Related papers: A Rate-Distortion Exponent Approach to Multiple De…
Error-correcting codes are combinatorial objects designed to cope with the problem of reliable transmission of information on a noisy channel. A fundamental problem in coding theory and practice is to efficiently decode the received word…
We define a virtual projection of a Reed-Solomon code $RS(q^{l},n,k)$ to an $RS(q,n,k)$ Reed-Solomon code. A new probabilistic decoding algorithm that can be used to perform fractional decoding beyond the $\alpha$- decoding radius is…
Typical random codes (TRC) in a communication scenario of source coding with side information at the decoder is the main subject of this work. We study the semi-deterministic code ensemble, which is a certain variant of the ordinary random…
Modern spacecraft communication systems rely on concatenated error correction schemes, typically combining convolutional and Reed-Solomon (RS) codes. This paper presents a decoder-side method that uses a machine learning model to estimate…
With the increasing number of images and videos consumed by computer vision algorithms, compression methods are evolving to consider both perceptual quality and performance in downstream tasks. Traditional codecs can tackle this problem by…
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…
An encoder wishes to minimize the bit rate necessary to guarantee that a decoder is able to calculate a symbol-wise function of a sequence available only at the encoder and a sequence that can be measured only at the decoder. This classical…
This article is focused on some variations of Reed-Muller codes that yield improvements to the rate for a prescribed decoding performance under the Berlekamp-Massey-Sakata algorithm with majority voting. Explicit formulas for the…
Transformers achieve superior performance on many tasks, but impose heavy compute and memory requirements during inference. This inference can be made more efficient by partitioning the process across multiple devices, which, in turn,…
We consider recursive decoding for Reed-Muller (RM) codes and their subcodes. Two new recursive techniques are described. We analyze asymptotic properties of these algorithms and show that they substantially outperform other decoding…
Recently, codes in the sum-rank metric attracted attention due to several applications in e.g. multishot network coding, distributed storage and quantum-resistant cryptography. The sum-rank analogs of Reed-Solomon and Gabidulin codes are…
A composite source, consisting of multiple subsources and a memoryless switch, outputs one symbol at a time from the subsource selected by the switch. If some data should be encoded more accurately than other data from an information…
Folded Reed-Solomon codes are an explicit family of codes that achieve the optimal trade-off between rate and error-correction capability: specifically, for any $\eps > 0$, the author and Rudra (2006,08) presented an $n^{O(1/\eps)}$ time…
Because of their importance in applications and their quite simple definition, Reed-Solomon codes can be explained in any introductory course on coding theory. However, decoding algorithms for Reed-Solomon codes are far from being simple…
This paper deals with rate distortion or source coding with fidelity criterion, in measure spaces, for a class of source distributions. The class of source distributions is described by a relative entropy constraint set between the true and…
We consider a rate-distortion problem with side information at multiple decoders. Several upper and lower bounds have been proposed for this general problem or special cases of it. We provide an upper bound for general instances of this…
In this paper, firstly, we study decoding of a general class of twisted generalized Reed-Solomon (TGRS) codes and provide a precise characterization of the key equation for TGRS codes and propose a decoding algorithm. Secondly, we further…
We establish the first information-theoretic limits for multimodal retrieval. Casting ranking as lossy source coding, we derive a single-letter rate-distortion function $R(D)$ for reciprocal-rank distortion and prove a converse bound that…
The source coding problem with action-dependent side information at the decoder has recently been introduced to model data acquisition in resource-constrained systems. In this paper, an efficient algorithm for numerical computation of the…
End-to-end optimized neural image compression (NIC) has obtained superior lossy compression performance recently. In this paper, we consider the problem of rate-distortion (R-D) characteristic analysis and modeling for NIC. We make efforts…