An LDPCC decoding algorithm based on Bowman-Levin approximation --Comparison with BP and CCCP--

TL;DR

This paper introduces the Bowman-Levin (BL) approximation algorithm for decoding low-density parity check codes, which outperforms belief propagation and CCCP in certain scenarios by leveraging a novel approach to Bethe free energy optimization.

Contribution

The paper presents a new BL approximation algorithm that modifies variable roles in Bethe free energy minimization, improving decoding performance over existing methods.

Findings

BL algorithm shows better average performance than BP and CCCP in decoding LDPCC.

BL algorithm successfully applies to decoding problems previously tackled by BP or CCCP.

The approach demonstrates potential for broader application in information processing tasks.

Abstract

Belief propagation (BP) and the concave convex procedure (CCCP) are both methods that utilize the Bethe free energy as a cost function and solve information processing tasks. We have developed a new algorithm that also uses the Bethe free energy, but changes the roles of the master variables and the slave variables. This is called the Bowman-Levin (BL) approximation in the domain of statistical physics. When we applied the BL algorithm to decode the Gallager ensemble of short-length regular low-density parity check codes (LDPCC) over an additive white Gaussian noise (AWGN) channel, its average performance was somewhat better than that of either BP or CCCP. This implies that the BL algorithm can also be successfully applied to other problems to which BP or CCCP has already been applied.