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Chase-Pyndiah decoding is widely used for decoding product codes. However, this method is suboptimal and requires scaling the soft information exchanged during the iterative processing. In this paper, we propose a framework for obtaining…

Information Theory · Computer Science 2025-08-29 Andreas Straßhofer , Diego Lentner , Gianluigi Liva , Alexandre Graell i Amat

This paper presents an improved FEC decoder design outperforming Chase-Pyndiah decoding of product codes by $0.23$ dB. To achieve this, the decoder does not require iteration-dependent coefficients, making it implementation-friendly for…

Information Theory · Computer Science 2026-05-14 Andreas Straßhofer

Iterative decoding is essential in modern communication systems, especially optical communications, where error-correcting codes such as turbo product codes (TPC) and staircase codes are widely employed. A key factor in achieving high error…

Information Theory · Computer Science 2025-06-06 Dmitry Artemasov , Oleg Nesterenkov , Kirill Andreev , Pavel Rybin , Alexey Frolov

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…

Information Theory · Computer Science 2018-05-15 Alireza Sheikh , Alexandre Graell i Amat , Gianluigi Liva

We propose a novel soft-aided low-complexity decoder for product codes based on dynamic reliability scores and error-and-erasure decoding. We observe coding gains of up to 1.2 dB compared to conventional hard-decision decoders.

Information Theory · Computer Science 2022-05-18 Sisi Miao , Lukas Rapp , Laurent Schmalen

We study low-complexity iterative decoding algorithms for product codes. We revisit two algorithms recently proposed by the authors based on bounded distance decoding (BDD) of the component codes that improve the performance of conventional…

Information Theory · Computer Science 2018-06-29 Alireza Sheikh , Alexandre Graell i Amat , Gianluigi Liva , Christian Häger , Henry D. Pfister

We propose a binary message passing decoding algorithm for product codes based on generalized minimum distance decoding (GMDD) of the component codes, where the last stage of the GMDD makes a decision based on the Hamming distance metric.…

Information Theory · Computer Science 2019-01-25 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…

Information Theory · Computer Science 2019-09-20 Alireza Sheikh , Alexandre Graell i Amat , Gianluigi Liva

We propose an improved soft-aided decoding scheme for product codes that approaches the decoding performance of conventional soft-decision TPD with only a 0.2 dB gap while keeping the complexity and internal decoder data flow similarly low…

Information Theory · Computer Science 2022-07-12 Sisi Miao , Lukas Rapp , Laurent Schmalen

The decoding performance of product codes and staircase codes based on iterative bounded-distance decoding (iBDD) can be improved with the aid of a moderate amount of soft information, maintaining a low decoding complexity. One promising…

Information Theory · Computer Science 2022-05-18 Sisi Miao , Lukas Rapp , Laurent Schmalen

Product codes (PCs) and staircase codes (SCCs) are conventionally decoded based on bounded distance decoding (BDD) of the component codes and iterating between row and column decoders. The performance of iterative BDD (iBDD) can be improved…

Information Theory · Computer Science 2021-09-08 Alireza Sheikh , Alexandre Graell i Amat , Alex Alvarado

We propose a novel soft-aided iterative decoding algorithm for product codes (PCs). The proposed algorithm, named iterative bounded distance decoding with combined reliability (iBDD-CR), enhances the conventional iterative bounded distance…

Information Theory · Computer Science 2021-09-08 Alireza Sheikh , Alexandre Graell i Amat , Gianluigi Liva , Alex Alvarado

We introduce a novel soft-aided hard-decision decoder for product codes adopting bit marking via updated reliabilities at each decoding iteration. Gains up to 0.8 dB vs. standard iterative bounded distance decoding and up to 0.3 dB vs. our…

Information Theory · Computer Science 2019-06-25 Gabriele Liga , Alireza Sheikh , Alex Alvarado

Products codes (PCs) are conventionally decoded with efficient iterative bounded-distance decoding (iBDD) based on hard-decision channel outputs which entails a performance loss compared to a soft-decision decoder. Recently, several hybrid…

Information Theory · Computer Science 2022-11-22 Sisi Miao , Lukas Rapp , Laurent Schmalen

We use density evolution to optimize the parameters of binary product codes (PCs) decoded based on the recently introduced iterative bounded distance decoding with scaled reliability. We show that binary PCs with component codes of 3-bit…

Information Theory · Computer Science 2019-08-27 Alireza Sheikh , Alexandre Graell i Amat , Gianluigi Liva , Alex Alvarado

Codes based on sparse matrices have good performance and can be efficiently decoded by belief-propagation (BP). Decoding binary stabilizer codes needs a quaternary BP for (additive) codes over GF(4), which has a higher check-node complexity…

Quantum Physics · Physics 2021-03-10 Kao-Yueh Kuo , Ching-Yi Lai

High-rate product codes (PCs) and staircase codes (SCs) are ubiquitous codes in high-speed optical communication achieving near-capacity performance on the binary symmetric channel. Their success is mostly due to very efficient iterative…

Information Theory · Computer Science 2022-01-19 Lukas Rapp , Laurent Schmalen

We implement a 1-Tb/s 0.63-pJ/bit soft-assisted product decoder in a 28-nm technology. The decoder uses one bit of soft information to improve its net coding gain by 0.2 dB, reaching 10.3-10.4 dB, which is similar to that of more complex…

Information Theory · Computer Science 2018-10-30 Christoffer Fougstedt , Alireza Sheikh , Alexandre Graell i Amat , Gianluigi Liva , Per Larsson-Edefors

In this work, we propose a new soft-input soft-output decoder called soft-output from covered space (SOCS) decoder. It estimates the a posteriori reliability based on the space explored by a list decoder, i.e., the set of vectors for which…

Information Theory · Computer Science 2025-07-21 Tim Janz , Simon Obermüller , Andreas Zunker , Stephan ten Brink

We combine two approaches to optimize the iterative decoding of product codes with precoded polar component codes. On one side, we generate bitwise soft messages based on the codebook probability, an approximation of an auxiliary quantity…

Information Theory · Computer Science 2025-08-29 Nicolás Alvarez Prado , Andreas Straßhofer
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