Related papers: Locality in Index Coding for Large Min-Rank
The problem of storing permutations in a distributed manner arises in several common scenarios, such as efficient updates of a large, encrypted, or compressed data set. This problem may be addressed in either a combinatorial or a coding…
We consider a wireless broadcast station that transmits packets to multiple users. The packet requests for each user may overlap, and some users may already have certain packets. This presents a problem of broadcasting in the presence of…
This paper focuses on a particular transmission scheme called local network coding, which has been reported to provide significant performance gains in practical wireless networks. The performance of this scheme strongly depends on the…
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…
This paper deals with scalar linear index codes for canonical multiple unicast index coding problems where there is a source with K messages and there are K receivers each wanting a unique message and having symmetric (with respect to the…
Codes for storage systems aim to minimize the repair locality, which is the number of disks (or nodes) that participate in the repair of a single failed disk. Simultaneously, the code must sustain a high rate, operate on a small finite…
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…
The \emph{index coding} problem has recently attracted a significant attention from the research community due to its theoretical significance and applications in wireless ad-hoc networks. An instance of the index coding problem includes a…
This paper proposes a novel achievable scheme for the index problem and applies it to the caching problem. Index coding and caching are noiseless broadcast channel problems where receivers have message side information.In the index coding…
In this paper, we study the impact of locality on the decoding of binary cyclic codes under two approaches, namely ordered statistics decoding (OSD) and trellis decoding. Given a binary cyclic code having locality or availability, we…
The two-sender unicast index coding problem consists of finding optimal coded transmissions from the two senders which collectively know the messages demanded by all the receivers. Each receiver demands a unique message. One important class…
In this paper, we generalize the well-known index coding problem to exploit the structure in the source-data to improve system throughput. In many applications, the data to be transmitted may lie (or can be well approximated) in a…
A locally decodable code (LDC) maps $K$ source symbols, each of size $L_w$ bits, to $M$ coded symbols, each of size $L_x$ bits, such that each source symbol can be decoded from $N \leq M$ coded symbols. A perfectly smooth LDC further…
In this paper, locally repairable codes with all-symbol locality are studied. Methods to modify already existing codes are presented. Also, it is shown that with high probability, a random matrix with a few extra columns guaranteeing the…
The two-sender unicast index coding problem is the most fundamental multi-sender index coding problem. The two senders collectively cater to the demands of all the receivers, by taking advantage of the knowledge of their side-information.…
A code over a finite field is called locally recoverable code (LRC) if every coordinate symbol can be determined by a small number (at most r, this parameter is called locality) of other coordinate symbols. For a linear code with length n,…
We focus on erasure codes for distributed storage. The distributed storage setting imposes locality requirements because of easy repair demands on the decoder. We first establish the characterization of various locality properties in terms…
We consider locally repairable codes over small fields and propose constructions of optimal cyclic and linear codes in terms of the dimension for a given distance and length. Four new constructions of optimal linear codes over small fields…
We investigate one possible generalization of locally recoverable codes (LRC) with all-symbol locality and availability when recovering sets can intersect in a small number of coordinates. This feature allows us to increase the achievable…
In this work it is shown that locally repairable codes (LRCs) can be list-decoded efficiently beyond the Johnson radius for a large range of parameters by utilizing the local error-correction capabilities. The corresponding decoding radius…