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Algebraic decoding algorithms are commonly applied for the decoding of Reed-Solomon codes. Their main advantages are low computational complexity and predictable decoding capabilities. Many algorithms can be extended for correction of both…
In this paper, we extend the work of (Abbondati et al., 2024) on decoding simultaneous rational number codes by addressing two important scenarios: multiplicities and the presence of bad primes (divisors of denominators). First, we…
In practice, LDPC codes are decoded using message passing methods. These methods offer good performance but tend to converge slowly and sometimes fail to converge and to decode the desired codewords correctly. Recently, tree-reweighted…
In this paper, we propose a source coding scheme that represents data from unknown distributions through frequency and support information. Existing encoding schemes often compress data by sacrificing computational efficiency or by assuming…
Maximum distance separable (MDS) codes are optimal where the minimum distance cannot be improved for a given length and code size. Twisted Reed-Solomon codes over finite fields were introduced in 2017, which are generalization of…
Guessing Random Additive Noise Decoding (GRAND) is a family of hard- and soft-detection error correction decoding algorithms that provide accurate decoding of any moderate redundancy code of any length. Here we establish a method through…
We propose a new class of efficient decoding algorithms for Reed-Muller (RM) codes over binary-input memoryless channels. The algorithms are based on projecting the code on its cosets, recursively decoding the projected codes (which are…
In distributed computing, slower nodes (stragglers) usually become a bottleneck. Gradient Coding (GC), introduced by Tandon et al., is an efficient technique that uses principles of error-correcting codes to distribute gradient computation…
By utilizing previously known areas in an image, intra-prediction techniques can find a good estimate of the current block. This allows the encoder to store only the error between the original block and the generated estimate, thus leading…
Reed--Solomon error-correcting codes are ubiquitous across computer science and information theory, with applications in cryptography, computational complexity, communication and storage systems, and more. Most works on efficient error…
Reed-Solomon (RS) codes are among the most ubiquitous codes due to their good parameters as well as efficient encoding and decoding procedures. However, RS codes suffer from having a fixed length. In many applications where the length is…
Twisted generalized Reed-Solomon (TGRS) codes were introduced to extend the algebraic capabilities of classical generalized Reed-Solomon (GRS) codes. This extension holds the potential for constructing new non-GRS maximum distance separable…
Gradient coding is a technique for straggler mitigation in distributed learning. In this paper we design novel gradient codes using tools from classical coding theory, namely, cyclic MDS codes, which compare favorably with existing…
Modern applications are driving demand for ultra-reliable low-latency communications, rekindling interest in the performance of short, high-rate error correcting codes. To that end, here we introduce a soft-detection variant of Guessing…
Guo, Kopparty and Sudan have initiated the study of error-correcting codes derived by lifting of affine-invariant codes. Lifted Reed-Solomon (RS) codes are defined as the evaluation of polynomials in a vector space over a field by requiring…
The performance of algebraic soft-decision decoding of Reed-Solomon codes using bit-level soft information is investigated. Optimal multiplicity assignment strategies of algebraic soft-decision decoding with infinite cost are first studied…
Noisy shuffling channels capture the main characteristics of DNA storage systems where distinct segments of data are received out of order, after being corrupted by substitution errors. For realistic schemes with short-length segments,…
Maximum distance separable (MDS) codes have significant combinatorial and cryptographic applications due to their certain optimality. Generalized Reed-Solomon (GRS) codes are the most prominent MDS codes. Twisted generalized Reed-Solomon…
Deep learning-based methods have garnered significant attention in remote sensing (RS) image compression due to their superior performance. Most of these methods focus on enhancing the coding capability of the compression network and…
Large-scale distributed learning aims at minimizing a loss function $L$ that depends on a training dataset with respect to a $d$-length parameter vector. The distributed cluster typically consists of a parameter server (PS) and multiple…