Publication

HDPC Codes with LDPC Matrices: Construction Based on Social Golfer Problem

2026

Abstract

In contrast to conventional low-density parity-check (LDPC) code construction, we propose to construct a sparse decoding matrix with auxiliary variable nodes (AVNs) and then derive the corresponding high-density parity-check (HDPC) code for encoding. To leverage the sparsity gain of AVNs while controlling AVN-induced harmful substructures, we adopt a parity-check row block (PCRB) structure and show that arranging PCRBs to obtain a 4-cycle-free decoding matrix forms a class of social golfer problems (SGPs). Focusing on an explicit affine-plane-based SGP solution, we construct a family of AVN-aided affine plane (AAP) codes. For the same blocklength and minimum distance, AAP codes achieve equal or greater dimension than Reed-Muller codes and exhibit low error floors under iterative decoding, which extend finite-geometry LDPC constructions to additional code families with 4-cycle-free decoding matrices.

Official source

https://infoscience.epfl.ch/entities/publication/4f82a68f-e27b-4ac9-9198-6c7035662ded

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2026

Abstract

Official source

https://infoscience.epfl.ch/entities/publication/4f82a68f-e27b-4ac9-9198-6c7035662ded

About this result

Related concepts (32)

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.

Concatenated error correction code

In coding theory, concatenated codes form a class of error-correcting codes that are derived by combining an inner code and an outer code. They were conceived in 1966 by Dave Forney as a solution to the problem of finding a code that has both exponentially decreasing error probability with increasing block length and polynomial-time decoding complexity. Concatenated codes became widely used in space communications in the 1970s.

Linear code

In coding theory, a linear code is an error-correcting code for which any linear combination of codewords is also a codeword. Linear codes are traditionally partitioned into block codes and convolutional codes, although turbo codes can be seen as a hybrid of these two types. Linear codes allow for more efficient encoding and decoding algorithms than other codes (cf. syndrome decoding). Linear codes are used in forward error correction and are applied in methods for transmitting symbols (e.g.

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HDPC Codes with LDPC Matrices: Construction Based on Social Golfer Problem

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