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Self-orthogonal codes are a subclass of linear codes that are contained within their dual codes. Since self-orthogonal codes are widely used in quantum codes, lattice theory and linear complementary dual (LCD) codes, they have received…
A new ensemble of structured codes is introduced. These codes are called Quasi Linear Codes (QLC). The QLC's are constructed by taking subsets of linear codes. They have a looser structure compared to linear codes and are not closed under…
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…
In a classical covering problem, we are given a set of requests that we need to satisfy (fully or partially), by buying a subset of items at minimum cost. For example, in the k-MST problem we want to find the cheapest tree spanning at least…
We construct constant-sized ensembles of linear error-correcting codes over any fixed alphabet that can correct a given fraction of adversarial erasures at rates approaching the Singleton bound arbitrarily closely. We provide several…
The paper considers the minimization of a separable convex function subject to linear ascending constraints. The problem arises as the core optimization in several resource allocation scenarios, and is a special case of an optimization of a…
We examine an error-correcting coding framework in which each coded symbol is constrained to be a function of a fixed subset of the message symbols. With an eye toward distributed storage applications, we seek to design systematic codes…
Linear erasure codes with local repairability are desirable for distributed data storage systems. An [n, k, d] code having all-symbol (r, \delta})-locality, denoted as (r, {\delta})a, is considered optimal if it also meets the minimum…
In this paper, we consider the problem of recursively designing uniquely decodable ternary code sets for highly overloaded synchronous code-division multiple-access (CDMA) systems. The proposed code set achieves larger number of users $K <…
As a subclass of linear codes, cyclic codes have efficient encoding and decoding algorithms, so they are widely used in many areas such as consumer electronics, data storage systems and communication systems. In this paper, we give a…
Spatially-coupled (SC) LDPC codes have recently emerged as an excellent choice for error correction in modern data storage and communication systems due to their outstanding performance. It has long been known that irregular graph codes…
Error-correcting codes are usually envisioned to counter errors by operating unitary corrections depending on the projective measurement results of some syndrome observables. We here propose a way to use them in a more integrated way, where…
We introduce a unified generalization of several well-established high-throughput coding techniques including staircase codes, tiled diagonal zipper codes, continuously interleaved codes, open forward error correction (OFEC) codes, and…
A circulant-based spatially-coupled (SC) code is constructed by partitioning the circulants in the parity-check matrix of a block code into several components and piecing copies of these components in a diagonal structure. By connecting…
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…
Index coding, a source coding problem over broadcast channels, has been a subject of both theoretical and practical interest since its introduction (by Birk and Kol, 1998). In short, the problem can be defined as follows: there is an input…
We introduce {\bf complementary information set codes} of higher-order. A binary linear code of length $tk$ and dimension $k$ is called a complementary information set code of order $t$ ($t$-CIS code for short) if it has $t$ pairwise…
A circulant-based spatially-coupled (SC) code is constructed by partitioning the circulants of an underlying block code into a number of components, and then coupling copies of these components together. By connecting (coupling) several SC…
Separable codes were introduced to provide protection against illegal redistribution of copyrighted multimedia material. Let $\mathcal{C}$ be a code of length $n$ over an alphabet of $q$ letters. The descendant code ${\sf…
We consider a communication problem in which an update of the source message needs to be conveyed to one or more distant receivers that are interested in maintaining specific linear functions of the source message. The setting is one in…