Publication

Belief Propagation Decoding for Short Codes on Structured Sparse Parity-Check Matrices

2025

Abstract

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.

Official source

https://infoscience.epfl.ch/entities/publication/23db317b-0e62-48a8-b9ae-f8f0789e1309

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2025

Abstract

Official source

https://infoscience.epfl.ch/entities/publication/23db317b-0e62-48a8-b9ae-f8f0789e1309

About this result

Related concepts (16)

Low-density parity-check code

In information theory, a low-density parity-check (LDPC) code is a linear error correcting code, a method of transmitting a message over a noisy transmission channel. An LDPC code is constructed using a sparse Tanner graph (subclass of the bipartite graph). LDPC codes are , which means that practical constructions exist that allow the noise threshold to be set very close to the theoretical maximum (the Shannon limit) for a symmetric memoryless channel.

Belief propagation

Belief propagation, also known as sum–product message passing, is a message-passing algorithm for performing inference on graphical models, such as Bayesian networks and Markov random fields. It calculates the marginal distribution for each unobserved node (or variable), conditional on any observed nodes (or variables). Belief propagation is commonly used in artificial intelligence and information theory, and has demonstrated empirical success in numerous applications, including low-density parity-check codes, turbo codes, free energy approximation, and satisfiability.

Error correction code

In computing, telecommunication, information theory, and coding theory, forward error correction (FEC) or channel coding is a technique used for controlling errors in data transmission over unreliable or noisy communication channels. The central idea is that the sender encodes the message in a redundant way, most often by using an error correction code or error correcting code (ECC). The redundancy allows the receiver not only to detect errors that may occur anywhere in the message, but often to correct a limited number of errors.

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