MVC LVC

LOi.noi dau 5

Chuong 1: Nhfing van de chung va nhfing khai ni~m co ban 7

1.1 v! tri, vai trc>va sa 1ugcl!ch Slrphat tri~n cua Ly thuy€tthong tin " 71.1.1 Vt tri, vai fro cua Ly thuylt thong tin ~ 7

1.1.2 Sa Iu(}'cItch sz(phat triin 9

1.2 Nhii'ngkhai ni~m ca ban - sa d6 h~ truy~n tin va nhi~m Vl;lcua n6 10

1.2.1 Cac dtnh nghla ca ban 10

1.2.2 Sa do khol cua h~ thong truye'ntin so' l1

1.2.3 Nhilngchi lieu chat Iuqngca ban cUamQth~truye'ntin 15

Chuong 2: Tin hi~u va nhi~u 162.1 Tin hi~u xac d!nh va cac d~c trung v~t 1ycua chung 16

2.2 Tin hi~u va nhi~u 1acac qua trlnh ng~u nhien 17

2.2.1 Ban chat ngdu nhien cua tin hi~u va nhilu 17

2.2.2 Dtnh nghla va phan Ioqi nhieu 17

2.3 Cac d~c trung thong ke cua tin hi~u ng~u nhien va nhi~u 20

2.3.1 Cac dqictrung thong ke 20

2.3.2 Khoang tuang quan .21

2.4 Cac d~c trung v~t1ycua tin hi~u ng~u nhien va nhi~u,bi€nd6i Wiener - Khinchin .., ..23

2.4.1 Nhfing khai ni~mxay d1;fngIy thuylt phil cua quatrinh ngdu nhien - m{ttdQphil cong suat 23

2.4.2 Cqipbien dili Wiener - Khinchin 26

2.4.3 Be'rQngphil cong suat 28

2.4.4 MiJ rQng cqipbien dili Wiener - Khinchin cho truo'ng

hQ'pR( r) khong kha rich tuy~t dol 30

2.5 Truy~ncac tin hi~u ngc1unhien qua cac m~ch vo tuyendi~n tuyen tinh 312.5.1 Bai loan tal tilu 312.5.2 Bai loan toi da 36

2.6 Bieu dien phuc cho the hi~n cua tin hi~u ngc1unhien - Tinhi~u diii h~p 43

2.6.1 C(lpbien d6i Hilbert va tin hifU gidi rich 432.6.2 Tin hifu ddi rqng va ddi hllP 49

2.7 Bieu dien hlnh h<;>ccho the hi~n cua tin hi~u ngc1unhien 512.7.1 Khai triln trlfc giao va bilu diln vec to'cua tin hifu 512.7.2 M(it dq xac suat cua vec to'ngJu nhien - Khodng

cach giila hai vec to'tin hifU 542.7.3 Khai nifm ve'may thu tal uu 58

Bai t~p 60

Chuong 3: Co so Iy thuyet thong tin thong ke 633.1 Thong tin, luqng thong tin, xac suat va thong tin, dan V!do

thong tin. 63

3.1.1 Dinh nghla dinh tinh thong tin va luf/ng thong tin 63

3.1.2 Quan hf giila dq bat dinh va xac suat 65

3.1.3 xac dinh luf)71gthong tin 68

3.2 Entropie va cac tinh chat cua entropie.: 703.2.1 Tinh chat thong ke cua nguon rm n;zcva s1/ra dm

cua khai nifm entropie 70

3.2.2 Dinh nghla entropie cua nguon rm rgc 713.2.3 Cac tinh chat cua entropiemqt chie'ucUanguonrm rgc 73

3.2.4 Entropie cua nguon rm rgc, nhi phan 75

3.2.5 Entropie cua truifng s1/kifndong thm 76

3.3 Entropie'c6 di~u ki~n va luqng thong tin cheo trung blob 783.3.1 Entropie co die'ukifn ve'mqt truiJngtin nay khi dii ro

mqt tin nhat dinh cua truiJngtin kia 78

3.3.2 Entropie co die'ukifn ve'truifng tin nay khi dii rotruifng tin kia 79

3.3.3 Hai trf}ngthai c¥c doan cua kenh truye'ntin 813.3.4 Cac tinh chat cua entropie co die'uki~n 823.3.5 Lu(fng thong tin cheo trung binh 843.3.6 Tinh chat cua I(A,B) 85

3.3.7 Mo hinh cua kenh truye'ntin co nhilu 863.4 Toc dQphat, khi nfmgph<it,dQthua, khi nfmgthong qua

cua kenh rOir~c ..873.4.1 Toc dq phat cua ngu6n rOirf}c... ..87

~

3.4.2 Khd nang phat cua ngu6n rOi rf}c 87

3.4.3 Dq thila cua ngu6n rOi rf}c 88

3.4.4 Cac d{ic trllng cua kenh rOirf}c va cac lof}ikenh rOirf}c 88

3.4.5 Lu(fng thong tin truye'n qua kenh trong mqt dan vithai gian 89

3.4.6 Khd nang thong qua cua kenh rOi rf}c 90

3.4.7 Tinh khd nang thong qua cua kenh nhi phan dOixungkhong nhif, d6ng nhat 91

3.4.8 Dinh If ma hoa thu hai cua Shannon 93

3.4.9 Khd niing thong qua cUakenh nhi phan dol xttng co xoa 93

3.5 Entropie cua ngu6n lien tl;lcva hrqng thong tin cheo trungbinh truy~n qua kenh lien tl;lckhong nh6" 95

3.5.1 Cac df}ng tin hi~u lien tlfc 95

3.5.2 Cac d{ic trung va tham so' cua kenh lien tlfc 96

3.5.3 Kenh lien tlfc chuG trong kenh rOi rf}c 97

3.5.4 Entropie cua ngu6n tin lien tlfc (cua mqt qua trinhngdu nhien lien tlfC) 97

3.5.5 M du wJt If minh hof} s¥ lifn vo hf}n cua entropie cuangu6n lien tlfC """""""""'" ...99

3.5.6 Lur[ng thong tin cheo trung binh truye'n theo kenh lientlfc khong nhif 100

3.6 Entropie vi phan co di~u ki~n va tinh chat cua cac tin hi~uGausse 102

3.6.1 Entropie vi phan co die'u ki~n 102

3.6.2 Entropie vi phan cua nhilu Gausse ~ 103

3.6.3 LulJng thong tin eheo trung binh truye'n theo kenhGausse 104

3.6.4 Tinh eh(ft eua cae tin hi~u co phan bo' ehudn 106

3.7 Kha nang th6ng qua cua k~nh Gausse 109

3.7.1 Khd nang thong qua eua kenh Gausse viii thc'Jigianrc'Jirfie 109

3.7.2 Khd nang thong qua eua kenh Gausse viii thm gianlien t,!-etrong mqt ddi ta'n hfin ehe' lll

3.7.3 Khd nang thong qua eua kenh Gausse viii thc'JigianI ', d ?" ' h 112Lentlfe trong al tan vo fin ............................................

3.7.4 Dinh ly mil hoG thit hai eUa Shannon dol viii kenh

lien tlfe 114

3.7.5 Vi d'!-:Khd nang thong qua eua mqt so' kenh thlfe te' 114

Hai t~p .115

Cbuong 4: Co sa If tbuyet ma boa 1194.1 Oie dinh nghia va khciini~mco ban 119

4.1.1 Cae dinh nghfa ea ban """""" 1194.1.2 Cae khai ni~m ea ban 1204.1.3 Khd nang khong ehe'sai eua mqt bq mil de'unhi phan ...1234.1.4 Mil de'unhi phan khong co dq thua 124

4.2 Ma thong k~ toi uu 1254.2.1 Dq delitrung binh eua tumilva mil hoa tolltU 125

4.2.2 Yey ea'ueua mqt phep mil hoa tolltU 1254.2.3 Dinh ly mil hoa thit nhat eua Shannon (d6i viii mil nhi

phan) .. .1264.2.4 Thwjt toan Huffman .127

4.3 cac cffutrUcd~i so va ma tuy~n tinh 1304.3.1 Mqt so'eau true dfii so'ea bdn .1304.3.2 Cae dfing tuyen tinh va mil tuyen tinh 1334.3.3 Cae bai toan tOlltUeua mil tuyen tinh nhi phan 136

4.4 Vanh da thuc va ma xyclic 1374.4.1 Vanh da thite ..137

4.4.2 Ideal cua vanh da thuc 140

4.4.3 Dinh nghla ma xyclic 1414.4.4 Ma trC;insinh cua ma xyclic 1424.4.5 Ma trC;inkilm tra cua ma xyclic 143

4.5 Milhoa cho cac mil xyclic 1444.5.1 Mo td tU:ma cua ma xyclic hi?thong 1444.5.2 ThuC;ittoemma hoa hi?thong 1454.5.3Thielhimahoa ~ 1454.5.4 TflOole dau kilm tra cua ma xyclic 1474.5.5 T huC;itloan thief IC;iptU:ma hi? thong theo

phuang phap nhdn " 1494.6 Giii mil nguBng 150

4.6.1 Hai thu tlfc gidi ma 150

4.6.2 Gidi ma theo Syndrom 150

4.6.3 Hi?t6ng kilm tra trifc giao va co khd niing trifc giao 152

4.6.4 Gidi ma nguiJng difa tren hi?t6ng kilm tra trifc giao .153

4.6.5 Gidi ma nguiJng difa tren hi?t6ng kilm tra co khd.niing trifc giao 156

4.7 Giii mil theo thu~t toan Meggit 158

4.8 Giii mil xyclic theo thu~t toan chia dich vang 160

4.8.1 Nhii?m Vlfcua thuC;itloan gidi ma 160

4.8.2 Gidi ma theo thuC;itloan chia dich vong : 161

4.8.3 Vi dlf .1624.9 Giii mil lu6i ".. ..163

4.9.1 Trflng thai va gidn d6Iu6i 1634.9.2 Gidi ma lu6i .167

4.10 Mil Hamming va mil co de)dai qrc d;;ti 173

4.11 Cac mil kh6i d1;Tatr~n so h<;>ccua truOng hihI h;;tn 175

4.11.1 Truirng hiiu hfln ciJ nguyen toGF(p) 1754.11.2 Cac tru:{YngmiJ r(mg cua trwyng nhi phdn, tnrirng

hiiu hfln GF (2 m) 176

4.11.3 Bilu diln da thuc cho trueIng hau hfln GF(2 m) 177

4.11.4 Cac fink chat cooda thitc va cacphd'ntit coo tnt(rnghiiu hq,n 178

4.11.5 XGcdink cac mil b&ngcac nghi~m 181

4.11.6 Mil Hamming ..1824.11.7 Mil BCH 183

4.11.8 Cac mil Reed-Solomon (RS) 186

4.12 Cacma ch~p ...1874.12.1 MiYdd'uva mi}t so'khai ni~m caban 1874.12.2 Cac miiTurbo ..., 192

Bai t*p , 195

Chuoog 5: Ly thuyet tho t6i uu 198

5.1 D~t bai toan va cac vffn d~ co ban 1985.1.1 Thu tin hi~u khi co nhieu lami}t bai loan thongke 1985.1.2 May thu tol ztu ..199

5.13 The'chong nhieu 1995.1.4 Hai loq,i sai ld'mkhi chr;mgiGthuyet 1995.1.5 Tieu chudn Kachennhicov ..200

5.1.6 Vi~c xit ly tol ztu cac tin hi~u 200

5.1.7 xGc suat gidi sai va quy tdc gidi tOl ztu 201

5.1.8 Ham hflp ty """"""""""""""""""""""""""""'" 202

5.1.9 Quy tdc hflp ly tol da ; 202

5.2 Xu ly toi tnI cac tin hi~u 'co tham so da bi€t, khai ni~m v~tho k€t 1l<JPva tho kh6ng k€t h<JP. 203

5.2.1 Dilt bai loan 2035.2.2 Gidi bai loan 203

5.23 Khai ni~m vi?'thu ke't hflp va thu khong ket hflp 207

5.3 Phcit tin hi~u trong nhi~u nha b<,'>lqcphoi h<JPtuy€n tinhth1;l d<,'>ng """"""""""""""""""""""""""""" 209

53.1 Dinh nghia hi} IflCphoi hflp tuye'n fink thl! di}ng 20953.2 Bai loan vi?'hi} IflC phol hflp 209533 Dilc fink bien td'nva dilc fink pha td'ncua hi}IflC

phol hflp 212

5.3.4 Phdn ling xung glt) cua m(}ch i(Jcphor hQP 214

5.3.5 Huang zIngra cua m(}ch i(Jcphor hQP 216

5.4 Ly lu~n chung v~ thu ket hQ'pcac tin hi~u nh! phan 216

5.4.1 L~p sa do gidi tor ztu m(Jt tuyen 216

5.4.2 xac sua/;sai khi thu klt hQPtin hi?u nhi phan 218

5.5 Xu ly t6i uu cac tin hi~u co tham s6 ng~u nhien -thu kh6ng ket hQ'p 226

5.5.1 Cac tham so'cua tin hi?u ia cac tham so'ngdl{nhien 2265.5.2 .xuif: tor Uucac tin hi?u co tham so'ngdu nhien bien

thien cham 226

5.5.3 xac suat h~u nghi?m cua tin hi?u co cac tham so'thayd6i ngdu nhien 227

5.5.4 .xuif: tor ztucac tin hi?u co pha ngdu nhien 2285.5.5 So sanh thu kef:hQPvOithu khong kef:hQP 2325.5.6 Chit thich ..233

5.6 Mil kh6i kh6ng gian, thOigian (STBC) 2335.6.1 Ky thu~t thu phan t~p., 2335.6.2 Ma khorkhong gian - thOigian dlfa tren hai may

phat G2 235Biiit~p 239

ChUO11g6: M~t ma .2436. 1 M~t mil khoa bi m~t 243

6.1.1 Sa do khorm(Jth? truye'ntin m~t ,243

6.1.2 M~t ma thay tht 2446.1.3 M~t ma hoan vi (MHV) 2476.1.4 M~t ma Hill ..2486.1.5 Cac h? m~t ma tich 2526.1.6 Cac h? ma dong 2556.1.7 Chudn ma dii ii?u lien lien (AES) 260

6.2 M~t milkhoa c6ng khai 2656.2.1 GiOithi?u ve'm~t ma khoa Gongkhai 2656.2.2 H? m~t RSA 268

6.2.3 H~ mc}fRabin 2716.2.4 H~ mc}fElgamal 2736.2.5 H~ mc}fMerkle - Hellman 275

Bai t~p 278

Ph1;l11;lc 282

Tai Ii~u tham khao... .306