Joint Optimization of Protograph LDPC Code Pair for Joint Source and Channel Coding

Double protograph low-density parity-check code has been shown to be a good solution for joint source-channel coding. Moreover, the source code and channel code (as one code pair) can be jointly optimized to achieve a good bit error rate (BER) performance. In this paper, first, an optimal design criterion of this code pair based on an extended curve-fitting algorithm is proposed. Second, a joint optimization procedure which searches for both the optimal decoding threshold and the optimal code pair is presented. In addition, for short-to-moderate-length codewords, the finite-length effect cannot be ignored and the procedure has to be modified with a new notion named length-N decoding threshold. The protograph extrinsic information transfer analysis and the BER simulation have shown that our optimized code pairs acquire lower decoding thresholds than conventional code pairs. Moreover, the optimized code pairs with short-to-moderate-length codewords can mitigate the finite-length effect and obtain low length-N decoding thresholds.