An ARQ Technique Using Related Parallel and Serial Concatenated Convolutional Codes Yufei Wu formerly with: Mobile and Portable Radio Research Group Virginia 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 or BER flooring effect at high SNR. RSC Encoder #1 RSC Encoder #2 Nonuniform Interleaver Input Parity Output Systematic Output

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 Nonuniform Interleaver Input Output

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. RSC Encoder #1 RSC Encoder #2 interleavers

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 RSC Encoder #1 RSC Encoder #2 equivalent interleaver

Equivalent PCCC Encoder If is not transmitted, then the encoder can be expressed as a PCCC encoder RSC Encoder #1 RSC Encoder #2

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 buffer 4.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.Transmit 7.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).

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.

E s /N 0 (dB) BER PS-ARQ PC-ARQ PC-FEC BER Comparison

E s /N 0 (dB) FER PS-ARQ PC-ARQ PC-FEC FER Comparison

E s /N 0 (dB) Throughput Efficiency PS-ARQ PC-ARQ PC-FEC Throughput Efficiency

E s /N 0 (dB) Complexity Load PS-ARQ PC-ARQ PC-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.