Proximal Decoding for LDPC Codes

Abstract

In this paper, we present an overview of the proximal decoding for LDPC codes proposed by Wadayama and Takabe. The related paper (Wadayama and Takabe, IEICE EA, no.3, pp.359–367, 2023) was awarded the 2022 IEICE Paper Award. The proximal gradient method, widely used in signal processing for solving inverse problems such as sparse signal reconstruction, has been applied to LDPC decoding problems for the first time in this paper. The core idea of the proposed method is to perform approximate maximum a posteriori probability (MAP) decoding by applying the proximal gradient method to iteratively minimize an objective function consisting of the negative log-likelihood corresponding to the communication channel and the code potential energy function corresponding to the code. By appropriately modifying the negative log-likelihood function, we can apply the proposed decoding method to a wide range of communication channels. Computational experiments have shown that the proposed decoding method provides a significant improvement in decoding performance compared with the existing de facto standard method (a combination of MMSE signal detection and belief propagation decoding) for LDPC-coded MIMO communication channels, which are important in modern wireless communication systems. The effectiveness of the proposed method has also been experimentally demonstrated for communication channels with colored Gaussian noise and nonlinearities, for which the construction of efficient decoding methods is challenging. Furthermore, the proposed method can be implemented using tensor computations and has an iterative structure suitable for deep-learning-specific hardware such as general purpose graphics processing units (GPGPUs) and AI accelerators. It also has high compatibility with machine learning techniques such as deep unfolding, and future research on practical applications is expected.