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

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

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 uk 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

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

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)

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

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

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

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.

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:

Throughput comparison 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 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.

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

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