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Traditionally, multi-trial error/erasure decoding of Reed-Solomon (RS) codes is based on Bounded Minimum Distance (BMD) decoders with an erasure option. Such decoders have error/erasure tradeoff factor L=2, which means that an error is…
We consider the problem of erasure/list decoding using certain classes of simplified decoders. Specifically, we assume a class of erasure/list decoders, such that a codeword is in the list if its likelihood is larger than a threshold. This…
Regenerating codes provide an efficient way to recover data at failed nodes in distributed storage systems. It has been shown that regenerating codes can be designed to minimize the per-node storage (called MSR) or minimize the…
Despite its reduced complexity, lattice reduction-aided decoding exhibits a widening gap to maximum-likelihood (ML) performance as the dimension increases. To improve its performance, this paper presents randomized lattice decoding based on…
This paper deals with the application of list decoding of Reed--Solomon codes to a concatenated code for key reproduction using Physical Unclonable Functions. The resulting codes achieve a higher error-correction performance at the same…
Sparse random linear network coding (SRLNC) is an attractive technique proposed in the literature to reduce the decoding complexity of random linear network coding. Recognizing the fact that the existing SRLNC schemes are not efficient in…
Data center networks (DCNs) require a low-cost, low-power optical transceiver to handle increased traffic from generative artificial intelligence, video streaming services, and more. Improving the required signal-to-noise ratio (RSNR) by…
We consider the decoding of linear and array codes from errors when we are only allowed to download a part of the codeword. More specifically, suppose that we have encoded $k$ data symbols using an $(n,k)$ code with code length $n$ and…
The classical family of $[n,k]_q$ Reed-Solomon codes over a field $\F_q$ consist of the evaluations of polynomials $f \in \F_q[X]$ of degree $< k$ at $n$ distinct field elements. In this work, we consider a closely related family of codes,…
We present a new decoding algorithm based on error locating pairs and correcting an amount of errors exceeding half the minimum distance. When applied to Reed--Solomon or algebraic geometry codes, the algorithm is a reformulation of the…
In this paper we devise a rational curve fitting algorithm and apply it to the list decoding of Reed-Solomon and BCH codes. The proposed list decoding algorithms exhibit the following significant properties. 1 The algorithm corrects up to…
In this work, we consider efficient maximum-likelihood decoding of linear block codes for small-to-moderate block lengths. The presented approach is a branch-and-bound algorithm using the cutting-plane approach of Zhang and Siegel (IEEE…
Locally repairable codes (LRCs) were originally introduced to enable efficient recovery from erasures in distributed storage systems by accessing only a small number of other symbols. While their structural properties-such as bounds and…
Regenerating codes are a class of recently developed codes for distributed storage that, like Reed-Solomon codes, permit data recovery from any arbitrary k of n nodes. However regenerating codes possess in addition, the ability to repair a…
Algebraic codes that achieve list decoding capacity were recently constructed by a careful ``folding'' of the Reed-Solomon code. The ``low-degree'' nature of this folding operation was crucial to the list decoding algorithm. We show how…
We study the secure decentralized Pliable Index CODing (PICOD) problem with circular side information sets at the users. The security constraint forbids every user to decode more than one message while a decentralized setting means there is…
Algorithms based on multiple decoding attempts of Reed-Solomon (RS) codes have recently attracted new attention. Choosing decoding candidates based on rate-distortion (R-D) theory, as proposed previously by the authors, currently provides…
Reed Muller (RM) codes are known for their good minimum distance. One can use their structure to construct polar-like codes with good distance properties by choosing the information set as the rows of the polarization matrix with the…
Error-correcting codes are a method for representing data, so that one can recover the original information even if some parts of it were corrupted. The basic idea, which dates back to the revolutionary work of Shannon and Hamming about a…
Point-to-multipoint communications are expected to play a pivotal role in next-generation networks. This paper refers to a cellular system transmitting layered multicast services to a multicast group of users. Reliability of communications…