Design of Length-Compatible Low-Density Parity-Check Codes

Length-compatible low-density parity-check (LC-LDPC) codes are a class of low-density parity-check (LDPC) codes which can support a wide range of lengths for a given rate. They may be obtained by applying shortening and puncturing schemes to good LDPC codes. However, this conventional approach does not always guarantee them to have a good performance because their degree distributions may be wildly varied. In this paper we propose a novel algorithm to generate a mother code for LC-LDPC codes of a given rate such that their degree distributions are almost the same as the degree distribution of the mother code. Numerical results show that LC-LDPC codes constructed by our approach perform much better than those by the conventional approach.