Hybrid ARQ using Serial Concatenated Convolutional Codes

over Fading Channels

Naveen ChandranGraduate Research Assistant

Lane Dept. of Comp. Sci. & Elect. Engg.West Virginia University

Matthew C. Valenti (presenter)Assistant Professor

Lane Dept. of Comp. Sci. & Elect. Engg.West Virginia University

mvalenti@wvu.edu

Overview FEC, ARQ, hybrid ARQ and retransmission

strategies. Concatenated Convolutional Codes.

“Turbo codes” Parallel (PCCC) vs. serial (SCCC) concatenations.

Survey of hybrid ARQ techniques using turbo codes.

Turbo Coding-ARQ System Model and process chart.

Simulation parameters and assumptions. Throughput efficiency. Summary and future work.

FEC and ARQ FEC – Forward Error Correction

Channel code used to only correct errors. ARQ – Automatic Repeat Request

Channel code used to detect errors. A feedback channel is present

If no detected errors, an acknowledgement (ACK) is sent back to transmitter.

If there are detected errors, a negative acknowledgement (NACK) is sent back.

Retransmission if NACK or no ACK. Several retransmission strategies:

Stop and wait, go-back-N, selective repeat, etc. Selective repeat has better throughout performance than the others

in the presence of propagation delays. However, throughput of stop and wait and selective repeat protocols

are the same if no transmission delay is assumed.

Hybrid FEC/ARQ Combines forward error correction with ARQ. Assumption: Availability of a noise free

feedback channel Uses an outer error detecting code in

conjunction with an inner error correcting code

The receiver first tries to correct as many errors as possible using the inner code.

If there are any remaining errors, the outer code will (usually) detect them.

Retransmission requested if the outer code detects an error.

Retransmission Strategies Two generic types of hybrid FEC/ARQ. Type I hybrid ARQ:

Discard erroneous received code word. Retransmit until packet correctly received or until pre-set

number of retransmissions is achieved. Small buffer size required but an inefficient scheme.

Type II hybrid ARQ: Store erroneous received code word. Optimally combine with retransmitted code word. Exploit incremental redundancy concept

Effective Code rate is gradually lowered until packet is decoded correctly.

System adapts to varying channel conditions. Larger buffer size required than Type-I but is a very efficient

scheme.

Turbo Codes Key features:

Concatenated Convolutional Codes. PCCC: Parallel Concatenated Convolutional Codes. SCCC: Serial Concatenated Convolutional Codes.

Nonuniform interleaving. Recursive systematic encoding.

RSC: Recursive Systematic Convolutional Codes. For PCCC both encoders are RSC. For SCCC at least the inner encoder is RSC.

Iterative decoding algorithm. MAP/APP based. Log-MAP: In logarithmic domain.

PCCC’s Features of parallel concatenated convolutional

codes (PCCC’s): Both encoders are RSC. Performance close to capacity limit for BER down to

about 10-5 or 10-6 (i.e. in the cliff region). BER flooring effect at high SNR.

RSCEncoder #1

RSCEncoder #2

NonuniformInterleaver

Input

ParityOutput

Systematic Outputix

SCCC’s Features of serially concatenated convolutional codes

(SCCC’s): Inner encoder must be recursive. Outer encoder can be recursive or nonrecursive. Performance not as good as PCCC’s at low SNR. However, performance is better than PCCC’s at high SNR because

the BER floor is much lower.

Outer Encoder

Inner Encoder

NonuniformInterleaver

Input Output

Turbo Codes and Hybrid ARQ

Turbo codes have been applied to hybrid ARQ. Narayanan and Stüber

Interleave the input to the turbo encoder with a different interleaving function for each retransmission.

Use log-likelihood ratios from last transmission. Rowitch and Milstein.

Rate-compatible punctured turbo (RCPT) codes. Buckley and Wicker

Use cross-entropy instead of a CRC to detect errors. Error detection threshold adaptively determined with a

neural network. All the above use PCCC’s.

Wu & Valenti (ICC 2000) had PCCC/SCCC approach.

Turbo Coding-ARQ System Model

ChannelInter-leaver

Feedback for

Type II Hybrid ARQ

ûk

yk

ak

nk

rk

Puncture& Buffer

TurboEncoder

BPSKModul-

ator

ChannelDe-Inter-

leaver

ChannelEstimator

TurboDecoder

uk

ErrorDetection

ACK

NACK

Coding-ARQ process chartStart with

Maximum Code Rate

Transmit code bits not previously sent

PCCC / SCCCError correction

Detect Errors after correctionErrors

Still?

NO

YESLowestRate?YES

NO

Reduce code rate to next lower rate

Go on to Next Data Frame

Simulation Parameters Input frame size N = 1024. Channel types:

AWGN Fully-interleaved Rayleigh Fading

Turbo Channel Code Parameters: PCCC and SCCC

Each comprised of two identical RSC codes. Constraint Length K = 5. Generator Polynomials in octal:

Feedback = 35. Feedforward = 23.

Encoders terminated with a 4 bit tail. Decoder uses max-log-MAP algorithm.

Simulation Parameters contd.

Puncturing: Period = 8. For PCCC, code rates range from 4/5 to 1/3. For SCCC

Outer code rate = 2/3 (Puncturing parity bits alternatively).

Inner code rate ranges from 1 to 1/2. Overall code rate ranges from 2/3 to 1/3.

Channel Interleaver: Spread interleaver with S=18. Interleaver Sizes:

PCCC – 1024. SCCC – 1544.

Simulation Assumptions Perfect channel estimates. Perfect error detection after turbo

decoding. Noise free feedback channel from

receiver to transmitter for ACK/NACK. No transmission delays.

Stop and wait performs just as well as selective repeat protocol.

SCCC puncturing patterns not optimized.

BER comparison: PCCC in AWGN Channel (N=1024)

-4 -2 0 2 4 6 810

-8

10-7

10-6

10-5

10-4

10-3

10-2

10-1

100

Es/No in dB

BE

R

r=4/5 r=8/11r=2/3 r=4/7 r=1/2 r=4/9 r=2/5 r=1/3

BER comparison: PCCC in Fading Channel (N=1024)

-5 0 5 1010

-8

10-7

10-6

10-5

10-4

10-3

10-2

10-1

100

Es/No in dB

BE

Rr=4/5 r=8/11r=2/3 r=4/7 r=1/2 r=4/9 r=2/5 r=1/3

BER comparison: SCCC in AWGN Channel (N=1024)

-5 0 5 1010

-8

10-7

10-6

10-5

10-4

10-3

10-2

10-1

100

Es/No in dB

BE

R

r=2/3 r=16/27r=8/15 r=16/33r=4/9 r=16/39r=8/21 r=16/45r=1/3

BER comparison: PCCC in Fading Channel (N=1024)

-5 0 5 1010

-7

10-6

10-5

10-4

10-3

10-2

10-1

100

Es/No in dB

BE

R

r=2/3 r=16/27r=8/15 r=16/33r=4/9 r=16/39r=8/21 r=16/45r=1/3

Throughput Efficiency Defined as expectation of the code rate as a

function of frame error rate (FER) at a particular value of signal to noise ratio (Es / No).

Mathematically defined as

is a particular code rate and is the probability mass function of the rate.

T E r FERE

Navs

o

FHG

IKJ

LNM

OQP

RS|T|UV|W|

r P r rir

i

i

[ ]

ri P r ri[ ]

Throughput Efficiency contd.

Probability that the system is transmitting at a particular rate is the product of:

Probability of frame errors at higher rates and Probability of success at current rate.

Probability mass function is given by:

P r r FER rE

NFER r

E

Ni is

oj

s

or rj i

[ ] , , FHG

IKJ

LNM

OQP

FHG

IKJ

LNMM

OQPP

1

Throughput comparison

-5 0 5 100

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Es/No in dB

Thr

ougp

ut e

ffic

ien

cy

PCCCSCCC

-5 0 5 100

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Es/No in dB

Thr

ougp

ut e

ffic

ienc

y

PCCCSCCC

AWGN Channel Fading Channel

Discussion In each case, the throughput of PCCC is

better than SCCC. Why?

For hybrid-ARQ, it’s the location of the “cliff” that matters, not the height of the floor.

Thus, hybrid ARQ is not able to exploit the benefits of SCCC.

However, the puncturing patterns were not optimized for SCCC.

Systems that combine PCCC/SCCC appear to be promising.

Summary Conclusion

Like PCCCs, SCCCs can be used as part of a type II hybrid FEC/ARQ scheme.

SCCCs offer lower BER floors than PCCCs. But, this comes at the cost of the “cliff” occurring at higher SNR. Initial results show that since the cliff region is the predominant

contributor towards throughput efficiency rather than the height of the BER floor, SCCCs have lower throughput efficiency than PCCCs.

Future Work Optimize puncturing patterns for SCCC to reduce the gap

between the throughput efficiencies of PCCC and SCCC. Exploit the fact that a PCCC code is a particular type of SCCC

code. Promising results could be achieved by using hybrid PCCC/SCCC

codes.

Puncturing Patterns

PCCC

Overall Rate 4/5 8/11 2/3 4/7 1/2 4/9 2/5 1/3

Puncturing Patterns

377 020 020

377 024 020

377 024 024

377 224 224

377 264 264

377 265 274

377 275 374

377 377 377

Table 1: Octal puncturing patterns for PCCC based systems with code polynomial g = (35,23), frame size N = 1024 and puncturing period P = 8.

Puncturing Patterns

Table 2: Octal puncturing patterns for SCCC based systems with code polynomial g = (35,23), frame size N = 1024 and puncturing period P = 8.

SCCC

Encoder Outer Inner Rates 2/3 1 8/9 4/5 8/11 2/3 8/13 4/7 8/15 1/2 Puncturing Patterns

377 252

377 0

377 200

377 202

377 242

377 252

377 352

377 356

377 357

377 377