1. Matthew C. Valenti (presenter)
Hybrid ARQ using Serial Concatenated Convolutional Codes over Fading Channels
Naveen Chandran
Graduate Research Assistant
Lane Dept. of Comp. Sci. & Elect. Engg.
West Virginia University
Matthew C. Valenti (presenter)
Assistant Professor

2. 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.

3. 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.

4. 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.

5. 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.

6. 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.

7. 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.
Input
RSC
Encoder #1
Systematic Output
Parity
Output
RSC
Encoder #2
Nonuniform
Interleaver

8. 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.
Input
Output
Outer
Encoder
Nonuniform
Interleaver
Inner
Encoder

9. 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.

10. Turbo Coding-ARQ System Modeluk
Turbo
Encoder
Puncture
& Buffer
Channel
Inter-
leaver
BPSK
Modul-
ator yk ak
ACK
NACK
Feedback for
Type II Hybrid ARQ nk
Channel
De-Inter-
leaver
Error
Detection
Turbo
Decoder rk ûk
Channel
Estimator

11. Coding-ARQ process chart
Start with Maximum Code Rate
Transmit code bits not previously sent
PCCC / SCCC
Error correction
Reduce code rate to next lower rate NO
Lowest
Rate?
YES
Errors
Still?
Detect Errors
after correction
Go on to Next Data Frame
YES NO

12. 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.

13. 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.

14. 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.

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

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

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

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

19. 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.

20. 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:

21. Throughput comparison
AWGN Channel
Fading Channel

22. 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.

23. Summary Conclusion Future Work
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.

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

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