相关论文: Algebraic Soft-Decision Decoding of Reed-Solomon C…

We introduce a novel universal soft-decision decoding algorithm for binary block codes called ordered reliability direct error pattern testing (ORDEPT). Our results, obtained for a variety of popular short high-rate codes, demonstrate that…

Surface codes reach high error thresholds when decoded with known algorithms, but the decoding time will likely exceed the available time budget, especially for near-term implementations. To decrease the decoding time, we reduce the…

This work develops a rate-distortion-based approach to stochastic Chase decoding of algebraic codes over binary memoryless symmetric (BMS) channels, replacing the heuristics traditionally used to determine flip probabilities with…

The Plotkin construction combines two codes to a code of doubled length. It can be applied recursively. The class of Reed-Muller (RM) codes is a particular example. Also, a special class of generalized concatenated codes (GCC) can be…

Sphere decoding (SD) of polar codes is an efficient method to achieve the error performance of maximum likelihood (ML) decoding. But the complexity of the conventional sphere decoder is still high, where the candidates in a target sphere…

This paper revisits the ordered statistics decoding (OSD). It provides a comprehensive analysis of the OSD algorithm by characterizing the statistical properties, evolution and the distribution of the Hamming distance and weighted Hamming…

Mart{\'\i}nez-Pe{\~n}as and Kschischang (IEEE Trans.\ Inf.\ Theory, 2019) proposed lifted linearized Reed--Solomon codes as suitable codes for error control in multishot network coding. We show how to construct and decode \ac{LILRS} codes.…

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…

Short-length Reed--Muller codes under majority-logic decoding are of particular importance for efficient hardware implementations in real-time and embedded systems. This paper significantly improves Chen's two-step majority-logic decoding…

Despite of tremendous research on decoding Reed-Solomon (RS) and algebraic geometry (AG) codes under the random and adversary substitution error models, few studies have explored these codes under the burst substitution error model. Burst…

In this paper, we introduce a novel explicit family of subcodes of Reed-Solomon (RS) codes that efficiently achieve list decoding capacity with a constant output list size. Our approach builds upon the idea of large linear subcodes of RS…

In this paper show that the list and bounded-distance decoding problems of certain bounds for the Reed-Solomon code are at least as hard as the discrete logarithm problem over finite fields.

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…

In this paper, we use reinforcement learning to find effective decoding strategies for binary linear codes. We start by reviewing several iterative decoding algorithms that involve a decision-making process at each step, including…

Neural-network decoders can achieve a lower logical error rate compared to conventional decoders, like minimum-weight perfect matching, when decoding the surface code. Furthermore, these decoders require no prior information about the…

Error-correcting codes are combinatorial objects designed to cope with the problem of reliable transmission of information on a noisy channel. A fundamental problem in coding theory and practice is to efficiently decode the received word…

We present error-correcting codes that achieve the information-theoretically best possible trade-off between the rate and error-correction radius. Specifically, for every $0 < R < 1$ and $\eps> 0$, we present an explicit construction of…

The sum-rank metric generalizes the Hamming and rank metric by partitioning vectors into blocks and defining the total weight as the sum of the rank weights of these blocks, based on their matrix representation. In this work, we explore…

This paper proposes the Symbolic-Stochastic Chase Decoding Algorithm (S-SCA) for the Reed-Solomon (RS) and BCH codes. By efficient usage of void space between constellation points for $q$-ary modulations and using soft information at the…

Polar codes are a family of capacity-achieving error-correcting codes, and they have been selected as part of the next generation wireless communication standard. Each polar code bit-channel is assigned a reliability value, used to…