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We discuss the decoding of Gabidulin and interleaved Gabidulin codes. We give the full presentation of a decoding algorithm for Gabidulin codes, which as Loidreau's seminal algorithm consists in localizing errors in the spirit of…
This paper presents a method to merge Generalized Minimum Distance decoding of Reed-Solomon codes with the extended Euclidean algorithm. By merge, we mean that the steps taken to perform the Generalized Minimum Distance decoding are similar…
In this paper, we first propose a general interpolation algorithm in a free module of a linearized polynomial ring, and then apply this algorithm to decode several important families of codes, Gabidulin codes, KK codes and MV codes. Our…
The main computational steps in algebraic soft-decoding, as well as Sudan-type list-decoding, of Reed-Solomon codes are bivariate polynomial interpolation and factorization. We introduce a computational technique, based upon re-encoding and…
We decode Reed-Solomon codes using soft information provided at the receiver. The Extended Euclidean Algorithm (EEA) is considered as an initial step to obtain an intermediate result. The final decoding result is obtained by interpolating…
Recently, codes in the sum-rank metric attracted attention due to several applications in e.g. multishot network coding, distributed storage and quantum-resistant cryptography. The sum-rank analogs of Reed-Solomon and Gabidulin codes are…
This paper is concerned with list decoding of $2$-interleaved binary alternant codes. The principle of the proposed algorithm is based on a combination of a list decoding algorithm for (interleaved) Reed-Solomon codes and an algorithm for…
In this work, we present a concatenated repetition-polar coding scheme that is aimed at applications requiring highly unbalanced unequal bit-error protection, such as the Beam Interlock System of the Large Hadron Collider at CERN. Even…
We show how Gabidulin codes can be list decoded by using a parametrization approach. For this we consider a certain module in the ring of linearized polynomials and find a minimal basis for this module using the Euclidean algorithm with…
Recently, Martinez-Penas and Kschischang (IEEE Trans. Inf. Theory, 2019) showed that lifted linearized Reed-Solomon codes are suitable codes for error control in multishot network coding. We show how to construct and decode lifted…
Two concatenated coding schemes incorporating algebraic Reed-Solomon (RS) codes and polarization-adjusted convolutional (PAC) codes are proposed. Simulation results show that at a bit error rate of $10^{-5}$, a concatenated scheme using RS…
An iterated refinement procedure for the Guruswami--Sudan list decoding algorithm for Generalised Reed--Solomon codes based on Alekhnovich's module minimisation is proposed. The method is parametrisable and allows variants of the usual list…
In this paper, the analysis of the performance of the concatenation of a short polar code with an outer binary linear block code is addressed from a distance spectrum viewpoint. The analysis targets the case where an outer cyclic code is…
An iterative decoding algorithm for convolutional codes is presented. It successively processes $N$ consecutive blocks of the received word in order to decode the first block. A bound is presented showing which error configurations can be…
We show that decoding of $\ell$-Interleaved Gabidulin codes, as well as list-$\ell$ decoding of Mahdavifar--Vardy codes can be performed by row reducing skew polynomial matrices. Inspired by row reduction of $\F[x]$ matrices, we develop a…
We consider interpolation-based decoding of Reed-Solomon codes using the Guruswami-Sudan algorithm (GSA) and investigate the effects of two modification techniques for received vectors, i.e., the re-encoding map and the newly introduced…
We propose a new partial decoding algorithm for $m$-interleaved Reed--Solomon (IRS) codes that can decode, with high probability, a random error of relative weight $1-R^{\frac{m}{m+1}}$ at all code rates $R$, in time polynomial in the code…
Assuming that we have a soft-decision list decoding algorithm of a linear code, a new hard-decision list decoding algorithm of its repeated code is proposed in this article. Although repeated codes are not used for encoding data, due to…
The new method for Reed-Solomon codes decoding is introduced. The method is based on the star trellis decoding of the binary image of Reed-Solomon codes.
Reed-Muller codes are among the most important classes of locally correctable codes. Currently local decoding of Reed-Muller codes is based on decoding on lines or quadratic curves to recover one single coordinate. To recover multiple…