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IEEE Open Journal of the Communications Society

Largely Constrained Noise-guessing Decoding of Short LDPC codes

Sahar Allahkaram, Francisco A. Monteiro, Joao Ribeiro, Carlos Salema

Published Jan 1, 2026• 0 citations
Publisher

Abstract

Pre-publication version of paper to be published in the IEEE Open Journal of the Communications Society with DOI 10.1109/OJCOMS.2026.3725587.
DOI
10.1109/ojcoms.2026.3725587

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Low-density parity-check (LDPC) codes have been widely used in practice due to their excellent error correction capabilities. However, the error correction performance of traditional decoding algorithms for LDPC codes is limited under short block lengths. To address this problem, this paper proposes an effective scheme that contains two stages for decoding short LDPC codes. In the first stage, the traditional belief propagation (BP) iterative algorithm is used to decode an LDPC code. The decoding process terminates if a codeword is obtained in this stage. Otherwise, the second stage decoding is invoked, in which the ordered reliability bits guessing random additive noise decoding (ORBGRAND) algorithm is applied. The accumulated log-likelihood ratios in the first stage are used to order the test error patterns in the ORBGRAND algorithm. Simulation results indicate that the proposed BP-ORBGRAND scheme can outperform the traditional BP iterative algorithm with relatively low additional complexity. Compared with the decoding scheme that concatenates the BP algorithm and the order statistics decoding (OSD) algorithm, the proposed decoding scheme has similar performance and the operations involved can be efficiently implemented in the hardware platform. All these indicate that the proposed scheme is desirable for practical purposes.
LDPC codes are deployed in many modern wired and wireless communication systems. While fully-parallel LDPC decoders are very efficient, they typically suffer from routing complexity. The Split-Row method effectively reduces this complexity with a minor performance loss. This paper shows the importance of symmetry in Split-Row architectures and proves that the implementation of Split-Row decoders based on new proposed smart column-permuted versions of parity check matrices leads to a better error performance as well as a more efficient hardware. Moreover, in order to achieve optimized column-permuted parity check matrices, a heuristic approach is proposed. This method is then generalized to support QC-LDPC codes. Applied to IEEE 802.3an (10GBASE-T Ethernet) and IEEE 802.11n (Wi-Fi) LDPC decoders, the new technique improves the error performance, while leading to almost 3× speed-up in the synthesis compile time and about 10% reduction in the critical path.