Improved soft-output M-algorithm for differential encoded LDPC coded systems with multiple-symbol differential detection

In this paper, we propose an improved soft-output M-algorithm (ISOMA) and use it to reduce the computational complexity of differential encoded LDPC (DE-LDPC) coded systems with multiple-symbol differential detection (MSDD). The proposed ISOMA combines the features of iterative tree search detection based on M-algorithm (ITS-MA) and soft-output M-algorithm (SOMA) approaches, which can guarantee that the log-likelihood ratio (LLR) of each coded bit can be computed with high reliability. Simulation results show that the computational complexity of the MSDD soft-input soft-output demodulator (SISOD) as well as the iterative decoding complexity of DE-LDPC coded systems with MSDD can be greatly reduced by the proposed ISOMA. Compared with the existing ITS-MA and SOMA, the proposed ISOMA has better performance in terms of the BER performance and the ability of reducing the decoding complexity of DE-LDPC systems with MSDD. In addition, it is shown that the approach of the ISOMA using a proper selected scaling factor (SF) in the computation of the extrinsic LLRs can be used to further improve the performance of the ISOMA.