Related papers: Irregular Product Codes
This paper investigates fundamental properties of nonlinear binary codes by looking at the codebook matrix not row-wise (codewords), but column-wise. The family of weak flip codes is presented and shown to contain many beautiful properties.…
In this paper, we consider the mismatched rate-distortion problem, in which the encoding is done using a codebook, and the encoder chooses the minimum-distortion codeword according to a mismatched distortion function that differs from the…
Given a topology of local parity-check constraints, a maximally recoverable code (MRC) can correct all erasure patterns that are information-theoretically correctable. In a grid-like topology, there are $a$ local constraints in every column…
In network communication, the source often transmits messages at several different information rates within a session. How to deal with information transmission and network error correction simultaneously under different rates is introduced…
Regenerating codes are a class of codes proposed for providing reliability of data and efficient repair of failed nodes in distributed storage systems. In this paper, we address the fundamental problem of handling errors and erasures during…
The problem of channel coding with the erasure option is revisited for discrete memoryless channels. The interplay between the code rate, the undetected and total error probabilities is characterized. Using the information spectrum method,…
Using tools developed in a recent work by Shen and the second author, in this paper we carry out an in-depth study on the average decoding error probability of the random matrix ensemble over the erasure channel under three decoding…
A general class of polynomial remainder codes is considered. Such codes are very flexible in rate and length and include Reed-Solomon codes as a special case. As an extension of previous work, two joint error-and-erasure decoding approaches…
Interleaved Reed-Solomon codes admit efficient decoding algorithms which correct burst errors far beyond half the minimum distance in the random errors regime, e.g., by computing a common solution to the Key Equation for each Reed-Solomon…
Csisz\'ar's channel coding theorem for multiple codebooks is generalized allowing the codeword lenghts differ across codebooks. Also in this case, for each codebook an error exponent can be achieved that equals the random coding exponent…
The error exponent of the typical random code is defined as the asymptotic normalized expectation of the logarithm of the probability of error, as opposed to the traditional definition of the random coding exponent as the normalized…
We put forth new models for universal channel coding. Unlike standard codes which are designed for a specific type of channel, our most general universal code makes communication resilient on every channel, provided the noise level is below…
We consider the following generalization of an $(n,k)$ MDS code for application to an erasure channel with additive noise. Like an MDS code, our code is required to be decodable from any $k$ received symbols, in the absence of noise. In…
Encoding data as a set of unordered strings is receiving great attention as it captures one of the basic features of DNA storage systems. However, the challenge of constructing optimal redundancy codes for this channel remained elusive. In…
We propose a decoding algorithm for the $(u\mid u+v)$-construction that decodes up to half of the minimum distance of the linear code. We extend this algorithm for a class of matrix-product codes in two different ways. In some cases, one…
A new channel coding approach was proposed in [1] for random multiple access communication over the discrete-time memoryless channel. The coding approach allows users to choose their communication rates independently without sharing the…
For every p in (0,1/2), we give an explicit construction of binary codes of rate approaching "capacity" 1-H(p) that enable reliable communication in the presence of worst-case additive errors}, caused by a channel oblivious to the codeword…
We consider the problem of coding for the substring channel, in which information strings are observed only through their (multisets of) substrings. Due to existing DNA sequencing techniques and applications in DNA-based storage systems,…
We consider the problem of sparse matrix multiplication by the column row method in a distributed setting where the matrix product is not necessarily sparse. We present a surprisingly simple method for "consistent" parallel processing of…
High-rate product codes (PCs) and staircase codes (SCs) are ubiquitous codes in high-speed optical communication achieving near-capacity performance on the binary symmetric channel. Their success is mostly due to very efficient iterative…