Related papers: A Rate-Distortion Perspective on Multiple Decoding…
We show that the known list-decoding algorithms for univariate multiplicity and folded Reed-Solomon codes can be made to run in $\tilde{O}(n)$ time. Univariate multiplicity codes and FRS codes are natural variants of Reed-Solomon codes that…
Recursive list decoding is considered for Reed-Muller (RM) codes. The algorithm repeatedly relegates itself to the shorter RM codes by recalculating the posterior probabilities of their symbols. Intermediate decodings are only performed…
In this paper, we present an iterative soft-decision decoding algorithm for Reed-Solomon codes offering both complexity and performance advantages over previously known decoding algorithms. Our algorithm is a list decoding algorithm which…
A fundamental question in designing lossy data compression schemes is how well one can do in comparison with the rate-distortion function, which describes the known theoretical limits of lossy compression. Motivated by the empirical success…
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,…
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…
This study addresses the use of Reed-Solomon error correction codes in QR codes to enhance resilience against failures. To fully grasp this approach, a basic cryptographic context is provided, necessary for understanding Reed-Solomon codes.…
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…
In this paper, we introduce a novel explicit family of subcodes of Reed-Solomon (RS) codes that efficiently achieve list decoding capacity with a constant output list size. Our approach builds upon the idea of large linear subcodes of RS…
In this work, we show new and improved error-correcting properties of folded Reed-Solomon codes and multiplicity codes. Both of these families of codes are based on polynomials over finite fields, and both have been the sources of recent…
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…
Depth image based rendering techniques for multiview applications have been recently introduced for efficient view generation at arbitrary camera positions. Encoding rate control has thus to consider both texture and depth data. Due to…
We present a novel systematic theoretical framework to analyze the rate-distortion (R-D) limits of learned image compression. While recent neural codecs have achieved remarkable empirical results, their distance from the…
We present a novel iterative decoding algorithm for Reed-Muller (RM) codes, which takes advantage of a graph representation of the code. Vertices of the considered graph correspond to codewords, with two vertices being connected by an edge…
Restricted Syndrome Decoding (ResSD) is a variant of linear code decoding problem where each of the error's entries must belong to a fixed small set of values. This problem underlies the security of CROSS, a post-quantum signature scheme…
Sequential rate-distortion (SRD) theory provides a framework for studying the fundamental trade-off between data-rate and data-quality in real-time communication systems. In this paper, we consider the SRD problem for multi-dimensional…
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 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…
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…
A rekindled the interest in auto-encoder algorithms has been spurred by recent work on deep learning. Current efforts have been directed towards effective training of auto-encoder architectures with a large number of coding units. Here, we…