Belief Propagation Decoding for Short Codes on Structured Sparse Parity-Check Matrices
Yifei Shen, Zongyao Li, Emmanuel Boutillon, Wenqing Song, Yuqing Ren, Chuan Zhang, Xiaohu You, Andreas Peter Burg · 2025
As successfully adopted in standard long code scenarios, belief propagation (BP) decoding has been considered a promising universal decoding candidate for next-generation wireless communications. However, when applied to short codes, BP decoding suffers from poor error correction performance due to harmful cycle structures in the Tanner graph. In this paper, we address this issue by designing a structured, sparse parity-check matrix (ssPCM) framework, composed of multiple cycle-free parity-check row blocks (PCRBs). The resulting ssPCMs feature regular row weights and perform better than the state-of-theart 4 -cycle-free row redundant PCMs across Bose-Chaudhuri-Hocquenghem (BCH) codes of length 63.