Related papers: The minimal set of Ingleton inequalities
An interference alignment perspective is used to identify the simplest instances (minimum possible number of edges in the alignment graph, no more than 2 interfering messages at any destination) of index coding problems where non-Shannon…
The minimal set of Shannon-type inequalities (referred to as elemental inequalities), plays a central role in determining whether a given inequality is Shannon-type. Often, there arises a situation where one needs to check whether a given…
We illustrate how computer-aided methods can be used to investigate the fundamental limits of the caching systems, which are significantly different from the conventional analytical approach usually seen in the information theory…
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…
This paper proposes lower bounds on a quantity called $L^p$-norm joint spectral radius, or in short, $p$-radius, of a finite set of matrices. Despite its wide range of applications to, for example, stability analysis of switched linear…
The Ingleton inequality is a classical linear information inequality that holds for representable matroids but fails to be universally valid for entropic vectors. Understanding the extent to which this inequality can be violated has been a…
Channel symmetry properties that imply the tightness of Shannon's random coding inner bound have recently been used to determine the capacity region of discrete-memoryless two-way channels (DM-TWCs). For channels without such symmetry…
One of the main theoretical motivations for the emerging area of network coding is the achievability of the max-flow/min-cut rate for single source multicast. This can exceed the rate achievable with routing alone, and is achievable with…
This paper investigates the problem of single-source multicasting over a communication network in the presence of restricted adversaries. When the adversary is constrained to operate only on a prescribed subset of edges, classical cut-set…
A new inner bound on the capacity region of a general index coding problem is established. Unlike most existing bounds that are based on graph theoretic or algebraic tools, the bound is built on a random coding scheme and optimal decoding,…
Explicit characterization of the capacity region of communication networks is a long standing problem. While it is known that network coding can outperform routing and replication, the set of feasible rates is not known in general.…
The question of what can be computed, and how efficiently, are at the core of computer science. Not surprisingly, in distributed systems and networking research, an equally fundamental question is what can be computed in a…
The problem of mismatched decoding for discrete memoryless channels is addressed. A mismatched cognitive multiple-access channel is introduced, and an inner bound on its capacity region is derived using two alternative encoding methods:…
An outer bound to the capacity region of the two-receiver discrete memoryless broadcast channel is given. The outer bound is tight for all cases where the capacity region is known. When specialized to the case of no common information, this…
We consider a network multicast example that relates the solvability of the multicast problem with the existence of an entropy function. As a result, we provide an alternative approach to the proving of the insufficiency of linear (and…
We study the minimum number of constraints needed to formulate random instances of the maximum stable set problem via linear programs (LPs), in two distinct models. In the uniform model, the constraints of the LP are not allowed to depend…
We consider the problem of error control in a coded, multicast network, focusing on the scenario where the errors can occur only on a proper subset of the network edges. We model this problem via an adversarial noise, presenting a formal…
Explicit characterization and computation of the multi-source network coding capacity region (or even bounds) is long standing open problem. In fact, finding the capacity region requires determination of the set of all entropic vectors…
This article focuses on Lp-estimates for the square root of elliptic systems of second order in divergence form on a bounded domain. We treat complex bounded measurable coefficients and allow for mixed Dirichlet/Neumann boundary conditions…
We show that the minimum distance projection in the L1-norm from an interior point onto the boundary of a convex set is achieved by a single, unidimensional projection. Application of this characterization when the convex set is a…