LDPC codes for soft decode-and-forward in half-duplex relay channels

We investigate the use of rate-compatible lowdensity parity-check (RC-LDPC) codes as part of a soft decodeand- forward (SDF) protocol over the half-duplex relay channel. We propose a new methodology to design the degree distribution of the RC-LDPC codes with a lower triangular parity-check matrix, enabling the additional parity bits to be linearly and systematically encoded at the relay. Our proposed methodology introduces the concept of a K-layer doping matrix to represent the structure of a lower triangular parity-check matrix. As a result of our methodology, the asymptotic performance of RC-LDPC codes can be analyzed and predicted using the multi-edge-type density evolution. Then, we derive the soft-re-encoding of the additional parity symbols at the relay using our designed RCLDPC codes. Moreover, we propose a novel method, which we refer to as soft fading, to compute the log-likelihood ratio (LLR) of the received signal at the destination for the SDF protocol. We demonstrate that our proposed soft fading method outperforms the best known method in the literature by up to 0.7 dB in terms of BER performance. Finally, we derive a new bound for the power multiplication factor at the relay, which limits the amount of soft-errors forwarded by the relay to the destination. The BER performance of our new RC-LDPC codes improves significantly once the power multiplication factor at the relay satisfies this bound.