Network Coding: An Optimization Approach

TL;DR

This paper introduces a mixed integer programming approach to compute the capacity of coded multicast networks, providing a unified framework that extends previous results and simplifies analysis for certain network families.

Contribution

It presents a novel optimization-based method for network capacity analysis, unifying and extending prior case-specific results with potential for future large noisy network studies.

Findings

Unified optimization framework for network capacity

Extension and refinement of existing capacity results

Simplified analysis for specific network families

Abstract

We consider the problem of computing the capacity of a coded, multicast network over a small alphabet. We introduce a novel approach to this problem based on mixed integer programming. As an application of our approach, we recover, extend and refine various results that were previously obtained with case-by-case analyses or specialized arguments, giving evidence of the wide applicability of our approach and its potential. We also provide two simple ideas that reduce the complexity of our method for some families of networks. We conclude the paper by outlining a research program we wish to pursue in the future to investigate the capacity of large networks affected by noise, based on the approach proposed in this paper.