Towards optimal edge weight distribution and construction of field-compatible low-density parity-check codes over GF(q)

Abstract

Non-binary low-density parity-check (NB-LDPC) codes can be directly constructed by using algebraic methods, or indirectly constructed by mapping well-designed binary parity-check matrices to non-binary parity-check matrices. Given the Tanner graph (TG) of a NB-LDPC code, the selection of edge weights in the TG significantly affects the performance of the NB-LDPC code. The authors introduce an edge weight distribution (EWD) parameter for the TG of NB-LDPC codes. By utilising particle swarm optimisation (PSO), the EWD is optimised and it has been demonstrated that the optimal EWD approaches a two-element distribution for large field size and high average variable-node degree. With the optimised EWD, the authors construct a class of field-compatible LDPC (FC-LDPC) codes over GF(q) whose parity-check matrices only include elements 0, 1 and 2, and can be encoded and decoded over different field sizes. The simulations demonstrate that the performance of the proposed FC-LDPC codes improves monotonically with increasing field size, and significantly outperforms that of the corresponding algebraic NB-LDPC codes or NB-LDPC codes generated with uniform distribution of non-zero elements over GF(q).