A Complex Network Approach to Designing Bernoulli Parity-Check Codes

In this paper, a complex network approach is presented to design the Bernoulli parity-check (BPC) codes with enhanced belief propagation (BP) decoding performance. By investigating the degree correlation between variable and check nodes, we propose the normal graph configuration model (NGCM) to adjust the assortativity coefficient of normal graphs, and investigate the impact of disassortativity on decoding performances. Numerical results demonstrate that, optimizing the disassortativity of normal graphs can significantly enhance the BP decoding performance in both the waterfall and error floor regions. This improvement leads to lower bit-error-rate (BER), frame-error-rate (FER), and decoding complexity. Our study has significant practical and theoretical value, especially for the interdisciplinary research of complex network and coding theory.