Related papers: On Multiple Decoding Attempts for Reed-Solomon Cod…
Tensor ring (TR) decomposition is a simple but effective tensor network for analyzing and interpreting latent patterns of tensors. In this work, we propose a doubly randomized optimization framework for computing TR decomposition. It can be…
Interleaved Reed-Solomon codes are applied in numerous data processing, data transmission, and data storage systems. They are generated by interleaving several codewords of ordinary Reed-Solomon codes. Usually, these codewords are decoded…
We examine an error-correcting coding framework in which each coded symbol is constrained to be a function of a fixed subset of the message symbols. With an eye toward distributed storage applications, we seek to design systematic codes…
This paper studies a variant of the rate-distortion problem motivated by task-oriented semantic communication and distributed learning systems, where $M$ correlated sources are independently encoded for a central decoder. The decoder has…
An iterative detection and decoding (IDD) scheme is proposed for multiuser multiple-antenna systems assisted by an active or a passive Reconfigurable Intelligent Surface (RIS). The proposed approach features an IDD strategy that…
Fundamental rate-distortion-perception (RDP) trade-offs arise in applications requiring maintained perceptual quality of reconstructed data, such as neural image compression. When compressed data is transmitted over public communication…
The fundamental limit of natural signal compression has traditionally been characterized by classical rate-distortion (RD) theory through the tradeoff between coding rate and reconstruction distortion, while the rate-distortion-perception…
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…
An algebraic soft-decision decoder for Hermitian codes is presented. We apply Koetter and Vardy's soft-decision decoding framework, now well established for Reed-Solomon codes, to Hermitian codes. First we provide an algebraic foundation…
The sum-rank metric is the mixture of the Hamming and rank metrics. The sum-rank metric found its application in network coding, locally repairable codes, space-time coding, and quantum-resistant cryptography. Linearized Reed-Solomon (LRS)…
We consider the problem of multiple descriptions (MD) source coding and propose new coding strategies involving both unstructured and structured coding layers. Previously, the most general achievable rate-distortion (RD) region for the…
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…
The rate-distortion performance of neural image compression models has exceeded the state-of-the-art for non-learned codecs, but neural codecs are still far from widespread deployment and adoption. The largest obstacle is having efficient…
Decoding a Reed-Solomon code can be modeled by a bilinear system which can be solved by Gr\"obner basis techniques. We will show that in this particular case, these techniques are much more efficient than for generic bilinear systems with…
Understanding the limits of list-decoding and list-recovery of Reed-Solomon (RS) codes is of prime interest in coding theory and has attracted a lot of attention in recent decades. However, the best possible parameters for these problems…
The classical family of Reed-Solomon codes consist of evaluations of polynomials over the finite field $\mathbb{F}_q$ of degree less than $k$, at $n$ distinct field elements. These are arguably the most widely used and studied codes, as…
We consider a remote source coding problem subject to a {distortion function}. Contrary to the use of the classical separable distortion criterion, herein we consider the more general, $f$-separable distortion measure and study its…
We propose a reduced complexity approach to pattern-based soft decoding of block codes. We start from the ORDEPT decoding algorithm which tests a list of partial error patterns organized in the order of their likelihood and attempts to…
The development of practical, high-performance decoding algorithms reduces the resource cost of fault-tolerant quantum computing. Here we propose a decoder for the surface code that finds low-weight correction operators for errors produced…
Robust optimization is a framework for modeling optimization problems involving data uncertainty and during the last decades has been an area of active research. If we focus on linear programming (LP) problems with i) uncertain data, ii)…