Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:1805.05270 · European Conference on Optical Communication

Iterative Bounded Distance Decoding of Product Codes with Scaled Reliability

Alireza Sheikh, Alexandre Graell i Amat, Gianluigi Liva

Published Sep 1, 2018• 24 citations
arXivHTMLPDF

Abstract

We propose a modified iterative bounded distance decoding of product codes. The proposed algorithm is based on exchanging hard messages iteratively and exploiting channel reliabilities to make hard decisions at each iteration. Performance improvements up to 0.26 dB are achieved.
DOI
10.1109/ecoc.2018.8535240

Related papers

Binary Message Passing Decoding of Product-Like Codes

Alireza Sheikh, Alexandre Graell i Amat, Gianluigi Liva

We propose a novel binary message passing decoding algorithm for product-like codes based on bounded distance decoding (BDD) of the component codes. The algorithm, dubbed iterative BDD with scaled reliability (iBDD-SR), exploits the channel reliabilities and is therefore soft in nature. However, the messages exchanged by the component decoders are binary (hard) messages, which significantly reduces the decoder data flow. The exchanged binary messages are obtained by combining the channel reliability with the BDD decoder output reliabilities, properly conveyed by a scaling factor applied to the BDD decisions. We perform a density evolution analysis for generalized low-density parity-check (GLDPC) code ensembles and spatially coupled GLDPC code ensembles, from which the scaling factors of the iBDD-SR for product and staircase codes, respectively, can be obtained. For the white additive Gaussian noise channel, we show performance gains up to 0.29 dB and 0.31 dB for product and staircase codes compared to conventional iterative BDD (iBDD) with the same decoder data flow. Furthermore, we show that iBDD-SR approaches the performance of ideal iBDD that prevents miscorrections.

arXiv:1902.03575•IEEE Transactions on Communications•Sep 11, 2019•49 citations

Iterative Bounded Distance Decoding With 2-Bit Reliability Marker For Product-Like Codes

Xiaowei Wu, Min Qiu, 展月英 +1 more

We propose a novel soft-aided hard-decision decoding scheme for product codes based on two-bit quantized reliability markers. In particular, one bit is used for a two-level tolerance miscorrection check to validate the bounded distance decoding (BDD) result, while the other identifies bits to be randomly flipped upon BDD failure and miscorrection. List decoding is incorporated to further facilitate the error performance. Density evolution is performed for the design of the quantization thresholds. Compared to iterative BDD, the proposed scheme requires only moderate increases in memory and computational overhead. Simulation results verify that our scheme outperforms several unquantized soft-aided decoders, while maintaining small memory costs and low BDD attempts.

arXiv:2610.21279•Oct 15, 2026•0 citations

Four-Level Quantized Soft Information Aided Hard-Decision Decoder for Product-Like Codes

Xiaowei Wu, Min Qiu, Yueying Zhan +1 more

We propose a novel low-complexity soft-aided hard-decision decoding scheme for product-like codes, termed iterative bounded-distance decoding (iBDD) with graded scaled reliability and bit-flipping (GSRF). This scheme operates on four-level quantized soft information. It incorporates a graded scaled reliability rule to assign decoding confidence to the bounded-distance decoding result, and employs a bit-flipping rule based on bit-level and component-code-level reliability. A selective re-decoding rule is designed to further facilitate the error performance while keeping the number of BDD attempts in reasonably low levels. The decoding parameter design of iBDD-GSRF is investigated for product codes and staircase codes, respectively. Simulation results on both codes verify that iBDD-GSRF achieves a gain of more than 0.4 dB over the conventional iBDD, comparable to several existing unquantized soft-aided decoders.

arXiv:2610.21187•IEEE Communications Letters•Jan 1, 2026•0 citations

Modified algorithm for hard decision decoding of product codes

Ali Al‐Shaikhi, M.A. Kousa

Product coding produces powerful long codes from short constituent codes. The conventional row-column decoding algorithm of the product code does not exploit its full power of correcting random errors and proposes a modification to the conventional decoding algorithm, which makes it capable of reaching the theoretical error correction capability of the code. In addition to its theoretical significance, the modified algorithm is shown to provide a gain of 0.5 dB over the conventional algorithm for AWGN channels.

IEEE Wireless Communications and Networking Conference•Oct 19, 2004•4 citations

A Soft-Input and Output Iterative Bounded-Distance and Encoding-Based Decoding Algorithm for Product Codes

Hitoshi Tokushige, M.P.C. Fossorier, Tadao Kasami

This letter deals with an iterative decoding algorithm (IDA) for product codes. In the IDA, a soft-input and output iterative bounded-distance and encoding-based decoding algorithm is used for the component codes. Simulation results over an AWGN channel with BPSK modulation is presented and show the effectiveness of the IDA.

IEICE Transactions on Fundamentals of Electronics Communications and Computer Sciences•Jan 1, 2009•0 citations

A Threshold-Based Binary Message Passing Decoder With Memory for Product Codes

Xinwei Zhao, Shancheng Zhao, Qingyong Deng +2 more

Product codes (PCs) are typically decoded using iterative bounded distance decoding (iBDD) to ensure a low decoding complexity. To obtain further performance gain, a soft-aided decoding algorithm, termed the iBDD with scaled reliability (iBDD-SR), was proposed for PCs. In this paper, we propose an enhanced iBDD-SR by introducing threshold and memory when passing messages between the component decoders. The resulting algorithm is referred to as the threshold-based binary message passing (TB-BMP) with memory. In the proposed decoding algorithm, the soft reliability of the BDD output at the current half-iteration is a weighted sum of the BDD output, the channel reliability, and the content of the memory unit, where the content of the memory unit at the current half-iteration is related to the selected threshold and the BDD output at last half-iteration. Due to the existence of memory, the Bayesian network is used to model the decoding process of the TB-BMP. Based on the Bayesian network, we derive the density evolution (DE) equations for the TB-BMP under the constraint of extrinsic message passing (EMP). The analytical results of the DE analysis can be used to guide the selection of the parameters of the TB-BMP decoder. Extensive simulation results show that the TB-BMP decoder outperforms the iBDD-SR over the binary-input additive white Gaussian noise (Bi-AWGN) channels. In particular, for a PC based on a two-error-correcting extended Bose-Chaudhuri-Hocquenghem (BCH) code of length 256, the TB-BMP decoder performs about 0.28 dB better than the iBDD-SR at a bit error rate (BER) of 10-7.

IEEE Transactions on Communications•Mar 29, 2024•9 citations
We propose a novel binary message passing decoding algorithm for product-like codes based on bounded distance decoding (BDD) of the component codes. The algorithm, dubbed iterative BDD with scaled reliability (iBDD-SR), exploits the channel reliabilities and is therefore soft in nature. However, the messages exchanged by the component decoders are binary (hard) messages, which significantly reduces the decoder data flow. The exchanged binary messages are obtained by combining the channel reliability with the BDD decoder output reliabilities, properly conveyed by a scaling factor applied to the BDD decisions. We perform a density evolution analysis for generalized low-density parity-check (GLDPC) code ensembles and spatially coupled GLDPC code ensembles, from which the scaling factors of the iBDD-SR for product and staircase codes, respectively, can be obtained. For the white additive Gaussian noise channel, we show performance gains up to 0.29 dB and 0.31 dB for product and staircase codes compared to conventional iterative BDD (iBDD) with the same decoder data flow. Furthermore, we show that iBDD-SR approaches the performance of ideal iBDD that prevents miscorrections.
We propose a novel soft-aided hard-decision decoding scheme for product codes based on two-bit quantized reliability markers. In particular, one bit is used for a two-level tolerance miscorrection check to validate the bounded distance decoding (BDD) result, while the other identifies bits to be randomly flipped upon BDD failure and miscorrection. List decoding is incorporated to further facilitate the error performance. Density evolution is performed for the design of the quantization thresholds. Compared to iterative BDD, the proposed scheme requires only moderate increases in memory and computational overhead. Simulation results verify that our scheme outperforms several unquantized soft-aided decoders, while maintaining small memory costs and low BDD attempts.
We propose a novel low-complexity soft-aided hard-decision decoding scheme for product-like codes, termed iterative bounded-distance decoding (iBDD) with graded scaled reliability and bit-flipping (GSRF). This scheme operates on four-level quantized soft information. It incorporates a graded scaled reliability rule to assign decoding confidence to the bounded-distance decoding result, and employs a bit-flipping rule based on bit-level and component-code-level reliability. A selective re-decoding rule is designed to further facilitate the error performance while keeping the number of BDD attempts in reasonably low levels. The decoding parameter design of iBDD-GSRF is investigated for product codes and staircase codes, respectively. Simulation results on both codes verify that iBDD-GSRF achieves a gain of more than 0.4 dB over the conventional iBDD, comparable to several existing unquantized soft-aided decoders.
Product coding produces powerful long codes from short constituent codes. The conventional row-column decoding algorithm of the product code does not exploit its full power of correcting random errors and proposes a modification to the conventional decoding algorithm, which makes it capable of reaching the theoretical error correction capability of the code. In addition to its theoretical significance, the modified algorithm is shown to provide a gain of 0.5 dB over the conventional algorithm for AWGN channels.
Product codes (PCs) are typically decoded using iterative bounded distance decoding (iBDD) to ensure a low decoding complexity. To obtain further performance gain, a soft-aided decoding algorithm, termed the iBDD with scaled reliability (iBDD-SR), was proposed for PCs. In this paper, we propose an enhanced iBDD-SR by introducing threshold and memory when passing messages between the component decoders. The resulting algorithm is referred to as the threshold-based binary message passing (TB-BMP) with memory. In the proposed decoding algorithm, the soft reliability of the BDD output at the current half-iteration is a weighted sum of the BDD output, the channel reliability, and the content of the memory unit, where the content of the memory unit at the current half-iteration is related to the selected threshold and the BDD output at last half-iteration. Due to the existence of memory, the Bayesian network is used to model the decoding process of the TB-BMP. Based on the Bayesian network, we derive the density evolution (DE) equations for the TB-BMP under the constraint of extrinsic message passing (EMP). The analytical results of the DE analysis can be used to guide the selection of the parameters of the TB-BMP decoder. Extensive simulation results show that the TB-BMP decoder outperforms the iBDD-SR over the binary-input additive white Gaussian noise (Bi-AWGN) channels. In particular, for a PC based on a two-error-correcting extended Bose-Chaudhuri-Hocquenghem (BCH) code of length 256, the TB-BMP decoder performs about 0.28 dB better than the iBDD-SR at a bit error rate (BER) of 10-7.