Index Assignment for Multichannel Communication under Failure

TL;DR

This paper addresses the challenge of optimizing index assignment in multichannel communication systems to minimize distortion, providing new bounds and algorithms for systems with multiple channels, including the first results for more than two channels.

Contribution

It introduces a novel combinatorial optimization framework for index assignment in multichannel systems and derives the first bounds for systems with more than two channels.

Findings

Derived lower bounds on distortion for fixed channel rates.

Developed an algorithm for near-optimal index assignment.

Established the equivalence to bandwidth minimization in Hamming graphs.

Abstract

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 maximum difference between the largest and the smallest number in any row or column. We develop a technique for deriving lower bounds on the distortion at given channel rates. The approach is constructive, thus allowing an algorithm that gives a closely matching upper bound. For the case of two communication channels with equal rates, the bounds coincide, thus giving the precise lowest achievable distortion at fixed rates. The bounds are within a small constant for higher number of channels. To the best of our knowledge, this is the first result concerning systems with more than two communication channels. The problem is also equivalent to the bandwidth minimization problem of Hamming graphs.