An algebraic approach to design low rate low density parity check code
Zhe Zhang, Liang Zhou, Junyi Du, Shenglong Peng · 2017
In this paper, we propose an algebraic approach to design extremely low rate low-density parity-check (LDPC) codes by employing the primitive polynomials. We first investigate the requirements for the polynomials to construct 4-cycle free LDPC codes and then propose an algebraic approach to design the parity check matrix. To achieve a better decoding performance in the extremely low rate region, we propose an extension method to construct more check nodes and virtual variable nodes to obtain more constraints. Our designed LDPC codes have simple encoding and simple decoding features. Simulation results show that our proposed rate-0.03 LDPC code can achieve 2.2 dB gain, compared to the LDPC code designed by the progressive edge growth algorithm with the optimized edge degree distributions described in [7].