Induced Weights on Quotient Modules and an Application to Error Correction in Coherent Networks

TL;DR

This paper develops a framework for error correction in quotient modules using induced distance functions, deriving bounds and applying them to coherent network error correction with adversarial errors.

Contribution

It introduces a method to define error correction in quotient modules with induced distances and extends classical bounds to this setting, applying them to network coding.

Findings

Derived analogues of Plotkin and Elias-Bassalygo bounds for quotient modules

Established asymptotic bounds for error correction in this context

Extended linear network coding schemes to handle adversarial errors

Abstract

We consider distance functions on a quotient module $M/K$ induced by distance functions on a module $M$. We define error-correction for codes in $M/K$ with respect to induced distance functions. For the case that the metric is induced by a homogeneous weight, we derive analogues of the Plotkin and Elias-Bassalygo bounds and give their asymptotic versions. These results have applications to coherent network error-correction in the presence of adversarial errors. We outline this connection, extending the linear network coding scheme introduced by Yang et al.