Design of Binary LDPC Codes With Parallel Vector Message Passing

Many studies were carried out for the construction of low density parity-check (LDPC) codes. They usually focused on introducing the construction methods for good LDPC codes instead of a general method for code optimization. This paper proposes a method with high versatility, called the parallel vector message passing-based edge exchange (PMPE), for optimizing a type of graph-based LDPC codes, without changing the code parameters of mother codes, such as the code length, code rate, and degree distribution. With the approximately nearest code-words searching approach, we find the optimization method can increase the Hamming distance of the LDPC codes. For the quasi-cyclic (QC) LDPC codes, an optimization method, called the parallel vector message passing oriented-to the QC-LDPC codes (QC-PMP), is further suggested, with which the quasi-cyclic characteristics of QC-LDPC codes can remain unchanged in the optimization. To evaluate the performance of the parity-check matrix corresponding to a Tanner graph, a very simple metric, the cycles metric, is introduced to work with the proposed PMPE and QC-PMP algorithms. The experimental results show that the performance of the LDPC codes optimized with the proposed PMPE can be improved significantly at low BER range compared with the mother codes of the random codes, including the regular MacKay code of rate 0.5 and the regular PEG code of rate 0.9. For the case of the regular and irregular QC-LDPC codes with different code lengths and code rates, the optimized LDPC codes with the proposed QC-PMP algorithm significantly outperform the mother codes.