Related papers: Computer-aided Characterization of Fundamental Lim…
It has been known that the insufficiency of linear coding in achieving the optimal rate of the general index coding problem is rooted in its rate's dependency on the field size. However, this dependency has been described only through the…
We develop a framework for approximation limits of polynomial-size linear programs from lower bounds on the nonnegative ranks of suitably defined matrices. This framework yields unconditional impossibility results that are applicable to any…
Maddah-Ali and Niesen, in a seminal paper, introduced the notion of coded caching. The exact nature of the fundamental limits in this context has remained elusive even as several approximate characterizations have been found. A new optimal…
This paper presents an algorithmic study of a class of covering mixed-integer linear programming problems which encompasses classic cover problems, including multidimensional knapsack, facility location and supplier selection problems. We…
Coded computing has emerged as a promising framework for tackling significant challenges in large-scale distributed computing, including the presence of slow, faulty, or compromised servers. In this approach, each worker node processes a…
Coded Caching, proposed by Maddah-Ali and Niesen (MAN), has the potential to reduce network traffic by pre-storing content in the users' local memories when the network is underutilized and transmitting coded multicast messages that…
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…
The problem of lossless data compression with side information available to both the encoder and the decoder is considered. The finite-blocklength fundamental limits of the best achievable performance are defined, in two different versions…
In the paper we consider the linear underdetermined system of a special type. Systems of this type appear in non-homogeneous network flow programming problems in the form of systems of constraints and can be characterized as systems with a…
Coded caching is a recently proposed technique that achieves significant performance gains for cache networks compared to uncoded caching schemes. However, this substantial coding gain is attained at the cost of large delivery delay, which…
Linear integer constraints are one of the most important constraints in combinatorial problems since they are commonly found in many practical applications. Typically, encodings to Boolean satisfiability (SAT) format of conjunctive normal…
We examine LDPC codes decoded using linear programming (LP). Four contributions to the LP framework are presented. First, a new method of tightening the LP relaxation, and thus improving the LP decoder, is proposed. Second, we present an…
Constrained coding is a fundamental field in coding theory that tackles efficient communication through constrained channels. While channels with fixed constraints have a general optimal solution, there is increasing demand for parametric…
One open problem in source coding is to characterize the limits of representing losslessly a non-identity discrete function of the data encoded independently by the encoders of several correlated sources with memory. This paper investigates…
Coded caching is a recently proposed technique for dealing with large scale content distribution over the Internet. As in conventional caching, it leverages the presence of local caches at the end users. However, it considers coding in the…
The multi-access variant of the coded caching problem with $N$ files, $K$ users and $K$ caches, where each user has access to $L$ neighbouring caches in a cyclic wrap-around manner, is considered. A cut-set based lower bound on the optimal…
We seek to impose linear, equality constraints in feedforward neural networks. As top layer predictors are usually nonlinear, this is a difficult task if we seek to deploy standard convex optimization methods and strong duality. To overcome…
Recently coded caching has emerged as a promising means to handle continuously increasing wireless traffic. However, coded caching requires users to cooperate in order to minimize the overall transmission rate. How users with heterogeneous…
This paper considers heterogeneous coded caching where the users have unequal distortion requirements. The server is connected to the users via an error-free multicast link and designs the users' cache sizes subject to a total memory…
In this work, we consider adaptive linear programming (ALP) decoding of linear codes over the finite field $\mathbb{F}_p$ of size $p$ where $p$ is a prime. In particular, we provide a general construction of valid inequalities for the…