An ARQ Technique Using Related Parallel and Serial

Concatenated Convolutional Codes

Yufei Wuformerly with:

Mobile and Portable Radio Research GroupVirginia Tech

now with:Motorola

Schaumburg IL

Matthew C. Valenti (presenter)Dept. of Comp. Sci. & Elect. Eng.

West Virginia University

Overview FEC, ARQ, and hybrid ARQ Concatenated Convolutional Codes

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

concatenations. Brief survey of hybrid ARQ techniques

using turbo codes. Relationships between PCCC and SCCC’s

How to encode a PCCC using a SCCC encoder. A new hybrid ARQ technique that uses

related SCCC and PCCC’s.

FEC and ARQ FEC

Forward Error Correction. Channel code used to 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.

Hybrid ARQ Hybrid ARQ 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. Combining strategies:

Type I hybrid ARQ: Discard previously received code word.

Type II hybrid ARQ: Keep previously received code word. Combine with received retransmitted code word. Variations: Code combining and diversity combining.

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. BER flooring effect at high SNR.

RSCEncoder #1

RSCEncoder #2

NonuniformInterleaver

Input

ParityOutput

Systematic Output

ix

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

InputOutput

Turbo Codes and Hybrid ARQ

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

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.

None propose using SCCC’s.

A General Purpose Encoder

It is possible to generate related PCCC and SCCC’s using a single encoder.

Outputs constitute a SCCC.

Outputs constitute a PCCC.

RSCEncoder

#1

s

p

RSCEncoder

#2

uu

p1~p1

~u ~ ~u p 1

~ ~u p 1

p p2s

2p

interleavers

~ ~u p ps 1 2

~ ~u p p ps p 1 2 2

We may express the general encoder as a SCCC encoder.

eq is an equivalent interleaver. RSC 1’s systematic output must be mapped

to the first half of the input into RSC 2. RSC 1’s parity output must be mapped to

the last half of the input into RSC 2.

Equivalent SCCC Encoder

RSCEncoder

#1eq

RSCEncoder

#2

u ~ ~u p 1

equivalentinterleaver

~ ~u p p ps p 1 2 2u p 1

Equivalent PCCC Encoder If is not transmitted, then the

encoder can be expressed as a PCCC encoder

p2p

RSCEncoder

#1

sRSC

Encoder #2

u s

p

u

p1~p1

~u~ ~u p ps 1 2

~up2

s

New Hybrid ARQ Technique

1. Encode data with error detection code.2. Then encode with the generalized encoder.3. Transmit the PCCC information

a. Store in a buffer4. Decode received PCCC code word.5. Check decoded PCCC code word for errors.

a. If no errors, then stop.b. Otherwise, send NACK to the transmitter.

6. Transmit7. Combine received with received to

create a received SCCC code word. Decode.8. Check decoded SCCC code word for errors.

a. If no errors then stop.b. Otherwise discard information and go back to (1).

~ ~u p ps 1 2

p2p

p2p

p2p

~ ~u p ps 1 2

Simulation Parameters 16 bit error detecting CRC code. 1,024 bit input into FEC encoder.

Includes the 16 parity bits. S-random or “spread” interleaver design. Both RSC 1 and RSC 2 are identical constraint

length 4 RSC encoders (rate ½). Both encoders are terminated with a 3-bit tail. Decoder uses 10 iterations of log-MAP. AWGN channel and BPSK/QPSK modulation. Compared with:

Conventional PCCC code Type-I hybrid ARQ PCCC with maximum of 1

retransmission.

-5 -4.5 -410

-6

10-5

10-4

10-3

10-2

10-1

100

Es /N0 (dB)

BE

R

PS-ARQPC-ARQPC-FEC

BER Comparison

-5 -4.5 -410

-5

10-4

10-3

10-2

10-1

100

E s /N0 (dB)

FER

PS-ARQPC-ARQPC-FEC

FER Comparison

-5 -4.5 -40

0.05

0.1

0.15

0.2

0.25

0.3

0.35

Es /N0 (dB)

Thro

ughp

ut E

ffici

ency

PS-ARQPC-ARQPC-FEC

Throughput Efficiency

-5 -4.5 -410

0

101

102

103

104

Es /N0 (dB)

Com

plex

ity L

oad

PS-ARQPC-ARQPC-FEC

Complexity Load

Summary Conclusion:

An SCCC encoder can be used to encode a PCCC. This result was used to develop a new hybrid

ARQ strategy. The proposed technique offers superior

performance over ARQ techniques derived solely from PCCC’s.

Future work: Comparison with other ARQ techniques.

Narayanan and Stuber Rowitch and Milstein

Use of other encoders and puncturing schemes. Determine what to do if there are residual errors.