Related papers: An Optimal Linear Coding for Index Coding Problem
This paper studies the problem of linear precoding for multiple-input multiple-output (MIMO) communication channels employing finite-alphabet signaling. Existing solutions typically suffer from high computational complexity due to costly…
The notion of symmetry is defined in the context of Linear and Integer Programming. Symmetric linear and integer programs are studied from a group theoretical viewpoint. We show that for any linear program there exists an optimal solution…
We study the channel coding problem when errors and uncertainty occur in the encoding process. For simplicity we assume the channel between the encoder and the decoder is perfect. Focusing on linear block codes, we model the encoding…
We study the problem of reducing the communication overhead from a noisy wire-tap channel or storage system where data is encoded as a matrix, when more columns (or their linear combinations) are available. We present its applications to…
Typical behavior of the linear programming problem (LP) is studied as a relaxation of the minimum vertex cover problem, which is a type of the integer programming problem (IP). To deal with the LP and IP by statistical mechanics, a…
Quantifying extra functions, herein referred to as outcome functions, over optimal solutions of an optimization problem can provide decision makers with additional information on a system. This bears more importance when the optimization…
The index coding problem involves a sender with K messages to be transmitted across a broadcast channel, and a set of receivers each of which demands a subset of the K messages while having prior knowledge of a different subset as side…
We propose a simple yet effective wireless network coding and decoding technique for a multiple unicast network. It utilizes spatial diversity through cooperation between nodes which carry out distributed encoding operations dictated by…
In large scale distributed linear transform problems, coded computation plays an important role to effectively deal with "stragglers" (distributed computations that may get delayed due to few slow or faulty processors). We propose a coded…
The question of whether to use one classifier or a combination of classifiers is a central topic in Machine Learning. We propose here a method for finding an optimal linear combination of classifiers derived from a bias-variance framework…
The following source coding problem was introduced by Birk and Kol: a sender holds a word $x\in\{0,1\}^n$, and wishes to broadcast a codeword to $n$ receivers, $R_1,...,R_n$. The receiver $R_i$ is interested in $x_i$, and has prior…
According to the structural balance theory, a signed graph is considered structurally balanced when it can be partitioned into a number of modules such that positive and negative edges are respectively located inside and between the…
In the algebraic view, the solution to a network coding problem is seen as a variety specified by a system of polynomial equations typically derived by using edge-to-edge gains as variables. The output from each sink is equated to its…
The Interior-Point Methods are a class for solving linear programming problems that rely upon the solution of linear systems. At each iteration, it becomes important to determine how to solve these linear systems when the constraint matrix…
In this paper, we present a generalized version of the matrix chain algorithm to generate efficient code for linear algebra problems, a task for which human experts often invest days or even weeks of works. The standard matrix chain problem…
We present an analysis of the transductive node classification problem, where the underlying graph consists of communities that agree with the node labels and node features. For node classification, we propose a novel optimization problem…
Research efforts of the past fifty years have led to a development of linear integer programming as a mature discipline of mathematical optimization. Such a level of maturity has not been reached when one considers nonlinear systems subject…
Error correction codes are a crucial part of the physical communication layer, ensuring the reliable transfer of data over noisy channels. The design of optimal linear block codes capable of being efficiently decoded is of major concern,…
When two or more users in a wireless network transmit simultaneously, their electromagnetic signals are linearly superimposed on the channel. As a result, a receiver that is interested in one of these signals sees the others as unwanted…
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…