Linear-encodable rate-compatible QC-LDPC codes with low error floor

A class of rate-compatible (RC) quasi-cycle low-density parity-check (QC-LDPC) codes that have linear encodable complexity and low error floor is presented. To ensure linear encoding complexity, a lower triangular (LT) form for the parity part of the mother parity-check matrix is designed. By the designed LT form, a recursive encoding strategy is proposed. This encoding strategy can achieve linear encodable complexity, which is completely proportional to the code length. To guarantee good performances for a wide range of code rates, a layered short-cycle optimization algorithm is designed to obtain good girth distribution, and a layered density evolution algorithm is used to optimize degree distributions of each code rate. Then, a class of RC QC-LDPC codes can be obtained by both extension and puncturing from the optimized QC-LDPC mother code with rate 1/2. Simulation results show that no error floor is exhibited for the proposed RC QC-LDPC codes at FER=10^-5. The practical performance at BER=10^-6 shows a gap of about 1.477 dB to the Shannon limit.