Related papers: Bounding Multiple Unicasts through Index Coding an…
In this work, we introduce maximally recoverable codes with locality and availability. We consider locally repairable codes (LRCs) where certain subsets of $ t $ symbols belong each to $ N $ local repair sets, which are pairwise disjoint…
A linear error correcting code is a subspace of a finite-dimensional space over a finite field with a fixed coordinate system. Such a code is said to be locally recoverable with locality $r$ if, for every coordinate, its value at a codeword…
A source coding problem over a noiseless broadcast channel where the source is pre-informed about the contents of the cache of all receivers, is an index coding problem. Furthermore, if each message is requested by one receiver, then we…
An optimal linear coding solution for index coding problem is established. Instead of network coding approach by focus on graph theoric and algebraic methods a linear coding program for solving both unicast and groupcast index coding…
New asymptotic upper bounds are presented on the rate of sequences of locally repairable codes (LRCs) with a prescribed relative minimum distance and locality over a finite field $F$. The bounds apply to LRCs in which the recovery functions…
Locally repairable codes, or locally recoverable codes (LRC for short) are designed for application in distributed and cloud storage systems. Similar to classical block codes, there is an important bound called the Singleton-type bound for…
We introduce the concept of quantum locally recoverable codes (qLRCs) with intersecting recovery sets. We derive a singleton-like bound for these codes by leveraging the additional information provided by the intersecting recovery sets.…
Circular-shift linear network coding (LNC) is a class of vector LNC with low encoding and decoding complexities, and with local encoding kernels chosen from cyclic permutation matrices. When $L$ is a prime with primitive root $2$, it was…
We introduce a family of balanced locally repairable codes (BLRCs) $[n, k, d]$ for arbitrary values of $n$, $k$ and $d$. Similar to other locally repairable codes (LRCs), the presented codes are suitable for applications that require a low…
We study a class of linear network coding (LNC) schemes, called circular-shift LNC, whose encoding operations consist of only circular-shifts and bit-wise additions (XOR). Formulated as a special vector linear code over GF($2$), an…
This paper considers the problem of network coding for multiple unicast connections in networks represented by directed acyclic graphs. The concept of interference alignment, traditionally used in interference networks, is extended to…
Recently, locally repairable codes (LRCs) with local erasure correction constraints that are unequal and disjoint have been proposed. In this work, we study the same topic and provide some improved and additional results.
Locally repairable convolutional codes (LRCCs) for distributed storage systems (DSSs) are introduced in this work. They enable local repair, for a single node erasure (or more generally, $ \partial - 1 $ erasures per local group), and…
We introduce a formal framework to study the multiple unicast problem for a coded network in which the network code is linear over a finite field and fixed. We show that the problem corresponds to an interference alignment problem over a…
For a code $\code$, its $i$-th symbol is said to have locality $r$ if its value can be recovered by accessing some other $r$ symbols of $\code$. Locally repairable codes (LRCs) are the family of codes such that every symbol has locality…
We show 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 new decoding radius is derived and the…
Three science and engineering problems of recent interests -index coding, locally recoverable distributed storage, and guessing games on graphs- are discussed and the connection between their optimal solutions is elucidated. By generalizing…
An index code is said to be locally decodable if each receiver can decode its demand using its side information and by querying only a subset of the transmitted codeword symbols instead of observing the entire codeword. Local decodability…
To recover simultaneous multiple failures in erasure coded storage systems, Patrick Lee et al introduce concurrent repair based minimal storage regenerating codes to reduce repair traffic. The architecture of this approach is simpler and…
Sum-rank codes are an important class of codes which can be utilized for linear network coding, space-time coding and distributed storage. They can not only reduce the size of network alphabet but also detect and correct more errors. Based…