu ca m hnh mng phn tn ny s c kim tra bng cng c m phng

Matllab.

ABSTRACT

Distributed Source Coding in Wireless sensor network with LDPC code:

Wireless sensor network technologys are more and more developing, applied

in ourlife ways. Project implementation will be integrated knowledge base on

wireless sensor network, a better understanding of distributed source coding based

on the correlation of the source: the distributed source coding type, and specific

distributed source coding using syndrome. The goal of the work is to find the best

practical implementation with respect to compression and coding of the data to be

transmitted by sensors in a wireless network. This is desirable because compression

will help reaching the tight requirements on transmitted effect in each sensor. The

recently developed scheme of distributed source coding is a revolutionary way of

doing this. LDPC code is the code used in the scheme reduces the number of data

bits transmitted power, reduce bit error rate and reducing energy consumption. The

effectiveness of this distributed network model will be tested using simulation tools

Matllab.

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MC LC

LI NI U ............................................................................................................ 1

TM TT N ...................................................................................................... 2

MC LC ................................................................................................................... 3

CC HNH V S DNG TRONG N ............................................................ 5

CC T VIT TT S DNG TRONG N .................................................... 6

CHNG I : TNG QUAN V MNG CM BIN KHNG DY ..................... 7

1.1 Gii thiu v mng cm bin khng dy ....................................................... 7

1.2 Cu trc mng WSN ...................................................................................... 7

1.2.1 Cu trc 1 node mng WSN ................................................................... 7

1.2.2 Cu trc mng cm bin khng dy ....................................................... 9

1.2.3 Kin trc giao thc mng WSN ............................................................ 10

1.2.4 Cc yu t nh hng n mng WSN ................................................. 13

1.3 Cc vn v m hnh trong mng cm bin khng dy ............................... 16

CHNG II : M NGUN PHN TN TRONG MNG CM BIN KHNG

DY ....................................................................................................................... 18

2.1 M ngun phn tn ......................................................................................... 18

2.2 DSC khng tn tht ........................................................................................ 20

2.2.1 M ha Slepian-Wolf ca hai ngun nh phn ......................................... 21

2.3 DSC tn tht.................................................................................................... 22

2.3.1 Trng hp i xng m nh phn ........................................................... 24

2.3.2 Trng hp Gaussian bc hai ................................................................... 24

2.4 La chn m LDPC ........................................................................................ 25

CHNG 3 : M NGUN PHN TN S DNG SYNDROME ...................... 26

3.1 M ngun phn tn s dng cc syndrome .................................................... 26

3.2 Thit k i xng ............................................................................................ 28

3.2.1 Cu trc b gii m .................................................................................. 30

3.2.2 a ngun .................................................................................................. 30

3.3 M ha LDPC ................................................................................................. 31

3.3.1 Gii thiu mt s loi m ......................................................................... 31

3.3.2 M LDPC ................................................................................................. 37

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3.4 M LDPC trong vic ci t phn tn ............................................................ 41

3.4.1 Vic xy dng m cho trng hp i xng ............................................. 42

CHNG 4 : M PHNG TRN MATLAB ......................................................... 44

4.1 Gii thiu v cng c m phng MATLAB................................................ 44

4.1.1 Gii thiu v MATLAB........................................................................ 44

4.1.2 Cch tm mt bn MATLAB s dng ............................................. 44

4.1.3 S dng MATLAB hiu qu ................................................................ 45

4.2 M phng trn MATLAB ............................................................................ 46

4.2.1 Thc hin m Hamming ....................................................................... 47

4.2.2 Thc hin m LDPC ............................................................................. 49

KT LUN CHUNG ................................................................................................ 51

PH LC .................................................................................................................. 52

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CC HNH V S DNG TRONG N

Hnh 1.1. M hnh mng cm bin khng dy8

Hnh 1.2. Cc thnh phn ca mt node cm ng..9

Hnh 1.2.2. Cu trc mng cm bin khng dy..11

Hnh 1.2.3. Kin trc giao thc ca mng cm bin12

Hnh 1.4. Mng WSN vi hai m hnh mng khc nhau..19

Hnh 2.1a. M ha ngun phn tn vi thng tin bin ti b gii m..21

Hnh 2.1b. Knh tng quan o gia X v Y..22

Hnh 2.2. Vng tc bt ca 2 ngun23

Hnh 2.2.1. Cu trc coset25

Hnh 2.4a. S khi ca m ha Wyner-Ziv25

Hnh 2.4b. Bn trong v bn ngoi vng t l ca DSC tn tht.26

Hnh 3.1. u ra c th ca Y nu X thuc coset {000, 111}..30

Hnh 3.2. Cu trc b to ma trn trong trng hp i xng 32

Hnh 3.2.2. nh ngha ma trn trong trn hp a ngun..33 Hnh 3.3.1.1a. Cu trc b m ha Turbo34

Hnh 3.3.1.1b. Cu trc b gii m Turbo...35

Hnh 3.3.2. Ma trn kim tra chn l cho m LDPC ( 20,3,4).41

Hnh 3.3a. Tanner th i din ca mt m (6,3).43

Hnh 3.3b. Gii m (6,3)..44

Hnh 3.4.1a . Gii m vi cc th Tanner trong trng hp my n..46

Hnh 3.4.1b. Gii m vi cc th Tanner trong trng hp hai my47

Hnh 4.2. Bn pht ca h thng..51

Hnh 4.3. Bn thu ca h thng ...52

Hnh 4.2.1a. Ma trn kim tra li chn l v chuyn v ca n52

Hnh 4.2.1b. Cc t m cu coset 000 trong m Hamming (7, 4) phn tn..53

Hnh 4.2.1. Kt qu s t l bt li m Hamming cc trng hp khc nhau54

Hnh 4.2.2. Kt qu t l bt li m ha LDPC qua knh AWGN..56

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CC T VIT TT S DNG TRONG N

T trong ting Anh Ngha ting Vit

WSN Wireless Sensor Network Mng cm bin khng dy

DSC Distributed Source Coding M ha ngun phn tn

LDPC Low Density Parity Check M kim tra chn l mt thp

DISCUS DSC in Sensor Network

Using Syndrome

M ha ngun phn tn trong mng

cm bin s dng Syndrome

ADC Analog to Digital

Converter

B chuyn i tn hiu tng t sang

tn hiu s

S-W Slepian-Wolf M ha Slepian-Wolf

QoS Quanlity of Service Cht lng dch v

MAC Media Access Control iu khin truy nhp thit b mng

AWGN Additive White Gaussian

Noise

Knh nhiu trng Gauss

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CHNG I : TNG QUAN V MNG CM BIN KHNG DY

1.1 Gii thiu v mng cm bin khng dy

Mng cm bin khng dy (Wireless Sensor Network WSN) l mt trong

nhng cng ngh mi pht trin nhanh chng nht, vi nhiu ng dng trong cc

lnh vc: iu khin qu trnh cng nghip, bo mt v gim st, cm bin mi

trng

Hnh 1.1. M hnh mng cm bin khng dy

WSN l mng lin kt cc node vi nhau nh sng radio. Nhng trong ,

mi node mng bao gm y cc chc nng cm nhn, thu thp, x l v

truyn d liu. Cc node mng thng l cc thit b n gin, nh gn, gi thnh

thp, v c s lng ln, c phn b khng c h thng trn phm vi rng, s

dng ngun nng lng (pin) hn ch thi gian hot ng lu di.

1.2 Cu trc mng WSN

1.2.1 Cu trc 1 node mng WSN

Mi node cm ng c cu thnh bi 4 thnh phn c bn nh hnh 1.2, b

cm nhn (sensing unit), b x l (a processing unit), b thu pht (a transceiver

unit) v b ngun (a power unit). Ngoi ra c th c thm nhng thnh phn khc

ty thuc vo tng ng dng nh l h thng nh v (location finding system), b

pht ngun (power generator) v b phn di ng (mobilizer).

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B ngun

Cm bin ADC

Lu tr

X lB phn

pht

H thng nh v

B pht ngun

B phn di ng

Hnh 1.2. Cc thnh phn ca mt node cm ng

Cc b phn cm ng (sensing units) bao gm cm bin v b chuyn i

tng t-s (ADC Analog to Digital Converter). Da trn nhng hin tng quan

st c, tn hiu tng t to ra bi sensor c chuyn sang tn hiu s bng b

ADC, sau c a vo b x l.

B x l thng c kt hp vi b lu tr nh (storage unit), quyt nh

cc th tc cho cc nt kt hp vi nhau thc hin cc nhim v nh sn.

Phn thu pht v tuyn kt ni cc nt vo mng. Chng gi v nhn cc d

liu thu c t chnh n hoc cc nt ln cn ti cc nt khc hoc ti sink. y

tn hiu c thu v phn tch.

Phn quan trng nht ca mt nt mng cm ng l b ngun. B ngun c

th l mt s loi pin. cc nt c thi gian sng lu th. b ngun rt quan trng,

n phi c kh nng np in t mi trng nh l nng lng nh sng mt tri.

Ngoi ra cn mt s cch cp ngun khc

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1.2.2 Cu trc mng cm bin khng dy

Giao tip khng dy multihop: Khi giao tip khng dy l k thut chnh, th

giao tip trc tip gia hai nt s c nhiu hn ch do khong cch hay cc vt cn.

c bit l khi nt pht v nt thu cch xa nhau th cn cng sut pht ln.V vy

cn cc nt trung gian lm nt chuyn tip gim cng sut tng th. Do vy cc

mng cm bin khng dy cn phi dng giao tip multihop.

Hot ng hiu qu nng lng: h tr ko di thi gian sng ca ton

mng, hot ng hiu qu nng lng l k thut quan trng mng cm bin khng

dy.

T ng cu hnh: Mng cm bin khng dy cn phi cu hnh cc thng s

mt cc t ng. Chng hn nh cc nt c th xc nh v tr a l ca n thng

qua cc nt khc (gi l t nh v).

X l trong mng v tp trung d liu: Trong mt s ng dng mt nt cm

bin khng thu thp d liu m cn phi c nhiu nt cng cng tc hot ng

th mi thu thp d liu, khi m tng nt thu d liu gi ngay n sink s rt

tn bng thng v nng lng. Cn phi kt hp cc d liu ca nhiu nt trong mt

vng ri mi gi ti sink s tit kim bng thng v nng lng.

Do vy , cu trc mng mi s:

- Kt hp vn nng lng v kh nng nh tuyn.

- Tch hp d liu v giao thc mng.

- Truyn nng lng hiu qu qua cc phng tin khng dy.

- Chia s nhim v gia cc nt ln cn

Cc nt cm ng c phn b trong mt sensor field nh hnh 1.2.2. Mi

mt nt cm ng c kh nng thu thp d liu v nh tuyn li n cc sink. D

liu c nh tuyn li n cc sink bi mt cu trc a im. Cc sink c th giao

tip vi cc nt qun l nhim v (task manager node) qua mng Internet hoc v

tinh.

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Hnh 1.2.2. Cu trc mng cm bin khng dy

1.2.3 Kin trc giao thc mng WSN

Trong mng cm ng, d liu sau khi c thu thp bi cc nt s c nh

tuyn gi n sink. Sink s gi d liu n ngi dng u cui thng qua internet

hay v tinh. Kin trc giao thc c s dng bi nt gc v cc nt cm bin (hnh

1.2.3).

Lp ng dng

Lp truyn ti

Lp mng

Lp lin kt l liu

Lp vt l

Phn qun l nng lng

Phn qun l di ng

Phn qun l nhim v

Hnh 1.2.3. Kin trc giao thc ca mng cm bin

Kin trc giao thc ny kt hp gia cng sut v chn ng, kt hp s

liu vi cc giao thc mng, s dng cng sut hiu qu vi mi trng v tuyn v

s tng tc gia cc nt cm bin. Kin trc giao thc bao gm lp vt l, lp lin

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kt d liu, lp mng, lp truyn ti, lp ng dng, phn qun l cng sut, phn

qun l di ng v phn qun l nhim v.

Lp ng dng: Ty vo tng nhim v ca mng cm bin m cc phn

mm ng dng khc nhau c xy dng v s dng trong lp ng dng. Trong lp

ng dng c mt s giao thc quan trng nh giao thc qun l mng cm bin

(SMP Sensor Management Protocol), giao thc qung b d liu v ch nh

nhim v cho tng sensor (TADAP Task Assignment and Data Advertisement),

giao thc phn phi d liu v truy vn cm bin (SQDDP Sensor Query and Data

Dissemination).

Lp truyn ti : gip duy tr lung s liu nu ng dng mng cm bin

yu cu. Lp truyn ti c bit cn khi mng cm bin kt ni vi mng bn ngoi,

hay kt ni vi ngi dng qua internet. Giao thc lp vn chuyn gia sink vi

ngi dng (nt qun l nhim v) th c th l giao thc gi ngi dng (UDP

User Datagram Protocol) hay giao thc iu khin truyn ti (TCP Transmission

Control Protocol) thng qua internet hoc v tinh. C.n giao tip gia sink v cc nt

cm bin cn cc giao thc kiu nh UDP v. cc nt cm bin b hn ch v b nh.

Hn na cc giao thc ny cn phi tnh n s tiu th cng sut, tnh m rng v

nh tuyn tp trung d liu .

Lp mng : quan tm n vic nh tuyn d liu c cung cp bi lp

truyn ti. Vic nh tuyn trong mng cm bin phi i mt vi rt nhiu thch

thc nh mt cc nt dy c, hn ch v nng lngDo vy thit k lp mng

trong mng cm bin phi theo cc nguyn tc sau:

- Hiu qu v nng lng lun c xem l vn quan trng hng u.

- Cc mng cm bin gn nh l tp trung d liu

- Tch hp d liu v giao thc mng.

- Phi c c ch a ch theo thuc tnh v bit v v tr

C rt nhiu giao thc nh tuyn c thit k cho mng cm bin khng

dy. Nhn tng quan, chng c chia thnh ba loi da vo cu trc mng, l

nh tuyn ngang hng, nh tuyn phn cp, nh tuyn da theo v tr. Xt theo

hot ng th chng c chia thnh nh tuyn da trn a ng

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(multipathbased), nh tuyn theo truy vn (query- based), nh tuyn tha thun

(negotiation - based), nh tuyn theo cht lng dch v (QoS Quanlity of

Service), nh tuyn kt hp (coherent-based).

Lp kt ni d liu : Lp kt ni d liu chu trch nhim cho vic ghp cc

lung d liu, d khung d liu, iu khin li v truy nhp mi trng. V mi

trng c tp m v cc nt cm bin c th di ng, giao thc iu khin truy nhp

mi trng (MAC Media Access Control) phi xt n vn cng sut v phi

c kh nng ti thiu ho vic va chm vi thng tin qung b ca cc nt ln cn.

Lp vt l : Lp vt l chu trch nhim la chn tn s, pht tn s sng

mang, iu ch, lp m v tch sng.

Phn qun l cng sut : iu khin vic s dng cng sut ca nt cm

bin. V d, nt cm bin c th tt khi thu ca n sau khi thu c mt bn tin t

mt nt ln cn. iu ny gip trnh to ra cc bn tin ging nhau. Khi mc cng

sut ca nt cm bin thp, nt cm bin pht qung b ti cc nt ln cn thng

bo n c mc cng sut thp v khng th tham gia vo cc bn tin chn ng.

Cng sut cn li s c dnh ring cho nhim v cm bin.

Phn qun l di ng : pht hin v ghi li s di chuyn ca cc nt cm

bin duy tr tuyn ti ngi s dng v cc nt cm bin. Nh xc nh c cc

nt cm bin ln cn, cc nt cm bin c th cn bng gia cng sut ca n v

nhim v thc hin.

Phn qun l nhim v : c th ln k hoch cc nhim v cm bin trong

mt vng xc nh. Khng phi tt c cc nt cm bin trong vng iu phi

thc hin nhim v cm bin ti cng mt thi im. Kt qu l mt s nt cm

bin thc hin nhim v nhiu hn cc nt khc tu theo mc cng sut ca n.

Nhng phn qun l ny l cn thit cc nt cm bin c th lm vic cng nhau

theo mt cch thc s dng hiu qu cng sut, chn ng s liu trong mng cm

bin di ng v phn chia ti nguyn gia cc nt cm bin.

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1.2.4 Cc yu t nh hng n mng WSN

1.2.4.1 Thi gian sng bn ngoi

Cc nt WSN vi ngun nng lng pin gii hn. V d: mt loi pin kim

cung cp 50Wh nng lng, n c th truyn cho mi nt mng ch tch cc

gn 1 thng hot ng. S tiu tn v tnh kh thi ca gim st v thay th pin cho

mt mng rng, th thi gian sng di hn c thit k. Trong thc t, pin rt cn

thit trong rt nhiu ng dng bo m mng WSN c th t ng s dng

khng cn thay th trong vi nm. S ci thin ca phn cng trong thit k pin v

k thut thu nng lng s gip ta mt phn trong vic tit kim pin.

1.2.4.2 S p ng

Gii php n gin nht ko di thi gian sng bn ngoi l iu khin

cc node trong 1 chu k lm vic vi chu k chuyn mch gia 2 ch : ch ng

(mode sleep) v ch hot ng (mode active). Trong khi qu trnh ng b ch

ng l 1 thch thc ca WSN, vn ln lin quan n na l chu trnh ng 1

cch ty c th lm gim kh nng p ng cng nh hiu sut ca cc sensor.

Trong mt s ng dng, cc s kin trong t nhin c tm thy v thng bo

nhanh, th s tr bi lch ng phi c gi gii hn chnh xc, thm ch trong s

tn ti ca nghn mng.

1.2.4.3 Tnh cht mnh

Mc tiu ca WSN l cung cp phm vi rng ln, bao ph chnh xc

(fine-grained coverage). Mc tiu ny ph bin s lng ln cc thit b khng

t tin. Tuy nhin cc thit b r thng km tin cy v thng d xy ra li. Tc

li cng s cao khi cc thit b cm ng c trin khai trong cc mi trng

kht khe v trong vng ca k ch. Giao thc thit k do cng phi xy dng k

so c th p ng tt. Rt kh chc chn rng vic nh dng ton cu ca h

thng l khng b hng vi cc thit b li.

1.2.4.4 Hiu sut

Cc ci tin ca lut Moore trong cng ngh m bo dung nng ca thit b

v cc mt: x l ngun, b nh - lu tr, thc hin truyn nhn v tuyn, ci thin

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nhanh chng s chnh xc ca b cm bin. Tuy nhin, vn kinh t c t ra

y l gi c trn mt node gim mnh (t hng trm la xung cn vi cent), n

c th lm cho dung nng ca vi node s b hn ch 1 mc nht nh. l l

do thit k cc giao thc cho hiu sut cao, n bo m rng h thng tng th s

c dung nng ln hn so vi dung nng ca cc thnh phn trong n cng li. Cc

giao thc cung cp mt kh nng hp tc gia lu tr, my tnh v cc ti nguyn

thng tin .

1.2.4.5 Tnh m rng

WSN c kh nng hot ng mt vng cc rng (ln hn 10 ngn, thm

ch l hng triu node trong mt gii hn v di).C mt vi hn ch v thng

lng v dung lng lm nh hng n scalability ca hot ng mng. V vy,

kh nng m rng ca h thng l rt quan trng i vi mng cm bin khng dy.

1.2.4.6 Tnh khng ng nht

S tn ti s khng ng nht trong dung nng ca thit b trong qu trnh

ci t thc t (c th l my mc, thng tin d liu v cm bin). S khng ng

nht s c nh hng quan trng n thit k.

1.2.4.7 T cu hnh

Do phm vi v cc ng dng trong t nhin, WSN l cc h thng phn phi

khng cn ch. Hot ng t ng l vn chnh c t ra trong thit k. Ngay

t khi bt u, cc node trong WSN c th c cu hnh theo topo mng ca

chng; t ng b, t kim tra, v quyt nh cc thng s hot ng khc ca h

thng.

1.2.4.8 T ti u v t thch nghi

Trong WSN, thng c nhng tn hiu khng chc chn v iu kin hot

ng trc khi trin khai. Di nhng iu kin , vic xy dng nhng my mc

c th t hc t sensor v thu thp cc php o mng, s dng nhng ci hc

c tip tc hot ng ci tin l iu rt quan trng.

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Ngoi ra, mt iu trc tin khng bit chc c l mi trng m WSN

hot ng c th thay i mnh m qua thi gian. Cc giao thc WSN s lm cho

thit b c th thch nghi vi mi trng nng ng trong khi n ang s dng.

1.2.4.9 Thit k c h thng

WSN c th l mt ng dng cao cho tng chc nng ring, nn cn c s

cn bng gia hai yu t:

Mi ng dng cn c nhng c im khai thc ng dng ring a ra

nhng hot ng pht trin cao.

Tnh mm do: cc phng php thit k phi ph bin cho cc hot ng.

1.2.4.10 Cch bit v bo mt

Phm vi hot ng ln, ph bin rng, nhy ca thng tin thu c bi v WSN lm

tng yu cu chnh cui cng l: bo m s cch bit v bo mt.

1.3. ng dng ca mng WSN

WSN c ng dng u tin trong cc lnh vc qun s. Cng vi s pht

trin ca ngnh cng nghip iu khin t ng, robotic, thit b thng minh, mi

trng, y t ... WSN ngy cng c s dng nhiu trong hot ng cng nhip v

dn dng.

Mt s ng dng c bn ca WSN:

Cm bin mi trng:

Qun s: pht hin mn, cht c, dch chuyn qun ch,

Cng nghip: h thng chiu sng, m, phng chy, r r,

Dn dng: h thng iu ha nhit , chiu sng

iu khin:

Qun s: kch hot thit b, v kh qun s,

Cng nghip: iu khin t ng cc thit b, robot,

Mi trng: Gim st l lt, bo, gi, ma, pht hin nhim, cht thi...

Y t: nh v, theo di bnh nhn, h thng bo ng khn cp,

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H thng giao thng thng minh:

Giao tip gia bin bo v phng tin giao thng, h thng iu tit lu

thng cng cng, h thng bo hiu tai nn, kt xe,

H thng nh v phng, tr gip iu khin t ng phng tin giao

thng,

Gia nh: nh thng minh: h thng cm bin, giao tip v iu khin cc

thit b thng minh,

WSN to ra mi trng giao tip gia cc thit b thng minh, gia cc thit

b thng minh v con ngi, giao tip gia cc thit b thng minh v cc h thng

vin thng khc (h thng thng tin di ng, internet,)

1.4. Cc vn v m hnh trong mng cm bin khng dy

Mng cm bin khng dy l mt cng ngh ang ni ln v c rt nhiu

tim nng. tng chnh l trin khai cc nt cm bin kch thc nh, s dng

nng lng hiu qu trong mt vng quan tm. S ny c th c chp nhn v

trin khai trn rt nhiu vng cm ng. C th l trong qun s, giao thng v gim

st L do ti sao cc nt phi l khng dy l bi v d dng trin khai v c kh

nng xy dng cc mng ng, m topo ca n c tnh m. Vic pht trin cng

ngh pin khin vic cung cp ngun l khng cn thit. Cc chip rt nh c th cm

ng v giao tip trong tng lai gn c th dng nng lng mt tri.

Cc mch cm bin cn c trang b chc nng truyn nhn cc bn tin.

Theo truyn thng, l thuyt thng tin tp trung vo vic thit k b gii m n

gin v t hu ht nng lc tnh ton cho bn m ha. y khng phi cch m

mng cm bin khng dy s dng. Bi v mi nt cm bin ph thuc vo ngun

cung cp nng lng hn ch, nn chng cn tp trung vo vic gim nng lng

tiu th. Kt qu l gnh nng v tnh ton cn phi chuyn t bn m ha sang cho

bn gii m. Chnh l to ra s cn thit phi c mt thut ton m ha t phc tp.

M hnh mng c th c thit k theo nhiu cch khc nhau. Chng ta

thng chia thnh 2 nhm: da trn s hp nht (fusion) v da trn tnh cht c

N TT NGHIP


bit (ad hoc). S khc nhau c bn gia 2 m hnh ny nh di y. Trong s

ad hoc mi mt cn c trang b c 2 kh nng truyn v nhn, trong khi vi s

tp trung th cc nt ch cn phi truyn. c minh ha hnh di y:

(a) Fusion (b) Ad Hoc

Hnh 1.4. Mng WSN vi hai m hnh mng khc nhau

Trong bi lun ny, ta s tp trung vo s thch thc ngy cng cao ca vic

s dng nng lng hiu qu. Mt cch lm c iu ny l tm kim cc

phng php tt hn cho vic nn cc b ti cc nt bng vic s dng s tng

quan v thi gian. Ngoi ra, trong hu ht cc trng hp l quan tm n s tng

quan gia cc d liu cm ng khc nhau. Chng ta c th s dng c d tha

gim khi lng d liu ca mi nt cn phi truyn. gii quyt vn ny th

chng ta s dng m ha ngun phn tn (Distributed source coding).

N TT NGHIP


CHNG II. M NGUN PHN TN TRONG MNG CM BIN

KHNG DY

2.1. M ngun phn tn

M ngun phn tn s dng khi m c s tng quan gia tp cc ngun vi

nhau. y chnh l mt trng hp c th ca mng cm bin, m c tng quan rt

l cao gia cc nt hng xm. C nhn mi nt s nn d liu khng ch ca chnh

n m cn da vo kt qu quan st c ca cc nt cm bin khc, do thut

ng phn tn ra i. khai thc mi tng quan ny v loi b d tha th mi

nt phi bit c mt vi th, l cc nt khc gi ci g?

Vic ny c th thc hin bng hai cch. Cch th nht l cc nt ny c th

giao tip vi nhau thng qua mt mng gi l mng lin kt cc nt cm bin, v

cch th hai l khng cn dng n. La chn th nht to ra thm cc d liu

khng mong mun cho vic thnh lp mng v yu cu nng lc x l trn mi nt

phi cao. Vn m ha ngun ny trong mng cm bin thc s l i lp vi vic

gim khi lng x l v nng lng tiu th. iu c th trnh c nu s

dng phng n th hai. By gi th iu u tin xut hin trong u chng ta vi

la chn ny l lm th no sensor ang hot ng c th nn c mi th khi

khng bit g v d liu ca cc sensor khc?

Nh Slepian v Wolf th d liu ny c th c nn cng nhiu nu cng

hiu r ci m cc sensor khc gi n. Ci ny c bit nh l nh l Slepian-

Wolf v d nhin ch p dng c trong l thuyt m thi. Cc d liu ny nhn

c tim cn v da trn nguyn l xy dng m nh phn ngu nhin. Nhng n

c th thc hin vi mt mc ch thc hnh v cho chng ta phng php tt

lm vc nh th no,

Gi s ta c hai nt cm bin v ta mun nn d liu ny v truyn i nhiu

c th. Chui d liu cm bin X l gi tr u vo cho b m ha m n s nn X

da trn s phn b tng quan gia X v Y. Y c gi khng nn n b gii m

v c gi l thng tin bn Y, minh ha hnh 2.1a. Mc ch by gi ca vic

N TT NGHIP


gii m chung l c lng c X da vo gi tr u ra v thng tin bn Y. S

tng quan ny cng nhiu th vic c lng ny c th xem l cng chnh xc.

ENCODER DECODER

X

Y

Hnh 2.1a. M ha ngun phn tn vi thng tin bin ti b gii m

Nu mun gii m d liu nn khng tn tht, theo l thuyt m ha ngun

c in, c th m ha vi tc bt Rx H(X) v Ry H(Y) ln lt i vi

ngun X v Y. Nu xt n s tng quan gia X v Y th c th m ha c hai

ngun vi entropy chung ca chng tha mn Rx + Ry H(X,Y). Ni cch khc,

vi H(X,Y) = H(X) + H(X|Y) = H(Y) + H(Y|X), th c th m ha mt ngun vi

entropy iu kin tng ng l Rx H(X|Y) hoc l Ry H(Y|X). Slepian v Wolf

cho rng c th thc hin c khng cn lin lc mng gia cc nt cm bin v

tc bt t c l H(X) - H(X|Y) hoc H(Y) - H(Y|X). C th d dng nhn thy

rng n suy bin n n gi tr gii hn ca m ha khng tn tht c in l H(X)

khi m tng quan bng khng (tc l H(X|Y)=0). Chng ta s hiu hn v

nguyn l m Slepian-Wolf trong chng 2.2.

L thuyt m ha khng tn tht hin nay ch c s dng trong trng hp

l cc ngun ring r. Wyner v Ziv pht trin thm bi vic xem xt ngun gi tr

lin tip, dn n mo m tn hiu c th entropy hu hn. By gi n thng l

trng hp c bit ca phn khc mng cm bin. Ci chnh l gii thiu bc

lng t trc khi m ha S-W, tng t nh lng t ha i km vi m ha

entropy bng vic nn ngun n. Bc lng t ha ny l mt phn trong l

thuyt bin dng tc v c th c thc hin bng nhiu cch khc nhau ph

thuc vo s phn b cng nh b nh ca gi tr u vo. C th tham kho thuyt

bin dng tc phn ph lc, m Wyner-Ziv s c miu t chng 2.4.

N TT NGHIP


S tng quan gia cc ngun c th c m hnh ha nh l mt knh

tng quan o trong X l u vo v Y l u ra ca knh (hnh 2.1b). Knh ny

c miu t bi xc sut li , l xc sut m Y sai khc so vi X. Do vy 1 xc

sut nh cho chng ta bit l X v Y tng quan nhiu vi nhau v n c th m

ha vi tc bt thp hn. Bi v m hnh c cp trong bi ny s dng

nguyn l m ha knh cho vic m ha ngun, c gi l s Wyner. Ni cch

khc, m ha knh tng tc bt bo v tn hiu vi nhiu, n c th c s

dng trong cch i lp gim tc trong cch iu khin. K thut ny da trn

vic xy dng m nh phn trong tt c gi tr c th c c ca mt gi tr u

vo c ghi vo coset khc nhau. L thuyt ny c gi l m ha ngun phn

tn s dng syndrome (DISCUS) v chng ta s hiu r hn chng3.1.

Virtual

ChannelDECODER

Z

X Y

Hnh 2.1b. Knh tng quan o gia X v Y

y chng ta s dng s bt i xng n gin, mt sensor gi d liu ca

chng bng nh dng cha nn. Vic thc hin rt ti u ny c th s dng s

i xng trong c hai sensor gi d liu nn da trn s tng quan vi

sensor khc, hoc thm ch mt s i xng thch ng trong cc nt truyn

tc khc nhau ph thuc vo cc yu t nh l cht lng knh truyn v c

im ca tn hiu. Ci ny s c miu t chng 3.2.

2.2. DSC khng tn tht

Slepian v Wolf miu t mt nh l v vic nn ngun khai thc s

tng quan vi mt ngun khc. N c gi l m ha ngun phn tn. tng

chnh l mt ngun X c th nn d liu ca n da trn s phn b tng quan vi

ngun th hai l Y m khng cn phi giao tip qua mng intersensor. Slepian v

N TT NGHIP


Wolf ch ra rng c th m ha cng tc bt nu hiu c b m ha gi ci

g hay khng. L thuyt ny c nn theo cng thc sau:

R1 H(X|Y), (1a)

R2 H(Y|X), (1b)

R1 + R2 H(X,Y), (1c)

V c th c v nh hnh 2.2

Ry

Rx

H(X,Y)

H(Y|X)

H(X|Y)

Hnh 2.2. Vng tc bt ca 2 ngun

Cc im trong gc c th t c bi m hnh m ha bt i xng. Tt c cc

im trn ng H(X,Y) nhn c bi c m hnh m ha thi gian chung v m

hnh m ha i xng.

Slepian v Wolf ch ra rng hai bin ring bit vi cc ch ci gii hn. Later

Cover m rng n thnh qu trnh c bit ty , cc ch ci c th m gii hn v

mt s bt k ca cc ngun tng quan. Trong thc t cc qu trnh ring r khng

hay s dng.

2.2.1. M ha Slepian-Wolf ca hai ngun nh phn

Chng ta c hai ngun nh phn 3 bt tng quan X v Y. S tng quan

gia chng cng l khong cch Hamming ti a l dH < 1 . By gi chng ta s m

ha bng cch m c th gii m khng bin dng. S dng l thuyt m ha ngun

c in c th nn ngun vi cc entropy tng ng H(X) v H(Y) ( y l 3 bt).

N TT NGHIP


Xem xt rng tn ti mt s ph thuc gia X v Y c th tit kim tng s cc bt

truyn i.

Quan st trng hp ny, trong Y c sn ti b gii m, khng c im

phn bit gia X = 000 v X = 111, t ta bit rng khong cc Hamming ln

nht t X n Y l 1. D , ta c th t tt c gi tr ra c th ca X vo cc coset.

Bng vic thc hin xy dng m nh phn thng minh c th c lng t m

trong coset tng ng l gi tr khi to ca X. Ni cch khc, ta c th xy dng

cc coset sau s dng cc t m ca X: {100,111}, {010,101}, v {001,110}. Bng

vic ch truyn ch s ca coset tch cc chng ta c th gim s lng bits truyn

i, y l gim t 3 xung cn 2.

M hnh xy dng m nh phn c minh ha hnh 2.2.1.

000

001

010

011

100

101

110

111

000 111

010 101

011 100

001 110

X U

00

01

10

11

Hnh 2.2.1: Cu trc coset

2.3. DSC tn tht

M ha Wyner Ziv chnh l m ha Slepian Wolf vi mt php o gn

ng, c ngha n l s nn tn hao ly t s mo tng quan nm trong s quan

tm. M ha ngun tn hao l cn thit khi ta khng c hn mt knh vi cng sut

vnh cu s b tr ( hay nu ta mun c kh nng gii m tn hiu vi mt

N TT NGHIP


tiu chun chnh xc ). M ha Wyner Ziv c th c m t nh mt php lng

t ha bng m ha Slepian Wolf nh trong hnh 2.4a.

Q Slepian-Wolf

X U Z

Hnh 2.4a S khi ca m ha Wyner-Ziv

Vng t l Wyner Ziv khng c ch r cho cc ngun chung, nhng

trong cc trng hp c bit quan trng v u vo Gaussian l tt c bit trong

cc ti liu ton hc. Vng t l Wyner Ziv chung c th c m t nh trong

hnh 2.4b vi gii hn bn trong v bn ngoi. Cc t l t c nm gia hai gii

hn ny.

R2

R1

Bin trong

Bin ngoi

Hnh 2.4b. Bn trong v bn ngoi vng t l ca DSC tn tht

V thuyt Wyner Ziv l mt s kt hp ca m ha Slepian Wolf v

thuyt t l phn b c m t cc phn 3 v 4, ta s a ra nhng v d quan

trng y.

N TT NGHIP


2.3.1. Trng hp i xng m nh phn

X v Y l hai ngun m nh phn v s tng quan gia chng c chun

ha nh mt knh i xng ca m nh phn vi xc sut li p v khong cch

Hamming nh php o b bp mo. Nu chng ta vit X = Y E vi E l mt

ngun Bernoulli, chc nng mo t l vi Y c bit ti php m ha v gii m

c cho l :

( ) ( ) { ( ) ( ) { }

{ }

Nu Y ch c hiu ti php gii m, th chc nng mo t l Wyner Ziv

c cho l :

( ) { ( ) ( )}

Hnh bo a gic li nh nht (l.c.e) ca H ( ) H(D) v im ( D = ,

R = 0 ), vi = ( 1 )* D + (1 D).. Cho 0.5, ( ) R X|Y (D) vi

s ngang bng ch hai im : im t l 0 (, 0) v im mo 0 (0, H() ). V vy

m ha Wyner Ziv ph thuc vo tn hao t l trng hp ng b m nh

phn. Khi D = 0, vn Wyner Ziv b thoi ha thnh vn Slepian Wolf vi

R*WZ (0) = RX|Y (0) = H (X|Y) = H ().

2.3.2. Trng hp Gaussian bc hai

Trong trng hp ny, chng ta c hai gi tr thng k ngu nhin Gaussian

l Xk v Yk vi tham s x 2 v y

2 v s tng quan cng hiu qu ( Ch : gi

tr ln hn a ra nhiu ngun tng quan trong trng hp ny ), v ta D =

(Dx , Dy ) l tiu chun mo. Sau nu [23] :

dx

, dy

th ta ly cc trng thi :

N TT NGHIP


[

( )

( ) ],

[

( )

( ) ],

[

( )

].

Vi ( )

Ta ly t l nh nht bng vic thit lp dx = Dx / x 2

og dy = Dy / y 2 c ly :

max = (

)

V RX +RY =

[( )

]

Km theo thuyt lm mo t l in hnh, chng ta c th m ha cc ngun

Gaussian t ghi nh

RX + RY =

[

]

thc hin s xem xt v s tng quan, ta t c mt t l :

R =

[

( )

]

thy rng R = 0 khi = 0 v R

[

] khi 1.

2.4. La chn m LDPC

M ha ngun phn tn s dng syndrome c th c thc hin bng vi

cch ph thuc vo k thut m ha knh m ta la chn. K thut chung hay dng

nht s dng m khi tuyn tnh, m cun v m mc. Nghin cu v m ha knh

dn n hai k thut, l m LDPC v m Tubor. M Tubor l mt m mc c

ghp bi mt interleaving v mt m cun. M Tubor c s dng trong m ha

ngun phn tn khng c trnh by trong bi lun ny. Trong bi lun ny chng

N TT NGHIP


ta chn theo s m khi tuyn tnh trong s cc dng nng cao nht ca m

LDPC. Ta chn nh th bi v n ci thin hiu nng so vi m Tubor v cng bi

v n cng c th mang theo s phn tn.

CHNG 3. M NGUN PHN TN S DNG SYNDROME

3.1. M ngun phn tn s dng cc syndrome

Trong qu trnh thit lp nn phn tn, cng nh khng phn tn, cc v d

tip ni nhau cn c lng t c c mt entropy hu hn.

Nh cp trc , s tng quan gia cc ngun trong mt mng cm

bin c th c m hnh ha nh mt knh tng quan. tng y l sau

khi s dng mt m knh km theo nn ngun d liu sau . T m c lng

t U chc chn tng quan vi X. Nu X cng tng quan vi thng tin bn Y, U

cng s tng quan vi Y. V vy knh tng quan c th c m t bng s

phn b trng thi P(Y|U). Thng tin bn cha thng tin I(U;Y) v U c khai thc

pha b gii m c tnh X. Hin nay, s phn b tng quan c th phn bit

tng i cho tng trng hp c th, nhng n thng c m phng trong bo

co nh mt Knh i Xng Nh Phn (BSC) hay mt knh vi Nhiu Gaussian

Trng Ph (Additive White Gaussian Noise).

V vy, lm th no chng ta c th gim bt tng s bit i din cho X m

khng cn bit chnh xc nhng mu tng ng ca Y? Ta s m t vi mt v d.

C X v Y u l cc t 3-bit c th xy ra vi s tng quan c a vo bng

khong cch Hamming khng nhiu hn mt. Nu Y c hiu ti c khi m ha

v gii m, th s khng c im no i din cho X vi nhiu hn 2 bit. (Cho Y, X

Y nm trong tp {000, 001, 010, 100} vi l php Xor ). Vi Y c hiu ch

b gii m, iu ny c th xy ra? Khng c im no gi c X = 000 v X =

111 v khong cch Hamming gia chng bng 3. Vi kh nng Y, mt trong s

nhng t m trong vic thit lp c la chn. Ngy nay, tt c nhng i din t

m c th ca X c rt gn thnh cc thit lp n gin mang n nhng thit lp

N TT NGHIP


thm ca X : {001, 110}, {010, 101}. Do vy, X ch cn truyn vi 2 bit thay v 3

bit.

000

111

111

110

101

011

000

001

010

100

Coset - 1

u ra ca Y

Hnh 3.1. u ra c th ca Y nu X thuc coset {000, 111}

y l v d u tin nhng n m t tng ca kch bn m ngun

phn tn. Mc tiu l pht hin mt m knh tt c th thc hin gn vi gii

hn Wyner Ziv t phn 5. Theo di bc u v hai t m ca X l mt m khi

tuyn tnh ( 3,1,3), cng c bit nh l m lp 3 bit. Cc thit lp khc cng b

bin th hoc tp hp li ca m lp. V vy, thay v m t X bi 3 bit gi tr, chng

ta m ha tp hp X km theo, vi mt gi tr 2 bit, nh trng hp khi Y c

hiu c b m ha v gii m. By gi vic ly li khi tuyn tnh c th c a

ra bi ma trn kim tra chn l H. Mi tp hp ca mt m tuyn tnh c tng

hp vi hm i xng duy nht s = HTc, vi c l t m hp l bt k no .

Cc cng ngh m ha knh trin vng c cp nh l nhng s lun

phin bao gm m turbo v m LDPC. C hai u c m t v kim tra bi

nhng nh nghin cu khc nhau. Chng ti chn ra kch bn LDPC trong thuyt

ny bi v n c chng minh s chuyn tip tt nht nn phn tn. Cng ngh

N TT NGHIP


m ha ny c tho lun thng xuyn trong chng 3.2 v c bit cho M

ngun phn tn chng 3.3.

3.2. Thit k i xng

Trng hp bt i xng ca m ngun phn tn khng linh hot v t l

phn b. Nu ta mun thay i tc ca cc ngun khc trong trng hp bt i

xng th chng ta cn s dng s chia s thi gian m u cho vn ng b;

cc sensor ny phi lin lc vi nhau ng b ha. y l iu m chng ta c

gng trnh khi. C hai gii php gii quyt vn ny. Ngi ta a ra mt

phng php da trn nguyn tc nh l s DISCUS, nhng li phi ci tin

thm cho m ha v gii m. Cch khc l dng phng php chia ngun.

Khng ging nh trng hp bt i xng l mt ngun gi thng tin tn

tht ca n v ngun khc gi thng d liu nn th trong trng hp ny, c hai

ngun s c th ch gi thng tin cc b m khng tha hip vi cht lng tn hiu

thit lp li b gii m. Mt s m ha ng b s c th m ha vi tc

trong vng tc hnh 2.4b.

Xt vic m ha hai ngun tng quan tn qut X v Y. ta s m ha theo

cch i xng, vd chng ta mun nn mi ngun vi bt k t l no trong khong

t H(X) n H(X|Y) i vi X , v khong t H(Y) n H(Y|X) i vi Y. Gi s

H(X) H(Y). Theo chin lc m ha knh, ta to hai ma trn Gx v Gy cha n(1-

H(X|Y)) v n(1-H(Y)) hng t c im gc (H(X|Y), H(Y)) (xem hnh 4).

gn cc t l khc nhau chng ta chuyn mt vi hng t Gx qua Gy di chuyn dc

theo ng H(X,Y) cho n khi t c im gc khc (H(X), H(Y|X)).

N TT NGHIP


Gc

Ga

Gs

Gc

Ga

Gsx

Gc

Gsy

G =

Gx =Gy =

Hnh 3.2. Cu trc b to ma trn trong trng hp i xng

Xt 1 b to ma trn Gc kch thc n(1-H(Y)) n vi cc hng l c lp

tuyn tnh, trong n l chiu di khi s dng trong m ha. B to ma trn ny c

th c dng chia khng gian ca chui Y chiu di n. nh vy Gy = Gc, v b

m ha ca Y gi syndrome lin kt vi ma trn Gx. Xt mt ma trn Ga kch thc

n(H(Y)-H(Y)) n , cc hng l c lp tuyn tnh. Mt ma trn c to ra bi vic

xp Gc v Ga c th c s dng chia khng gian chui chiu di n vi nH(X)

coset. gim t l gy ra bi ma trn sau khi xp t H(X) bt/mu xung H(X|Y)

bt/mu chng ta xy dng mt ma trn Gs vi n(H(X)-H(X|Y)) hng c lp tuyn

tnh. Gx by gi c to ra bi Gc, Ga v Gs. B gi m ca X gi syndrome ca

chui chiu di n ca X v Gx n b gii m. B gii m ly li c chui Y

chiu di n da trn thng tin ny v bit v thng k ca Y. m ha X chng ta

cn c b to ma trn Gx. B gii m nhn li c chui chiu di n c th dng

mt thut ton gii m chun khi phc chui X s dng phn b chung p(x,y)

ca X v Y.

trao i t l gia hai b m ha ca X v Y, bt k hng no ca Gs c

th c chuyn t Gx n Gy. Cui cng khi Gx ch cn li Gc v Ga, hai b m

ha ca X v Y ss truyn vi tc ln lt l H(X) v H(Y|X) bt/mu. Qu trnh

phn b ny c th c xem nh l vic chia b to ma trn G thnh hai (Gx v

Gy) c minh ha hnh 3.2.

N TT NGHIP


3.2.1. Cu trc b gii m

Hy nh rng trong trng hp i xng ny gii m ngun cn phi tm

c coset ni m ngun sau nn X tn ti v tm c t m v coset ny m gn

vi thg tin bin Y nht. by gi trong trng hp i xng, c hai ngun gi thng

tin cc b nn chin lc gii m khng th p dng. Chng ta s quay li ci ny

trong trng hp c bit ca gii m LDPC

3.2.2. a ngun

Mt mng cm bin vi hai sensor m chng ta xem xt cho n nay th

khng phi l nhiu. ngi ta mong mun v hon ton cn thit c th trnh by

mt l thuyt v trng hp nhiu hn hai ngun. Ci hay ca tng c trnh

by n nay trong bi lun ny l khng c c mt thch thc no. V d v hai

ngun trong m ngun phn tn i xng d dng m rng thnh a ngun.

G1

G2

GL

GL-1

G1

G2

GL-1

G1

G2

G1

Gx1 Gx2 Gx(L-1) Gx(L)

Hnh 3.2.2. nh ngha ma trn trong trn hp a ngun

Vi L ngun, ta to ra 1 th t ca mt s ngun bt k {X1,XL} nh l

H(X1|X2, , XL) H(Xi|Xi+1, , XL) H(XL). Khng khc vi nguyn tc

chung, chunga ta c th sp xp cc ngun theo kiu cch ny. Ta c th t c

im gc H(X1|X2, , XL) , , H(Xi|Xi+1, , XL) , , H(XL) bng vic quy

nh ngha b to nhiu ma trn t b to 1 ma trn n cho mi m, nh hnh

3.2.2.

N TT NGHIP


Qu trnh bt u vi vic nh ngha b to ma trn GL vi n(1-H(XL))

hng c lp tuyn tnh. Cc ma trn khc c th c c bng vic nh ngha lp

li Gi-1 nh l xp Gi v mt ma trn Ai-1 vi n(H(Xi|Xi+1, , H(XL)) H(Xi-1|Xi,

,XL)) hng c lp tuyn tnh. R rng th nh trong trng hp hai ngun, cc

im khng phi l im gc c th t c bi vic trao i cc hng c bit ca

cc b to ma trn gia chng.

3.3. M ha LDPC

3.3.1. Gii thiu mt s loi m

3.3.1.1. M Turbo

Trong l thuyt thng tin, m turbo l mt tp hp cc chuyn tip sa li

hiu sut cao. Tn m xut pht t cc vng lp thng tin phn hi c s dng

p ng cho cc ng c tng p.

B m ha :

Hnh 3.3.1.1a Cu trc b m ha Turbo

- B m ha bao gm 3 khi bit nh : Khi u tin l khi m bit d liu ti

trng; Khi th 2 gm n/3 bit chn l tnh ton, s dng mt h thng

quy (m RSC); Khi th 3 l n/2 bit chn l cho bit hon v ca cc d liu

ti trng, cng s dng m RSC.

- Trn hnh, M l mt b nh Register. Tr v lu lng u vo dk xut hin

vi trnh t khc nhau. Ti phin u tin, trnh t dk xut hin c 2 u ra

N TT NGHIP


ca b m ha. Nu cc b m ha C1 v C2 c s dng tng ng trong

n1 v n2 th mc gi tr ca chng ln lt bng :

R1 = (n1 + n2) / (2n1 + n2)

R2 = (n1 + n2) / (n1 + 2n2)

B gii m :

Hnh 3.3.1.1b Cu trc b gii m Turbo

- Hai b gii m nh c ni tip vi nhau. Cc b gii m DEC1 hot

ng tc thp hn (vd, R1), do n ginh cho cc m ha C1, v DEC2

l cho C2 tng ng. DEC1 gy ra tr L1 , DEC2 gy ra tr L2 .

Nhc im : M turbo ch s dng 2 m cu hnh song song m ha ton

b khi u vo K ca cc bit d liu. Cc b m ha thnh phn s dng m

chp quy ( RSC) vi kh nng gii hn ( 8 -16 trng thi ). Chnh v vy,

kh nng qun l cha thc s chnh xc, cng nh mc d phng cho

mi bit u vo cha c linh hot.

3.3.1.2. M Hamming

Trong vin thng (telecommunication), m Hamming l mt m sa li

tuyn tnh (linear error-correcting code), c t tn theo tn ca ngi pht minh

ra n, Richard Hamming. M Hamming c th pht hin mt bit hoc hai bit b li

N TT NGHIP


(single and double-bit errors). M Hamming cn c th sa cc li do mt bit b sai

gy ra. Ngc li vi m ca ng, m chn l (parity code) n gin va khng c

kh nng pht hin cc li khi 2 bit cng mt lc b hon v (0 thnh 1 v ngc

li), va khng th gip sa c cc li m n pht hin thy.

a. Cc m trc thi k ca Hamming

M chn l

M chn l thm mt bit vo trong d liu, v bit cho thm ny cho bit s

lng bit c gi tr 1 ca on d liu nm trc l mt s chn hay mt s l. Nu

mt bit b thay i trong qu trnh truyn d liu, gi tr chn l trong thng ip s

thay i v do c th pht hin c li (Ch rng bit b thay i c th li

chnh l bit kim tra). Theo quy c chung, bit kim tra c gi tr bng 1 nu s

lng bit c gi tr 1 trong d liu l mt s l, v gi tr ca bit kim tra bng 0 nu

s lng bit c gi tr 1 trong d liu l mt s chn. Ni cch khc, nu on d

liu v bit kim tra c gp li cng vi nhau, s lng bit c gi tr bng 1 lun

lun l mt s chn.

Vic kim tra dng m chn l l mt vic khng c chc chn cho lm, v

nu s bit b thay i l mt s chn (2, 4, 6 - c hai, bn hoc su bit u b hon

v) th m ny khng pht hin c li. Hn na, m chn l khng bit c bit

no l bit b li, k c khi n pht hin l c li xy ra. Ton b d liu nhn

c phi b i, v phi truyn li t u. Trn mt knh truyn b nhiu, vic

truyn nhn thnh cng c th mt rt nhiu thi gian, nhiu khi cn khng truyn

c na. Mc d vic kim tra bng m chn l khng c tt cho lm, song v

n ch dng 1 bit kim tra cho nn n c s tng ph (overhead) thp nht, ng

thi, n cho php phc hi bit b tht lc nu ngi ta bit c v tr ca bit b tht

lc nm u.

M hai-trong-nm

Trong nhng nm ca thp nin k 1940, Bell c s dng mt m hiu phc

tp hn mt cht, gi l m hai-trong-nm (two-out-of-five code). M ny m bo

mi mt khi 5 bit (cn c gi l khi-5) c chnh xc hai bit c gi tr bng 1.

N TT NGHIP


My tnh c th nhn ra l d liu nhp vo c li nu trong mt khi 5 bit khng 2

bit c gi tr bng 1. Tuy th, m hai-trong-nm cng ch c th pht hin c mt

n v bit m thi; nu trong cng mt khi, mt bit b ln ngc thnh gi tr 1, v

mt bit khc b ln ngc thnh gi tr 0, quy lut hai-trong-nm vn cho mt gi tr

ng (remained true), v do n khng pht hin l c li xy ra.

Ti din d liu

Mt m na c dng trong thi gian ny l m hot ng bng cch nhc

i nhc li bit d liu vi ln (ti din bit c truyn) m bo bit d liu c

truyn, truyn n ni nhn trn vn. Chng hn, nu bit d liu cn c truyn c

gi tr bng 1, mt m ti din n=3 s cho truyn gi gi tr "111". Nu ba bit nhn

c khng ging nhau, th hin trng ny bo cho ta bit rng, li trong truyn

thng xy ra. Nu knh truyn khng b nhiu, tng i m bo, th vi hu

ht cc ln truyn, trong nhm ba bit c gi, ch c mt bit l b thay i. Do

cc nhm 001, 010, v 100 u tng ng cho mt bit c gi tr 0, v cc nhm

110, 101, v 011 u tng ng cho mt bit c gi tr 1 - lu s lng bit c gi

tr 0 trong cc nhm c coi l c gi tr 0, l a s so vi tng s bit trong nhm,

hay 2 trong 3 bit, tng ng nh vy, cc nhm c coi l gi tr 1 c s lng

bit bng 1 nhiu hn l cc bit c gi tr 0 trong nhm - chng khc g vic cc

nhm bit c i x nh l "cc phiu bu" cho bit d liu gc vy. Mt m c

kh nng ti dng li thng ip gc trong mt mi trng nhiu li c gi l m

"sa li" (error-correcting code).

Tuy nhin, nhng m ny khng th sa tt c cc li mt cch ng n

hon ton. Chng hn chng ta c mt v d sau: nu mt knh truyn o ngc

hai bit v do my nhn thu c gi tr "001", h thng my s pht hin l c li

xy ra, song li kt lun rng bit d liu gc l bit c gi tr bng 0. y l mt kt

lun sai lm. Nu chng ta tng s ln cc bit c nhc li ln 4 ln, chng ta c

th pht hin tt c cc trng hp khi 2 bit b li, song chng ta khng th sa

cha chng c (s phiu bu "ha"); vi s ln nhc li l 5 ln, chng ta c th

sa cha tt c cc trng hp 2 bit b li, song khng th pht hin ra cc trng

hp 3 bit b li.

N TT NGHIP


b. M Hamming

Cng nhiu bit sa li thm vo trong thng ip, v cc bit y c b tr

theo mt cch l mi b tr ca nhm cc bit b li to nn mt hnh thi li ring

bit, th chng ta c th xc nh c nhng bit b sai. Trong mt thng ip di 7-

bit, chng ta c 7 kh nng mt bit c th b li, nh vy, ch cn 3 bit kim tra (23

= 8) l chng ta c th, khng nhng ch xc nh c l li trong truyn thng c

xy ra hay khng, m cn c th xc nh c bit no l bit b li.

Hamming nghin cu cc k hoch m ha hin c, bao gm c m hai-

trong-nm, ri tng qut ha khi nim ca chng. Khi u, ng xy dng mt

danh mc (nomenclature) din t h thng my, bao gm c s lng bit dng

cho d liu v cc bit sa li trong mt khi. Chng hn, bit chn l phi thm 1 bit

vo trong mi t d liu (data word). Hamming din t phng php ny l m

(8,7). N c ngha l mt t d liu c tng s bit l 8 bit, trong ch c 7 bit l

cc bit ca d liu m thi. Theo phng php suy ngh ny, m ti din (nhc li)

trn phi c gi l m (3,1). T l thng tin l t l c tnh bng vic ly con s

th hai chia cho con s th nht. Nh vy vi m ti din (3,1) trn, t l thng

tin ca n l

Hamming cn pht hin ra nan vi vic o gi tr ca hai hoc hn hai

bit na, v miu t n l "khong cch" (distance) (hin nay n c gi l khong

cch Hamming (Hamming distance) - theo ci tn ca ng). M chn l c khong

cch bng 2, v nu c 2 bit b o ngc th li trong truyn thng tr nn v hnh,

khng pht hin c. M ti din (3,1) c khong cch l 3, v 3 bit, trong cng

mt b ba, phi b i ngc trc khi chng ta c mt t m khc. M ti din

(4,1) (mi bit c nhc li 4 ln) c khong cch bng 4, nn nu 2 bit trong cng

mt nhm b o ngc th li o ngc ny s i thot m khng b pht hin.

Cng mt lc, Hamming quan tm n hai vn ; tng khong cch v ng

thi tng t l thng tin ln, cng nhiu cng tt. Trong nhng nm thuc nin k

1940, ng xy dng mt s k hoch m ha. Nhng k hoch ny u da trn

nhng m hin tn ti song c nng cp v tin b mt cch su sc. B quyt

cha kha cho tt c cc h thng ca ng l vic cho cc bit chn l gi ln nhau

N TT NGHIP


(overlap), sao cho chng c kh nng t kim tra ln nhau trong khi cng kim tra

c d liu na.

Thut ton cho vic s dng bit chn l trong 'm Hamming' thng thng

cng tng i n gin:

Tt c cc bit v tr l cc s m ca 2 (powers of two) c dng lm bit

chn l. (cc v tr nh 1, 2, 4, 8, 16, 32, 64 v.v. hay ni cch khc 20, 21, 22, 23, 24,

25, 2

6 v.v.)

Tt c cc v tr bit khc c dng cho d liu s c m ha. (cc v tr 3,

5, 6, 7, 9, 10, 11, 12, 13, 14, 15, 17, etc.)

Mi bit chn l tnh gi tr chn l cho mt s bit trong t m (code word).

V tr ca bit chn l quyt nh chui cc bit m n lun phin kim tra v b qua

(skips).

- V tr 1 (n=1): b qua 0 bit(n-1), kim 1 bit(n), b qua 1 bit(n), kim 1

bit(n), b qua 1 bit(n), v.v.

- V tr 2(n=2): b qua 1 bit(n-1), kim 2 bit(n), b qua 2 bit(n), kim 2






- V tr 16(n=16): b qua 15 bit(n-1), kim 16 bit(n), b qua 16 bit(n),

kim 16 bit(n), b qua 16 bit(n), v.v.

- V tr 32(n=32): b qua 31 bit(n-1), kim 32 bit(n), b qua 32 bit(n),

kim 32 bit(n), b qua 32 bit(n), v.v.

- v tip tc nh trn.

Ni cch khc, bit chn l ti v tr 2k kim cc bit cc bit v tr t c gi tr

logic ca php ton AND gia k v t l khc 0

N TT NGHIP


3.3.2. M LDPC

Cui th k 20 v u th k 21, hng lot cc loi m c pht minh.

Trong phi k ti mt s loi m in hnh nh : Reed-Solomon, Turbo, m

xon, m TCMChnh v vy c ngi ni rng y l th k ca l thuyt m

ha. Cng trong thi gian , mt loi m c tn l m kim tra chn l mt thp

LDPC (Low Density Parity Codes) ra i. Khi Mackay chng minh n c kh

nng tim cn ti hn Shannon ngay lp tc n gy c s ch ti cc nh khoa

hc.

Nu nh trong khong 20 nm trc, ngi ta thng ni nhiu ti m Turbo

nh l mt loi m tt nht ci tin hiu sut knh th gi y iu khng

cn ng na. Mt hng pht trin mi m ra c tn l LDPC_ m kim tra

chn l mt thp, ang tr thnh mt la chn tt nht thay th cho m Turbo

trong tng lai khng xa. M LDPC cho php cc nh thit k c th tim cn c

ti hn Shannon. V l thuyt ngi ta chng mnh c rng : m LDPC khng

c di m ln c th t c iu . Tuy nhin, t ngi bit c rng m

LDPC c Gallager xut t nhng nm 60 ca th k trc. Nhng vo thi

, khoa hc my tnh cha c pht trin, kh nng tnh ton ca cc chic

computer thi vn cn hn ch. Chnh iu ny khng th nhn thy c

nhng u im vt tri ca m LDPC, v lm n ri vo qun lng. Mi ti nhng

nm 90 th Mackay bng thut gii tng tch (Sum-product Agorithm ) mi chng

minh c rng cc m LDPC khng u trn knh Gauss ch cch ti hn Shannon

0.054 dB.

V c bn chng ta co th nh ngha m LDPC nh sau. LDPC (Low

Density Parity Check Code), hay gi l m kim tra chn l mt thp, k thut

m ha m sa li trc FEC (Forward-Error Correction) thuc h m khi (Block

Codes). LDPC c trng bi ma trn sa sai kch thc ln gm cc gi tr 0 v 1

vi mt gi tr 1 thp (low density). Theo nh inh ngha ca Gallager, th m

LDPC (n,,) nh mt m khi tuyn tnh nh phn c di nc c trng bi

ma trn kim tra H vi mi ct cha phn t 1 v mi hng cha phn t 1. S

lng ct ca H bng di khi l n v s lng hng bng s du kim tra chn

N TT NGHIP


l (j = n-k

, trong k l di ca bn tin). ng thi, , phi rt nh so vi

n. V t l m ha R 1

.

Di y l v d ca m Gallager LDPC c cu trc th hin trong hnh

3.3.2 th hin mt m LDPC (20,3,4 ) :

0 0

0 0

0 0

0 0

0 0

0 0

1 0

1 0

0

1

0

0

0 0 0 0 0

0 1

0 0

0 0

0 0

0 1

0 0

0 0

0 0

0

1

0

1

0 0 0 1 1

1 0

0 0

0 0

0 0

0 1

0 0

0 0

0 0

1

1

0

0

0 0 0 0 1

0 0

0 0

0 0

0 1

0 0

1 0

1 0

0 0

1

0

0

1

0 0 0 1 0

1 1

0 0

1 1

0 0

0 0

0 0

0 0

0 0

0

1

0

0

0 0 0 0 0

0 0

1 1

0 0

1 0

0 0

0 0

0 1

0 0

0

0

1

0

0 0 0 0 0

0 0

0 0

0 0

0 0

1 1

0 0

0 0

1 1

0

0

0

1

0 0 0 0 0

0 0

0 0

0 0

0 0

0 0

1 0

0 0

0 0

0

0

0

0

0 1 1 1 1

0 1

0 0

0 0

1 0

0 0

0 0

1 0

1 0

0

0

0

0

0 1 0 0 0

0 0

0 1

0 1

0 0

0 0

0 1

0 0

0 0

0

0

0

0

0 0 0 0 0

0 0

0 1

0 0

0 0

0 1

1 0

0 0

0 0

1

0

1

0

0 1 0 0 1

0 0

0 1

0 0

0 0

0 0

0 1

0 1

0 0

1

0

0

0

0 0 0 1 0

Hnh 3.3.2 Ma trn kim tra chn l cho m LDPC ( 20,3,4)

Do m LDPC thuc lp m khi truyn tnh do n mang y c tnh

cht ca mt m khi tuyn tnh. Chui bt tin chiu di l ksau khi m ha s thu

c mt t m c di tng ng l n. T l gia R=k/n s c coi l t l m.

Trong mt t m LDPC bt k u c n-k bt m kim tra. Kch thc ma trn

kim tra H cng c kch thc khng ngoi l chnh l (n-k) n. iu kin

mt m LDPC c coi la tha mn cng ging nh m khi tuyn tnh C.HT = 0.

Trong , HT l ma trn chuyn v ca ma trn H.

M ha kim tra chn l mt thp l mt dng ca cc m block khng

tuyn tnh vi b gii m lp i lp li. Mt m LDPC c m t bi chnh ma trn

N TT NGHIP


H kim tra tnh chn l ca n hay th Tanner i din tng ng vi n.

th ny c s dng trong thut ton gii m truyn thng ip.

Mt m LDPC l mt m nh phn tuyn tnh vi mt ma trn kim tra chn

l ri rc M N, c ngha l H bao gm hu ht bit 0 v mt s bit 1 lin quan. M

ny c th c lp li thng xuyn hoc khng. Mt m LDPC thng xuyn c

gi tr chnh xc wc trn tng ct v gi tr chnh xc wr = wc (N/M) trn tng hng

ca H, vi wc v wr l nh so vi N.

Mi m kim tra chn l, bao gm m LDPC, c th c xc nh bi mt

th Tammer. Mt th Tammer l i din cho mt m tng ng mt thit

lp ca cc kim tra chn l c th phn bit b m. th bao gm hai kiu node,

mt l cho tng m chn l C1, C2,, Cm,CM, v N node, mt l cho tng bit m

ha v1, v2, ., vM. Cc node kim tra c kt ni n cc bit node m chng kim

tra. c bit, mt nhnh kt ni node kim tra m n node bit n khi v ch khi ln

kim tra chn l th m bao gm n ln bit ( ngha l ch khi Hm,n = 1). V vy, th

l tng t vi ma trn H. Ln kim tra chn l th m c lu nh mt s hn

ch khu vc c trng thi nj=1 hijxj = 0. Mt cu hnh c a ra l mt t m

hp l khi v ch khi tt c s hn ch khu vc c p ng.

N TT NGHIP


Hnh 3.3a :Tanner th i din ca mt m (6,3)

- Gii m LDPC

Vi gii m LDPC, ta tm c xc sut tng bit vn ca vector r nhn c

bng 1 hoc 0, c hiu l t m c tnh bt ngun t r p ng hn ch HT =

0. Nhn c mt vector r, gii quyt trc tip cho xc sut P (vn = b|r), ngha l bit

th n bng vi 1 hoc 0 l rt phc tp.

Gallager a ra mt cng ngh lp i lp li, c hiu l thut ton sinh

tng, vi xc sut umn (b) vi ln kim tra th m c p ng bi vector c nhn

r, c hon thnh t node kim tra Cm n bit node vn. Xc sut kim tra p ng

umn(b) c tp hp t tt c cc bit in hnh trong ln kim tra th m hn vn.

Tng t nh vy, xc sut bit qmn(b) m bit th n c gi tr vn = b, c thc hin

t bit node vn kim tra node Cm. Xc sut bit qmn(b) ny c tp hp t tt c

cc kim tra m bit th n tham gia hn Cm.

Ta a ra v d (6, 3) v m LDPC t hnh 3.3. Cc bn tin bao gm cc xc

sut umn kim tra c ch ra t cc node, v cc bn tin bao gm xc sut qmn (b) di

ng t cc bit node n cc node kim tra. Vic x l c lp li cho n khi n

tp trung n mt gii php t m hoc cho n khi mt s ln lp xc nh trc c

N TT NGHIP


th t c. Ta theo di thut ton truyn bn tin in hnh trn bit node v4 v

node kim tra C2. Cc bit node c khi to vi gi tr kh nng bt ngun t mt

my d. Gi s rng bit node v4 t n xc sut q24(b) vi v4 = 1 n node kim tra

C2. Node kim tra C2 tp hp cc kh nng vo t tt c cc bit khc bao gm kim

tra 2 (v2 v v5), tnh ton mt kh nng u24(b) vi kim tra chn l C2 c p ng

khi cho v4 = 1, v t c bn tin ny n bit node v4. Node kim tra C2 truyn

thng tin n gin n v2, vi v2 =1, v n v5 vi v5 = 1. Khi bot node v4 nhn

c thng tin kim tra p ng t tt c cc node kim tra t C2 v truyn bn tin

ny tr li node C2, thng tin tng ng n C1, v.v. Qu trnh x l c m t

trong hnh 3.3 :

(b) q24 (b) (a) 24 (b)

Hnh 3.3b. Gii m (6,3)

3.4. M LDPC trong vic ci t phn tn

Trong khi m ha LDPC (hay m ha khi tuyn tnh chung) trong cu trc

m ha truyn thng m rng bng thng (tng tc ), th trong DSC n c s

dng cho vic nn bng thng. V vy, chng ta c mt trng thi xung t v

chng ta c th ngh v n nh l s chuyn tip cc quy lut ca b m ha v gii

m. t c knh t m nh k vng, chng ta nhn t m ngun vi ma trn

kim tra chn l H ( Nh rng trong m knh cho pht hin li, chng ta nhn vi

N TT NGHIP


ma trn chung G khi GHT = I). iu ny s em li cho chng ta syndrome t m

nhn c ngha truyn thng, v trong cng mt kiu cho chng ta by gi l

syndrome pha b m ha, c ngha l ch s chng ta mun truyn trn knh.

Chng ta cng s gi ma trn s dng pha m ha cho ma trn chung G, nhng

lu rng ln thit lp ny th y l s i din ca ma trn chung trong vic

s dng c lng.

3.4.1. Vic xy dng m cho trng hp i xng

Ta a G m ha, ngha l vic nn, mt u vo nh phn ty ng b,

ta nhn X vi G v tm ra syndrome Z ca di (n k) p ng. y l ci m ta

truyn i trn knh v n i din cho ch s ca coset c cha t m hot ng.

Mc tiu l ti to cch s dng bit nhn c ny t cc cm bin khc nhau

nh chng ti nhn ra.

Vi vic gii m, b gii m phi c c tnh vi s tun t X c di n

t syndrome Z c di (n k) v b p ng tun t Y c di n. iu ny c

thc hin bi mt phin bn iu chnh ca thut ton tng sn phm c m t

trong phn 8. i vi cc trng hp gc (ngun m ha cc thng tin bn), chng

ti s dng th yu t m t trong hnh 3.4.1a. iu ny da trn cu trc ging

nhau nh hnh 3.2.2, vi vic thit lp c mt tp cc rng buc (hnh vung) v

mt tp hp cc bin (vng trn). Ngoi ra chng ti cn cc bit nhn c t thng

tin ph v mt dng b sung cc rng buc da trn cc thng tin tng quan.

t c bt k t l mong mun trong vng t l, chng ta thm mt

dng cc bit bin nn cc thng tin ph th Tanner v nhng hn ch tng

ng thuc mt m my duy nht tng ng cho cc thng tin ph (Hnh 3.4.1b) .

Gii m mt ln na t c bng cc thut ton tng hp sn phm trn biu

ny. Vic m rng ny ca th c th c thc hin trong cng mt cch thc

bao gm nhiu ngun vo cc thit lp LDPC phn phi i xng. Cc m my

n b sung c kt ni vi cc th thng qua dng hn ch s tng quan gia

cc th song phn

N TT NGHIP


fx1Sx1

Sx2

Sx3

Sxn

fx2

fx3

fxn

X1 f1 Y1

X2 f2 Y2

X3 f3 Y3

X4 f4 Y4

X5 f5 Y5

Xn fn Yn

Hnh 3.4.1a : Gii m vi cc th Tanner trong trng hp my n

fx1Sx1

Sx2

Sx3

Sxn

fx2

fx3

fxn

X1 f1 Y1

X2 f2 Y2

X3 f3 Y3

X4 f4 Y4

X5 f5 Y5

Xn fn Yn

fY1 SY1

SY2

SY3

SYn

fY2

fY3

fYn

Hnh 3.4.1b : Gii m vi cc th Tanner trong trng hp hai my

N TT NGHIP


CHNG 4. M PHNG TRN MATLAB

4.1 Gii thiu v cng c m phng MATLAB

4.1.1 Gii thiu v MATLAB

MATLAB l mt mi trng tnh ton s v lp trnh, c thit k bi

cng ty MathWorks. MATLAB cho php tnh ton s vi ma trn, v th hm s

hay biu thng tin, thc hin thut ton, to cc giao din ngi dng v lin kt

vi nhng chng trnh my tnh vit trn nhiu ngn ng lp trnh khc.

MATLAB gip n gin ha vic gii quyt cc bi ton tnh ton k thut so vi

cc ngn ng lp trnh truyn thng nh C, C++, v Fortran.

MATLAB c s dng trong nhiu lnh vc, bao gm x l tn hiu v

nh, truyn thng, thit k iu khin t ng, o lng kim tra, phn tch m hnh

ti chnh, hay tnh ton sinh hc. Vi hng triu k s v nh khoa hc lm vic

trong mi trng cng nghip cng nh mi trng hn lm, MATLAB l ngn

ng ca tnh ton khoa hc.

4.1.2 Cch tm mt bn MATLAB s dng

Mi nm Mathworks - cng ty sn xut v phn phi MATLAB a ra th

trng 2 bn cp nht rxxxxa vo u nm v rxxxb vo cui nm (vi xxxx l nm

pht hnh). Vi cc bn bt u tm hiu v s dng Matlab, nn s dng bn

r2008a v dung lng khng qu ln, chy nhanh vi cc my tnh c ti nguyn

phn cng khng cao.

Vi cc bn sinh vin mun s dng MATLAB, bn cn c phn mm

MATLAB, thng thng l qua 1 trong cc cch sau:

Tm trn mng internet hoc mua cc ca hng a, dung lng ca b ci

MATLAB c y cc Toolbox l khong 3.5 Gb cho bn r2008a, khong 5Gb

cho bn r2012a. y l cch nhanh nht v thng dng nht do gi ca MATLAB l

rt cao. Nu download trn mng, bn nn download bng phn mm utorrent, tm

kim bn MATLAB bn cn trang isohunt.com. Cch ci t v b kha bn c

th tm trn youtube hoc c hng dn ngay trong a ci.

N TT NGHIP


Xin bn trial trn trang ch ca Mathworks,bn cn hon thnh form ng k.

S dng MATLAB c bn quyn trng i hc bn hc.

4.1.3 S dng MATLAB hiu qu

Mun thnh tho s dng MATLAB bn cn phi t mnh g cc cu lnh

v xem kt qu cu lnh, mc li v tm cch sa li. Cch hc "trial and error" ny

theo ti l cch tt nht hc lp trnh. Thi gian v cng sc bn b ra bao nhiu

s mang li cho bn nhiu kin thc by nhiu.

Nu bn c nn tng l mt ngn ng lp trnh nh C, C++ hay Pascal, ...

vic lm quen vi MATLAB s rt d dng, ch cn mt ngy l bn c th bit

cch s dng c MATLAB. Tuy nhin s dng c khng c ngha l thnh

tho hay xut sc, lp trnh MATLAB c t duy ring, khng ging ht vi t duy

lp trnh ca ngn ng no c v vi tng ngi dng, ty theo mc ch s

dng MATLAB m t duy lp trnh cng khc nhau.

Kh nng ng dng to ln ca MATLAB l nh cc Toolbox c vit bi

nhng chuyn gia hng u trong nhiu lnh vc. Khng ai hc tt c cc

Toolbox ca MATLAB c. tit kim thi gian v cng sc khng cn thit, mi

ngi dng MATLAB ch cn tm hiu mt hay mt vi Toolbox lin quan n

cng vic ca mnh l .

Ti liu v MATLAB hin nay c rt nhiu, c ting Vit v ting Anh.

s dng MATLAB, khng nht thit phi c nhiu sch. Bn hy chn mt

cun bt k lin quan n lnh vc ng dng ca MATLAB m bn quan tm

c, lm theo cc v d v suy ngh. Ti liu quan trng nht chnh l Help ca

MATLAB, nu nh bn c kh nng t hc tt, Help l ti liu duy nht bn cn v

n c sn khi ci MATLAB.

gip cc bn d dng hn trong vic s dng MATLAB, chng ti cung

cp cc bi hc c bn, c dch t ti liu "Introduction to Programming in

MATLAB" t MIT OpenCoursewares gm 5 bi (Nhng bn c kh nng ngoi

ng nn tm hiu trc tip bn gc t trang web ca MIT Opencoursewares) cn cc

phn hng dn s dng cc Toolbox c t thc hin, hoc su tm v dch t

N TT NGHIP


cc sch cng nh t Help ca MATLAB. Nu nh c nhng sai st, rt mong c

s gp t cc bn.

Xt cho cng MATLAB ch l cng c thc hin tng, MATLAB c

th cho ta kt qu nhng n khng thay ta suy ngh, khng mang cho ta kin thc.

Nm chc kin thc chuyn mn l cha kha s dng MATLAB c hiu qu. V

d mun thit k b iu khin PID, bn cn hiu cc thnh phn P, I, D c tc

dng nh th no ti cht lng h thng trc khi dng cu lnh ca MATLAB

chnh nh tham s t ng.

4.2 . M phng trn MATLAB

Mc ch ca vic thc hin ny l xy dng mt m ngun phn tn c th

dung n cho 1 tp cc d liu ECG s dng s m ha LDPC. ECG l mt loi

d liu y t v l mt d liu u vo chun cho mt v d v mng cm bin khng

dy trong y t, ng dng ca m ngun phn tn DSC. D liu ny c tp ra c

2 (hoc nhiu hn) sensor vi mt phn b tng quan khng gian bit. S

tng quan ny l mt dng ca nhiu phn b Gauss, ch s N vi gi tr trung

bnh l 0 v phng sai bit. S tng quan ny thay i vi phng sai (cng

sut) nhiu: Cng sut nhiu cng cao th tng quan cng t.

Trong m hnh an ta s dng knh truyn hon ho. D nhin n khng c

trong thc t, nhng ta ch quan tm n m ha ngun. Li gy ra do s khng

hon ho ca knh truyn c th c gii quyt bng m ha knh hay l tm kim

mt m ha chung cho ngung v knh. Mt m hnh thit k mc cao ca bn pht

ch ra hnh 4.2, v bn thu hnh 4.3.

Q S-W

X U Z

Hnh 4.2: Bn pht ca h thng

N TT NGHIP


DECODER S-W

Y

Hnh 4.3: Bn thu ca h thng

4.2.1 Thc hin m Hamming

u tin, to 1 b m ngun phn tn vi ma trn Hamming (7,4), xy dng

mt ma trn kin tra li chn-l H c 7 ct v 7 - 4 = 3 hng.B to ma trn c s

dng bn pht l chuyn v ca ma trn H, G = HT. Ma trn kim tra li chn-l v

chuyn v ca n c m t hnh 4.2.1a. Lu rng b to ma trn c dung

y khng ging vi b to ma trn ca m LDPC c s dng sa li. Cc

mu u vo ECG c lng t ha dung b lng t ti u PDF. B lng t

y l ti u cho phn b Gauss, mc d d liu ECG khng phi phn b Gauss.

Tuy nhin, phn b Gauss dng nh l tt hn trong trng hp ny. B lng t

c th c thit k cho bt k t l t c no. y chng ta lng t cc mu

u vo vi b lng t 7 bit tng ng vi b m phn tn.

1 0 0 1 1 1 0

0 1 0 1 1 0 1

0 0 1 0 1 1 1H = H

T =

1 0 0

0 1 0

0 0 1

1 1 0

1 1 1

1 0 1

0 1 1

Hnh 4.2.1a: Ma trn kim tra li chn l v chuyn v ca n

N TT NGHIP


Cc t m tch cc ( lng t ha) c nhn vi ma trn G v truyn i

n b gii m. Tp cc gi tr u ra ca cc bit c m ha i din cho cc

coset ca m knh. Nhiu t m thuc cng 1 coset nh c trnh by chng

trn. Trong m Hamming (7, 4) c 27 t m v 23 coset khc nhau. Do vy c 24 t

m m u ra cng cc bit m ha, thuc cng 1 coset. Mc ch l thit k mt m

knh chun vi khong cch ti thiu gia cc t m trong coset l ln.

Cc t m ca coset 000 c ch ra hnh 4.2.1b.

0000000

0001011

0010111

0011100

0100110

0101101

0110001

0111010

1000101

1001110

1010010

1011001

1100011

1101000

1110100

1111111

Hnh 4.2.1b: Cc t m cu coset 000 trong m Hamming (7, 4) phn tn

B gii m ca m hamming l b gii m c kh nng chnh xc ti a. Khi

n nhn c 1 chui bit t knh truyn, n s tm coset (c nh ngha trc v

tn s bit) v cc t m cha trong n. Sau s dng thng tin bn Y (lin quan

n t m tch cc X), b gii m kh nng chnh xc ti a s duyt qua cc t m

trong coset nhn c v tm mt ci gn ng nht (vi mt s iu kin). Kt qu

c lng X ca X l u ra ca b gii m. Mc ch chung ca h thng ny l

ti thiu X - X gy ra bi s phc tp v tr ca vic m ha (b m ha Slepian-

Wolf), v mt tiu ch trung thc bn trong (b lng t ha). Li ny cng l

thc o tt trong h thng ca chng ta.

N TT NGHIP


Hnh 4.2.1 Kt qu s t l bt li m Hamming cc trng hp khc nhau

4.2.2 Thc hin m LDPC

Vi vic m ha LDPC chng ta to cc ma trn kim tra li chn-l ln hn

v mt thp hn. Theo nh l m ha ngun ca Shannon th vic m ha trong

trng hp chiu di khi ln hn cho hiu nng tt hn, v to ra nhiu ma trn

ln hn. Ma trn kim tra li H c xy dng ngu nhin. Cc t m lng t

nhiu hn trong chiu di khi t c (v d l103) v nhn vi ma trn H nh l

trong v d v m Hamming. Cc bt m ha i din cho 1 khi cc chui bt ca

coset v c gi qua knh truyn gii m v khi phc d liu.

B gii m s dng mt phin bn p thch hp ca thut ton sum-product

c miu t chng 4.2 trong s quyt nh khng ch da trn chui bt

nhn c v rang buc v kim tra chn l trong biu Tanner m cn quan tm

n chui cc bt tng quan ca thng tin bin Y. Do hn ch v mt thi gian nn

n khng c thc hin v kim tra.

1 2 3 4 5 6 7 8 9 10 11 12

10-10

10-8

10-6

10-4

10-2

BIT and BLOCK Detection for (7,4) Hamming Code

SNR(dB)

BE

R

Simulated BER(Hard Decoding)

Simulated BER(Soft Decoding)

Theoritical BER(Hard DEcoding)

Theoritical BER(Soft Decoding)

N TT NGHIP


Hnh 4.2.2 Kt qu t l bt li m ha LDPC qua knh AWGN

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7

10-2.69

10-2.67

10-2.65

10-2.63

10-2.61

N TT NGHIP


KT LUN CHUNG

Mc ch chnh ca vic nghin cu ny l s dng mt nn tng m ha

thng minh tng thi gian sng ca sensor trong mng cm bin khng dy. Cc

sensor ny phi hot ng m khng phi cp thm ngun v quan trng hn c l

cn gim khi lng d liu m mi sensor s phi truyn. M ha ngun phn tn

cho thy kt qu mong mun nu thc hin chnh xc. Chng ta miu t cch nn

d liu da trn s tng quan vi cc ngun khc m khng cn thit phi thnh

lp mng lin kt cm bin (intersensor).

Nh vic thc hnh chng ta s dng m LDPC nn d liu. M ha LDPC

c bit n nh l mt dng ca m ha knh v vn ang ci tin v cng gn

hn vi gii hn Shannon. Khi s dng m ha ngun phn tn cho thy hiu nng

tt hn so vi m turbo v t c gii hn Slepian-Wolf. Trong n ny, chng

ta ch kim tra v mt l thuyt vi mt m Hamming(7,4) nh l b m ha phn

tn. N cho thy hiu nng khng c tt lm, nhng n nh l mt bc tranh tng

th v k thut, trin khai, v s dng trong m hnh m ha ngun phn tn.

Th minh ha l thuyt ca n trong mi trng thc t, chng ta s dng

m ha ngun phn tn trong mng ca cc nt cm bin y t o c cc tn hiu

ECG trong c th ngi. y ch l phn trong vic thc hin nn d liu da trn

s tng quan trong mng cm bin, nhng c th l mt phn tt yu trong vic

lm gim nng lng tiu th v v th s tng thi gian sng cho sensor.

Hng pht trin ti :

Do kh nng cn hn ch, cng vi vic thi gian khng kp p ng, em

mi ch dng li mc nghin cu v m phng cc thut ton p dng vo M

ngun phn tn. Chnh v vy, hng nghin cu sp ti ca em s l nghin cu

cch a c cc thut ton ny vo mng cm bin khng dy nh theo yu cu.

ng thi c th s dng m phng ny a vo phn cng thc t kim chng

chnh xc v gp phn ng dng vo thc t.

N TT NGHIP


PH LC

1. Thuyt bin dng tc

Khi xem xt cc ngun tng t, khng gii m cc tn hao v s gii

hn cng sut ca mt knh thc. Thay v c s bin dng khng kim sot c t

cc knh chng ti c th gii thiu mt s suy thoi c kim sot nht nh hoc

bin dng tn hiu trc khi truyn. Ting n nhiu hn trn cc knh c sn, chng

ta cng phi tng bin dng ny, hay ni cch khc: gim t l ngun. Mt v d

n gin nhng trc quan ca kt qu ny c th hin trong hnh 1.

D

R

Hnh 1 : Hnh nh in hnh ca chc nng bp mo t l

Chc nng bp mo t l cho chng ta gii hn l thuyt cho tt nh th no

chng ta c th lm tn hao nn vi s liu bin dng ni chung v ngun chung.

T l chung chc nng bin dng mo d kin :

d D

c cho bi :

N TT NGHIP


R(D) = { }

{ }

= { } ( )

= { } ( )

Vi yi l cc u ra, p = p (xn, ym ) v P l ma trn knh.

Chc nng bp mo t l l kh c th tm ra cho cc ngun chung v cc s

liu bin dng, nhng c th c phn loi trng hp c bit. Cho mt ngun

gaussian t nh vi k vng bnh phng mo s liu 2N = D v cng sut u vo

2X c chc nng mo t l bng

R(D) =

(

)

T iu ny ta c th gii quyt v nhn c tnh nng tc bin dng :

D(R) =

Do la chn tc mt s nh i- tt trn mt chp nhn lng bin

dng thnh cc tn hiu hoc do hn ch nht nh (v d nh hn ch cng sut,

ting n knh).

L thuyt bin dng t l m t c s dng trong cc v d thc t thng qua cc

hnh thc khc nhau ca lng t, mt s phc tp hn so vi nhng thnh phn

khc.

1.1. S lng t ha v hng

S lng t ha v hng c hon thnh da trn mt v d v ngun ti

mt thi im. iu ny c th c c lng hay ti u cho s phn tn ca

ngun. Mt cch ti u l da vo thut ton Lloy Max tng qut. Vic thit k

lng t ti u t c thng qua vic tm ra s thay i li lng t ha nh nht

qua tng trng thi.

vi n = 0, . . . , N 1

N TT NGHIP


vi n = 1, . . . , N 1

Vi rn l s mc i din, dn l s mc quyt nh v N l s mc lng t

ha. Cc trng thi ny c lm sng t qua 2 cng thc :

( ) vi n = 1, . . . , N 1

( )

( )

vi n = 0, . . . , N 1

c gii quyt bng cch lp i lp li t mt s gi tr ban u. Cng thc 6 ch ra

rng trong lng t ti u ha mc i din c cho l trng tm ca khong

thi gian quyt nh tng ng, v cc mc quyt nh t chnh gia hai mc i

din. Cc c trng lng t ha s c cc khong thi gian quyt nh ln ni xc

sut xy ra ca tn hiu u vo l nh, v ngc li. y l cch m mc lng t

ha s ng gp vi s lng tng t hn ch ti a cc li lng t.

1.2. S lng t ha Vector c hng

S lng t ha c hng c a ra, nh chnh tn gi, trn mt vector

ca cc v d. Khi s lng t ha c hon thnh vi nhiu hn mt v d, cc

mc quyt nh tr nn a chiu hay a vng hn, v tn hiu c lng t tr

thnh im i din ca mt vng. Mc i din c quyt nh da trn N gi tr

lin tc ca tn hiu u vo. Nu cc vng l Voronoi ( hoc cc phn Dirichlet )

v cc mc i din l cc trung tm ca cc vng tng ng, s lng t ha c

ti u.

Cc vector i din nh dng cho codebook ca lng t ha mt vector.

Ch s t m kch hot c truyn trn knh v c ti cu trc y ha hn trn

mt bn pha nhn. Codebook thng c thit k qua vic th nghim ca VQ.

C ngha l, u ra ca ta a ra mt dy bit tun t xc nh c ta gi s ging

nh mt ngun VQ tim tng s c dng, v chng ta tm ra codebook bng cc

thut ton lp.

N TT NGHIP


Cc tng quan khc theo thi gian mt ngun l, cc dng VQ tt hn. S

lng t ha vector c th c ch ra cung cp mo tn hiu c t l thp nht

cho mt mc nn c a ra. Tuy nhin, do s chiu cao v kch thc

codebook ln, n yu cu n dn n phc tp tnh ton cao v s chm tr v

khng thc t [19, 20].

1.3. S lng t ha lng nhau

php lng t ha lng nhau, chng ta c hai php lng t ha vi t l

lng khc nhau ca tng loi. iu ny ch ra y l mt code chun hay code

khng chun. Code khng chun c th c xem nh l mt bc cu trc tp

hp; ban u lng t ha s dng code chun, sau s dng code khng chun

t t m trong mt tp hp.

Lch trnh lng t ha lng nhau c th ddwwocj twhcj hin cho bt k cc

ngun v d b chn li, c ngha l n c th c cu trc trong bt k hng no.

Nu c hai loi code nm trong khng gian hai chiu th chng ta c th gi n l

lng t ha mng li an xen. iu ny tr nn ging vi lng t ha vector, v

vic ti u ca cc vng Voronoi l mt chc nng c thit k ct yu. Trong

khng gian hai chiu, cu trc ti u c tm ra hnh thnh li lc gic.

2. Cc cu lnh c bn trong MATLAB

Khi khi ng MATLAB, chng trnh s hin th ln mt ca s lnh cho

php bn son tho nhng dng lnh vi cu trc >> dng lnh. Cc bn c th

thy mt chng trnh gii quyt bi ton tm nghim thc ca phng trnh bc 2

nh sau:

function giaiptbac2()

>>a = input('a = ');

>>b = input('b = ');

>>c = input('c = ');

N TT NGHIP


>>d = b*b-4*a*c

>>if d < 0

>>k = 'phuong trinh vo nghiem'

>>elseif d == 0

>>x1 = -b/(2 * a)

>>x2 = x1

>>else

>>x1 = (-b + sqrt(d))/(2 * a)

>>x2 = (-b - sqrt(d))/(2 * a)

>>end

Thut ton v cc cu lnh cng tng t nh cc ngn ng lp trnh C, C++ bi

MATLAB l mt loi hp ng.

Di y l mt v d

>> c = [1:2:7; 8:2:14; 20:-1:17]

c =

1 3 5 7

8 10 12 14

20 19 18 17

* To vector ct d t ma trn c : d=c( :)

N TT NGHIP


>> d = c(:)

d =8

20

10

19

12

18

* Ma trn chuyn v dng k hiu nhy n '

>> c1 = c'

c1 = 8 20 10 19 12 18

* Ma trn c cc phn t l 1 : ones(r,c) r s hng, c s ct

>> ones(3,4)

ans =

1 1 1 1

1 1 1 1

1 1 1 1

Ma trn l mt dng ca mng d liu. Cc php ton vi ma trn v mng

c MATLAB h tr bng command window help chn operation c hin th

trn giao din khi ng ca MATLAB. Nh vy bn c th thc hin mi yu cu

ca bi ton. Mt ch nho nh khi thc hin php nhn trong ma trn, MATLAB

N TT NGHIP


phn bit nhn tng phn t ca ma trn bng k hiu .* cn nhn 2 ma trn l k

t *.

Ngoi ra, mt iu khc bit trong MATLAB vi cc ngn ng lp trnh

hng i tng khc l cch s dng du chm phy. Du ; t cui cu

lnh mc nh khi cu lnh thc hin xong s khng hin th kt qu. Cn nu

khng c th mc nh kt qu c hin th.

Ngoi phng php g lnh trc tip ca s chng trnh, MATLAB cn

h tr to mt script m-file cha cc cu lnh g ca s lnh, cc cu lnh ny

cng thc thi ging nh ca s lnh.

Cch to m-file:

Menu File => New =>Script

V d, bn to mt file vidu.m, sau khi hon thnh nhng cu lnh trong m-

file, bn lu v tr li ca s chng trnh vit dng lnh >> vidu. Sau cc cu

lnh trong file s c thc hin, kt qu s c hin th.

Ch rng, MATLAB s khng thc hin c chng trnh nu nh ng

dn ca m-file (matlabpath) khng chnh xc. Nh vy, mt yu cu bt buc ngi

vit code phi m bo chnh xc tuyt i ng dn ca m-file khi thc hin

chng trnh.

3. Code s dng trong n :

3.1. Code Hamming :

close all;clear all;clc;

SNRdB=1:1:12; %SNR in dB

SNR=10.^(SNRdB./10); %SNR in linear scale

info_word_length=1000; %No. of information words

n=7;k=4; %Parameters of hamming code

N TT NGHIP


ber=zeros(length(SNR),2); %Simulated BER

info_word=floor(2*rand(k,info_word_length)); %Generation of 0 and 1 for

infromation bits

code_bit5=xor(info_word(1,:),xor(info_word(2,:),info_word(3,:))); %First Parity

Bit

code_bit6=xor(info_word(1,:),xor(info_word(3,:),info_word(4,:))); %Second

Parity Bit

code_bit7=xor(info_word(1,:),xor(info_word(2,:),info_word(4,:))); %Third Parity

Bit

code_word=[info_word;code_bit5;code_bit6;code_bit7]; %Coded information

Word with parity bits

code_word(code_word==0)=-1; %Converting 0 bits to 1

decoded_bit=zeros(n,info_word_length); %HARD Decoding Output

decoded_block=zeros(n,info_word_length); %SOFT Decoding Output

H=[1 1 1;1 0 1;1 1 0;0 1 1;1 0 0;0 1 0;0 0 1]; %Parity Check Matrix

C=de2bi((0:2^(k)-1)); %All bits of length k(Stored in valid code

words matrix 'C')

C(1:16,5)=xor(C(:,1),xor(C(:,2),C(:,3))); %First Parity Bit

C(1:16,6)=xor(C(:,1),xor(C(:,3),C(:,4))); %Second Parity Bit

C(1:16,7)=xor(C(:,1),xor(C(:,2),C(:,4))); %Third Parity Bit

distance=zeros(1,2^k);

for i=1:length(SNR)

y=(sqrt(SNR(i))*code_word)+randn(n,info_word_length); %Received Codes

%For BIT(Hard) Detection

decoded_bit(y>0)=1; %All positive received bits converted to +1

decoded_bit(y

N TT NGHIP


%Decoding Received Codes into valid codewords

for l=1:info_word_length

%HARD Decoding

hi= decoded_bit(:,l)'*H; %Syndrome Detection

for j=1:n %Matching 'hi' to every row vector of H and flipping the

corresponding bit of 'z' using xor

if (hi==H(j,:))

decoded_bit(j,l)=~decoded_bit(j,l); %NOT operation on the

corresponding bit

end

end

%SOFT Decoding

for m=1:(k^2) %Tacking distance of each column of the received word

to a valid codeword

distance(m)=norm(y(:,l)-C(m,:)');

end

[minval,minind]=min(distance); %Finding index of the minimum distance

valid codeword

decoded_block(:,l)=C(minind,:); %Decoding as the min distance codewor

end

ber(i,1)=length(find(decoded_bit(1:4,:)~=info_word)); %BER in BIT

Detection

ber(i,2)=length(find(decoded_block(1:4,:)~=info_word)); %BER in BLOCK

Detection

end

ber=ber/(k*info_word_length);

semilogy(SNRdB,ber(:,1),'r-

N TT NGHIP


semilogy(SNRdB,ber(:,2),'m-

N TT NGHIP


SNR=10.^(SNRdB/10); %SNR in linear scale

Iteration=4;

ber=zeros(length(SNR),Iteration); %Simulated BER(Each column corresponds to

one iteration)

%% Encoding

X_pi(1:N)=X(Interleaver(1:N)); %Interleaving input bits for RSC-1 encoder

C0=zeros(1,N); %Code Bit for encoder RSC-0

C1=zeros(1,N); %Code Bit for encoder RSC-1

for i=1:N

k = i;

while (k >= 1)

C0(i) = xor ( C0(i),X(k) );

C1(i) = xor ( C1(i),X_pi(k) );

k=k-2;

end

end

P0 = xor (X,[0,C0(1:end-1)]);

P1 = xor (X_pi,[0,C1(1:end-1)]);

Input_matrix=2*[0,1;0,1;0,1;0,1]-1; %First column represents input=0 and

second column represents input=1

%Each row represents state 00,10,01 and 11 respectively

Parity_bit_matrix=2*[0,1;1,0;0,1;1,0]-1; %Parity bits corresponding to inputs of

above matrix

mod_code_bit0=2*X-1; %Modulating Code Bits using BPSK Modulation

mod_code_bit1=2*P0-1;

mod_code_bit2=2*P1-1;

dlg = ProgressDialog();

dlg.FractionComplete = 0;

N TT NGHIP


dlg.StatusMessage = sprintf('Encoding completed...');

%% Decoding

for k = 1:length(SNR) %Simulation starts here

R0=sqrt(SNR(k))*mod_code_bit0+randn(1,N); % Received Codebits

Corresponding to input bits


Corresponding to parity bits of RSC-0


Corresponding to parity bits of RSC-1

R0_pi(1:N)=R0(Interleaver(1:N)); %Interleaving received codebits

corresponding to input bits to be used by RSC-1

BCJR=0; %First iteration will be done by BCJR-0

Apriori=ones(2,N); %First row for prob. of i/p 0 and second row for prob.

of i/p 1

Apriori=Apriori*0.5; %Initializing all apriori to 1/2

for iter=1:Iteration %Iterativ

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