An Expurgating-Based Method for Constructing Multi-Rate Non-Binary Quasi-Cyclic LDPC Codes

This letter presents a new method for constructing the multi-rate non-binary quasi-cyclic low-density parity-check codes by expurgating a high-rate mother code. A matrix-theoretic approach is applied to design the parity-check matrices of the proposed codes. The resulting codes possess a quasi-cyclic structure, which is desirable for hardware implementations of the encoder and decoder. The codes can also be encoded directly with parity-check matrices due to the block dual-diagonal structure. Simulation results show that the codes can achieve good performance within a wide range of code rates both in the waterfall region and in the error-floor region.