Related papers: Constrained coding upper bounds via Goulden-Jackso…
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…
The two-user broadcast channel (BC) with receivers connected by bidirectional cooperation links of finite capacities, known as conferencing decoders, is considered. A novel capacity region outer bound is established based on multiple…
In this work, we present an abstract framework for some algebraic error-correcting codes with the aim of capturing codes that are list-decodable to capacity, along with their decoding algorithm. In the polynomial ideal framework, a code is…
Cicho\'n's diagram describes the connections between combinatorial notions related to measure, category, and compactness of sets of irrational numbers. In the second part of the 2010's, Goldstern, Kellner and Shelah constructed a forcing…
Huffman coding is well known to be useful in certain decision problems involving minimizing the average number of (freely chosen) queries to determine an unknown random variable. However, in problems where the queries are more constrained,…
We improve Levenshtein's upper bound for the cardinality of a code of length four that is capable of correcting single deletions over an alphabet of even size. We also illustrate that the new upper bound is sharp. Furthermore we construct…
We construct a new family of explicit codes that are list decodable to capacity and achieve an optimal list size of $O(\frac{1}{\epsilon})$. In contrast to existing explicit constructions of codes achieving list decoding capacity, our…
Locally recoverable (LRC) codes have recently been a focus point of research in coding theory due to their theoretical appeal and applications in distributed storage systems. In an LRC code, any erased symbol of a codeword can be recovered…
Let $A_q(n,d)$ be the maximum order (maximum number of codewords) of a $q$-ary code of length $n$ and Hamming distance at least $d$. And let $A(n,d,w)$ that of a binary code of constant weight $w$. Building on results from algebraic graph…
The uplink of a Cloud Radio Access Network (CRAN) architecture is studied, where decoding at the cloud takes place at distributed decoding processors. To mitigate the impact of straggling decoders in the cloud, the cloud re-encodes the…
The pivotal storage density win achieved by solid-state devices over magnetic devices recently is a result of multiple innovations in physics, architecture, and signal processing. Constrained coding is used in Flash devices to increase…
We study the classic Max-Cut problem under multiple cardinality constraints, which we refer to as the Constrained Max-Cut problem. Given a graph $G=(V, E)$, a partition of the vertices into $c$ disjoint parts $V_1, \ldots, V_c$, and…
The degree of a CSP instance is the maximum number of times that any variable appears in the scopes of constraints. We consider the approximate counting problem for Boolean CSP with bounded-degree instances, for constraint languages…
Constrained sequence codes have been widely used in modern communication and data storage systems. Sequences encoded with constrained sequence codes satisfy constraints imposed by the physical channel, hence enabling efficient and reliable…
This paper investigates properties of concatenated polar codes and their potential applications. We start with reviewing previous work on stopping set analysis for conventional polar codes, which we extend in this paper to concatenated…
In this work, a coding technique called cost constrained Geometric Huffman coding (ccGhc) is developed. ccGhc minimizes the Kullback-Leibler distance between a dyadic probability mass function (pmf) and a target pmf subject to an affine…
Constraint "at most one" is a basic cardinality constraint which requires that at most one of its $n$ boolean inputs is set to $1$. This constraint is widely used when translating a problem into a conjunctive normal form (CNF) and we…
Huffman coding finds an optimal prefix code for a given probability mass function. Consider situations in which one wishes to find an optimal code with the restriction that all codewords have lengths that lie in a user-specified set of…
In many high-dimensional problems,polynomial-time algorithms fall short of achieving the statistical limits attainable without computational constraints. A powerful approach to probe the limits of polynomial-time algorithms is to study the…
Biclustering techniques have been widely used to identify homogeneous subgroups within large data matrices, such as subsets of genes similarly expressed across subsets of patients. Mining a max-sum sub-matrix is a related but distinct…