A novel approach for construction of rate-compatible low-density parity-check codes

In this paper, we construct rate compatible low density parity-check (RC-LDPC) codes from a new perspective. In traditional methods, the columns of parity-check matrix, each of which corresponds to a bit of a codeword, are deleted or added to obtain codes at various rates. Different from them, only the rows of parity-check matrix are operated in our method. Since the number of columns remains unchanged, the block lengths of RC-LDPC codes across a range of rates are always invariable. In our novel construction method, new rows are appended to form the new matrices corresponding to lower-rate codes while some selected rows are eliminated to obtain higher-rate codes. We employ a modified progressive edge growth (PEG) construction with zigzag pattern to actualize linear-time encoding. Before implementing this modified PEG algorithm, a constrained density evolution algorithm is applied to optimize the degree distributions of the mother code. To those columns in the left portion of a mother parity-check matrix which correspond to information bits of a codeword, specified weights are allocated as the condition of the posterior PEG algorithm. We also demonstrate that a single decoder can be used over the entire range of rates. Moreover, the decoder always operates at a high code rate so that energy consumption and circuit size can be reduced. In addition, based on our construction of RC-LDPC codes, a novel effective scheme for hybrid ARQ protocols has been proposed as well.