Related papers: The minimal set of Ingleton inequalities
A framework for linear-programming (LP) decoding of nonbinary linear codes over rings is developed. This framework facilitates linear-programming based reception for coded modulation systems which use direct modulation mapping of coded…
Characterising the capacity region for a network can be extremely difficult. Even with independent sources, determining the capacity region can be as hard as the open problem of characterising all information inequalities. The majority of…
We develop a new `subspace layered least squares' interior point method (IPM) for solving linear programs. Applied to an $n$-variable linear program in standard form, the iteration complexity of our IPM is up to an $O(n^{1.5} \log n)$…
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…
We apply polynomial techniques (linear programming) to obtain lower and upper bounds on the covering radius of spherical designs as function of their dimension, strength, and cardinality. In terms of inner products we improve the lower…
An inexact Newton type method for numerical minimization of convex piecewise quadratic functions is considered and its convergence is analyzed. Earlier, a similar method was successfully applied to optimizaton problems arising in numerical…
The bandwidth of a graph is the labeling of vertices with minimum maximum edge difference. For many graph families this is NP-complete. A classic result computes the bandwidth for the hypercube. We generalize this result to give sharp lower…
Channel capacity bounds are derived for a point-to-point indoor visible light communications (VLC) system with signal-dependent Gaussian noise. Considering both illumination and communication, the non-negative input of VLC is constrained by…
Linear constraints for a matrix polytope with no fractional vertex are investigated as intersecting research among permutation codes, rank modulations, and linear programming methods. By focusing the discussion to the block structure of…
In this paper, the analysis of the performance of the concatenation of a short polar code with an outer binary linear block code is addressed from a distance spectrum viewpoint. The analysis targets the case where an outer cyclic code is…
Efficient decoding is crucial to high-throughput and power-sensitive wireless communication scenarios. A theoretical analysis of the performance-complexity tradeoff toward low-complexity decoding is required for a better understanding of…
We present a class of linear programming approximations for constrained optimization problems. In the case of mixed-integer polynomial optimization problems, if the intersection graph of the constraints has bounded tree-width our…
We generalise some well-known graph parameters to operator systems by considering their underlying quantum channels. In particular, we introduce the quantum complexity as the dimension of the smallest co-domain Hilbert space a quantum…
In this paper, we discuss the algorithm engineering aspects of an O(n^2)-time algorithm [6] for computing a minimum-area convex polygon that intersects a set of n isothetic line segments.
This paper is concerned with the analysis of the randomized subspace iteration for the computation of low-rank approximations. We present three different kinds of bounds. First, we derive both bounds for the canonical angles between the…
The capacity of the AWGN broadcast channel is achieved by superposition coding, but superposition of individual coded modulations expands the modulation alphabet and distorts its configuration. Coded modulation over a broadcast channel…
The goal of this paper is to derive new classes of valid convex inequalities for quadratically constrained quadratic programs (QCQPs) through the technique of lifting. Our first main result shows that, for sets described by one bipartite…
In this paper, we present an improved union bound on the Linear Programming (LP) decoding performance of the binary linear codes transmitted over an additive white Gaussian noise channels. The bounding technique is based on the second-order…
We present novel bounds on the capacity of the independent and identically distributed binary deletion channel. Four upper bounds are obtained by providing the transmitter and the receiver with genie-aided information on suitably-defined…
Nonlocal correlations created in networks with multiple independent sources enable surprising phenomena in quantum information and quantum foundations. The presence of independent sources, however, makes the analysis of network nonlocality…