Related papers: Coding with Constraints: Minimum Distance Bounds a…
It has been widely observed that there exists a fundamental trade-off between the minimum (Hamming) distance properties and the iterative decoding convergence behavior of turbo-like codes. While capacity achieving code ensembles typically…
This work is motivated by the problem of error correction in bit-shift channels with the so-called $ (d,k) $ input constraints (where successive $ 1 $'s are required to be separated by at least $ d $ and at most $ k $ zeros, $ 0 \leq d < k…
This paper studies the problem of code symbol availability: a code symbol is said to have $(r, t)$-availability if it can be reconstructed from $t$ disjoint groups of other symbols, each of size at most $r$. For example, $3$-replication…
Reed-Solomon codes, a type of BCH codes, are widely employed in communication systems, storage devices and consumer electronics. This fact demonstrates the importance of BCH codes -- a family of cyclic codes -- in practice. In theory, BCH…
A code over a finite alphabet is called locally recoverable (LRC) if every symbol in the encoding is a function of a small number (at most $r$) other symbols. We present a family of LRC codes that attain the maximum possible value of the…
We investigate threshold-based multi-trial decoding of concatenated codes with an inner Maximum-Likelihood decoder and an outer error/erasure (L+1)/L-extended Bounded Distance decoder, i.e. a decoder which corrects e errors and t erasures…
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)…
Block codes are considered for improving the reliability of messages stored in a computer memory with both stuck-at defects and random errors. It is assumed that the side information about the state of the defects is available to the…
Considerable interest has been paid in recent literature to codes combining local and global properties for erasure correction. Applications are in cloud type of implementations, in which fast recovery of a failed storage device is…
We propose a modified iterative bounded distance decoding of product codes. The proposed algorithm is based on exchanging hard messages iteratively and exploiting channel reliabilities to make hard decisions at each iteration. Performance…
In this paper, network error control coding is studied for robust and efficient multicast in a directed acyclic network with imperfect links. The block network error control coding framework, BNEC, is presented and the capability of the…
We present a new decoding algorithm based on error locating pairs and correcting an amount of errors exceeding half the minimum distance. When applied to Reed--Solomon or algebraic geometry codes, the algorithm is a reformulation of the…
Distributed storage systems for large-scale applications typically use replication for reliability. Recently, erasure codes were used to reduce the large storage overhead, while increasing data reliability. A main limitation of…
We consider a variable-length source coding problem subject to local decodability constraints. In particular, we investigate the blocklength scaling behavior attainable by encodings of $r$-sparse binary sequences, under the constraint that…
Locally repairable codes (LRCs) are error correcting codes used in distributed data storage. Besides a global level, they enable errors to be corrected locally, reducing the need for communication between storage nodes. There is a close…
A major issue of locally repairable codes is their robustness. If a local repair group is not able to perform the repair process, this will result in increasing the repair cost. Therefore, it is critical for a locally repairable code to…
This paper concerns non-overlapping codes, block codes motivated by synchronisation and DNA-based storage applications. Most existing constructions of these codes do not account for the restrictions posed by the physical properties of…
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)…
In the context of distributed storage systems, locally repairable codes have become important. In this paper we focus on codes that allow for multi-erasure pattern decoding with low computational effort. Different optimality requirements,…
This paper presents encoding and decoding algorithms for several families of optimal rank metric codes whose codes are in restricted forms of symmetric, alternating and Hermitian matrices. First, we show the evaluation encoding is the right…