Related papers: Decoding of Interleaved Reed-Solomon Codes Using I…
A novel recursive list decoding (RLD) algorithm for Reed-Muller (RM) codes based on successive permutations (SP) of the codeword is presented. A low-complexity SP scheme applied to a subset of the symmetry group of RM codes is first…
We present a practical algorithm to decode erasures of Reed-Solomon codes over the q elements binary field in O(q \log_2^2 q) time where the constant implied by the O-notation is very small. Asymptotically fast algorithms based on fast…
A collection of sets satisfies a $(\delta,\varepsilon)$-proximity gap with respect to some property if for every set in the collection, either (i) all members of the set are $\delta$-close to the property in (relative) Hamming distance, or…
In this article we count the number of generalized Reed-Solomon (GRS) codes of dimension k and length n, including the codes coming from a non-degenerate conic plus nucleus. We compare our results with known formulae for the number of…
Hinging on ideas from physical-layer network coding, some promising proposals of coded random access systems seek to improve system performance (while preserving low complexity) by means of packet repetitions and decoding of linear…
A novel permutation decoding method for Reed-Muller codes is presented. The complexity and the error correction performance of the suggested permutation decoding approach are similar to that of the recursive lists decoder. It is…
This paper presents an algorithm for decoding homogeneous interleaved codes of high interleaving order in the rank metric. The new decoder is an adaption of the Hamming-metric decoder by Metzner and Kapturowski (1990) and guarantees to…
Compared with classical block codes, efficient list decoding of rank-metric codes seems more difficult. Although the list decodability of random rank-metric codes and limits to list decodability have been completely determined, little work…
Multishot network coding is considered in a worst-case adversarial setting in which an omniscient adversary with unbounded computational resources may inject erroneous packets in up to $t$ links, erase up to $\rho$ packets, and wire-tap up…
We consider a coded compressed sensing approach for the unsourced random access and replace the outer tree code proposed by Amalladinne et al. with the list recoverable code capable of correcting t errors. A finite-length random coding…
The variable-length Reverse Multi-Delimiter (RMD) codes are known to represent sequences of unbounded and unordered integers. When applied to data compression, they combine a good compression ratio with fast decoding. In this paper, we…
Reed-Muller (RM) and polar codes are a class of capacity-achieving channel coding schemes with the same factor graph representation. Low-complexity decoding algorithms fall short in providing a good error-correction performance for RM and…
An algorithm of improving the performance of iterative decoding on perpendicular magnetic recording is presented. This algorithm follows on the authors' previous works on the parallel and serial concatenated turbo codes and low-density…
We investigate the decoding region for Algebraic Soft-Decision Decoding (ASD) of Reed-Solomon codes in a discrete, memoryless, additive-noise channel. An expression is derived for the error correction radius within which the soft-decision…
Linearized Reed-Solomon codes are defined. Higher weight distribution of those codes are determined.
Reed-Muller (RM) codes are conjectured to achieve the capacity of any binary-input memoryless symmetric (BMS) channel, and are observed to have a comparable performance to that of random codes in terms of scaling laws. On the negative side,…
Despite their exceptional error-correcting properties, Reed-Solomon (RS) codes have been overlooked in distributed storage applications due to the common belief that they have poor repair bandwidth: A naive repair approach would require the…
Determining the weight distribution of a linear code is a classical and fundamental topic in coding theory that has been extensively investigated. Repeated-root cyclic codes, which form a significant subclass of error-correcting codes, have…
Reed-Muller (RM) codes are among the oldest, simplest and perhaps most ubiquitous family of codes. They are used in many areas of coding theory in both electrical engineering and computer science. Yet, many of their important properties are…
We establish an equivalence between two important random ensembles of linear codes: random linear codes (RLCs) and random Reed-Solomon (RS) codes. Specifically, we show that these models exhibit identical behavior with respect to key…