Related papers: Algebraic codes for Slepian-Wolf code design
Distributed source coding is traditionally viewed in the block coding context -- all the source symbols are known in advance at the encoders. This paper instead considers a streaming setting in which iid source symbol pairs are revealed to…
In source coding, either with or without side information at the decoder, the ultimate performance can be achieved by means of random binning. Structured binning into cosets of performing channel codes has been successfully employed in…
In this paper, a new algebraic soft-decision decoding algorithm for Reed-Solomon code is presented. It is based on rational interpolation and the interpolation points are constructed by Berlekamp-Messay algorithm. Unlike the traditional…
Reed-Solomon (RS) codes have been increasingly adopted by distributed storage systems in place of replication,because they provide the same level of availability with much lower storage overhead. However, a key drawback of those RS-coded…
This paper is concerned with a class of low density generator matrix codes (LDGM), called repetition and superposition (RaS) codes, which have been proved to be capacity-achieving over binary-input output-symmetric (BIOS) channels in terms…
This work studies the problem of distributed compression of correlated sources with an action-dependent joint distribution. This class of problems is, in fact, an extension of the Slepian-Wolf model, but where cost-constrained actions taken…
Large-scale systems with arrays of solid state disks (SSDs) have become increasingly common in many computing segments. To make such systems resilient, we can adopt erasure coding such as Reed-Solomon (RS) code as an alternative to…
Constructing Reed-Solomon (RS) codes that can correct insertion and deletion (ins-del) errors has been the focus of several recent studies. However, efficient decoding algorithms for such codes have received less attention and remain a…
We consider Slepian-Wolf (SW) coding of multiple sources and extend the packing bound and the notion of perfect code from conventional channel coding to SW coding with more than two sources. We then introduce Hamming Codes for Multiple…
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…
In the last few years, there has been a great interest in extending the information-theoretic scenario for the non-asymptotic or one-shot case, i.e., where the channel is used only once. We provide the one-shot rate region for the…
Decoding algorithms for Reed--Solomon (RS) codes are of great interest for both practical and theoretical reasons. In this paper, an efficient algorithm, called the modular approach (MA), is devised for solving the Welch--Berlekamp (WB) key…
A large class of MDS linear codes is constructed. These codes are endowed with an efficient decoding algorithm. Both the definition of the codes and the design of their decoding algorithm only require from Linear Algebra methods, making…
The problem of repairing linear codes and, in particular, Reed Solomon (RS) codes has attracted a lot of attention in recent years due to their extreme importance to distributed storage systems. In this problem, a failed code symbol (node)…
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…
The problem of distributed data compression for function computation is considered, where (i) the function to be computed is not necessarily symbol-wise function and (ii) the information source has memory and may not be stationary nor…
Spatially-Coupled (SC)-LDPC codes are known to have outstanding error-correction performance and low decoding latency. Whereas previous works on LDPC and SC-LDPC codes mostly take either an asymptotic or a finite-length design approach, in…
The aim of this paper is to prove theorems for the Slepian-Wolf source coding and the broadcast channel coding (independent messages and no common message) based on the the notion of a stronger version of the hash property for an ensemble…
Our work addresses the well-known open problem of distributed computing of bilinear functions of two correlated sources ${\bf A}$ and ${\bf B}$. In a setting with two nodes, with the first node having access to ${\bf A}$ and the second to…
Distributed Arithmetic Coding (DAC) is an effective implementation of Slepian-Wolf coding, especially for short data blocks. To research its properties, the concept of DAC codeword distribution along proper and wrong decoding paths has been…