Related papers: A Matrix Completion Approach to Linear Index Codin…
Reliable and low latency multicast communication is important for future vehicular communication. Sparse random linear network coding approach used to ensure the reliability of multicast communication has been widely investigated. A…
Finite linear least squares is one of the core problems of numerical linear algebra, with countless applications across science and engineering. Consequently, there is a rich and ongoing literature on algorithms for solving linear least…
Low-rank matrix completion consists of computing a matrix of minimal complexity that recovers a given set of observations as accurately as possible. Unfortunately, existing methods for matrix completion are heuristics that, while highly…
An index coding problem is called unicast-uniprior when each receiver demands a unique subset of messages while knowing another unique subset of messages apriori as side-information. In this work, we give an algorithm to compute the minrank…
We present new deterministic algorithms for several cases of the maximum rank matrix completion problem (for short matrix completion), i.e. the problem of assigning values to the variables in a given symbolic matrix as to maximize the…
We study three fundamental problems of Linear Algebra, lying in the heart of various Machine Learning applications, namely: 1)"Low-rank Column-based Matrix Approximation". We are given a matrix A and a target rank k. The goal is to select a…
Set- and vector-valued optimization problems can be re-formulated as complete lattice-valued problems. This has several advantages, one of which is the existence of a clear-cut solution concept which includes the attainment as the infimum…
In this paper, we present FPT-algorithms for special cases of the shortest lattice vector, integer linear programming, and simplex width computation problems, when matrices included in the problems' formulations are near square. The…
In the pliable variant of index coding, receivers are allowed to decode any new message not known a priori. Optimal code design for this variant involves identifying each receiver's choice of a new message that minimises the overall…
In color image processing, image completion aims to restore missing entries from the incomplete observation image. Recently, great progress has been made in achieving completion by approximately solving the rank minimization problem. In…
We consider the problem of multiple description scalar quantizers and describing the achievable rate-distortion tuples in that setting. We formulate it as a combinatorial optimization problem of arranging numbers in a matrix to minimize the…
Originally developed for imputing missing entries in low rank, or approximately low rank matrices, matrix completion has proven widely effective in many problems where there is no reason to assume low-dimensional linear structure in the…
We are interested in finding a solution to the tensor complementarity problem with a strong M-tensor, which we call the M-tensor complementarity problem. We propose a lower dimensional linear equation approach to solve that problem. At each…
We consider the problem of efficiently solving large-scale linear least squares problems that have one or more linear constraints that must be satisfied exactly. Whilst some classical approaches are theoretically well founded, they can face…
The essence of distantly supervised relation extraction is that it is an incomplete multi-label classification problem with sparse and noisy features. To tackle the sparsity and noise challenges, we propose solving the classification…
The affine rank minimization problem consists of finding a matrix of minimum rank that satisfies a given system of linear equality constraints. Such problems have appeared in the literature of a diverse set of fields including system…
The index coding problem aims to optimise broadcast communication by taking advantage of receiver-side information to improve transmission efficiency. In this letter, we explore the application of Construction $\pi_A$ lattices to index…
An approach is established for maximizing the Lower bound on the Mismatch capacity (hereafter abbreviated as LM rate), a key performance bound in mismatched decoding, by optimizing the channel input probability distribution. Under a fixed…
While linear programming (LP) decoding provides more flexibility for finite-length performance analysis than iterative message-passing (IMP) decoding, it is computationally more complex to implement in its original form, due to both the…
Content delivery networks often employ caching to reduce transmission rates from the central server to the end users. Recently, the technique of coded caching was introduced whereby coding in the caches and coded transmission signals from…