Practical relay code design based on protograph codes

The low-density parity-check (LDPC) code design for three-terminal (namely, source, relay, and destination) relay network while considering decode-and-forward protocol is studied. Numerous works have been done on LDPC relay code design with parity bits forwarding approach, where additional parity bits are generated at the relay and forwarded to the destination. Most of the previous works assume that the forwarded parity bits are received perfectly at the destination and hence ignore the impact of relay-destination channel. This assumption is unrealistic in practical/finite-length codeword scenario. In this study, a protograph based LDPC code design is proposed while lifting the above unrealistic assumption. A Gaussian approximated density evolution is presented for the proposed scheme, which considers that the overall codeword experiences source-destination and relay-destination channels. For various designed codes with different rates, the authors show that the asymptotic thresholds of the designed codes are very close to the corresponding capacity bounds. Asymptotically, our designed code gives similar decoding threshold compared to the existing optimised irregular LDPC codes, while protograph codes are simpler to optimise and encode than the irregular LDPC codes. More importantly, proposed code performs better than the existing LDPC-based relay codes for finite-length scenarios.