In this letter, we propose two modifications to belief propagation (BP) decoding algorithm. The modifications are based on reducing the reliability of messages throughout the iteration process, and are particularly effective for short low-density parity-check codes, where the existence of cycles makes the original BP algorithm perform suboptimal. The proposed algorithms, referred to as "normalized BP" and "offset BP," reduce the absolute value of the outgoing log-likelihood ratio messages at variable nodes by using a multiplicative factor and an additive factor, respectively. Simulation results show that both algorithms perform more or less the same, and both outperform BP in error performance.

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IEEE Communications Letters
Department of Systems and Computer Engineering

Yazdani, M.R. (Mohammad R.), Hemati, S. (Saied), & Banihashemi, A. (2004). Improving Belief Propagation on Graphs with Cycles. IEEE Communications Letters, 8(1), 57–59. doi:10.1109/LCOMM.2003.822499