Network Coding: Connections Between Information Theory And Estimation Theory

TL;DR

This paper establishes fundamental mathematical relations between information theory and estimation theory in network-coded systems, revealing insights into network capacity, topology effects, and potential for optimized precoding solutions.

Contribution

It proves the existence of closed-form relations between mutual information gradients and system matrices in network coding, linking network topology and capacity analysis.

Findings

Existence of closed-form relations between mutual information and system matrices.

Insights into effects of network topology, node mobility, errors, and delays.

Implications for network capacity and precoding solutions.

Abstract

In this paper, we prove the existence of fundamental relations between information theory and estimation theory for network-coded flows. When the network is represented by a directed graph G=(V, E) and under the assumption of uncorrelated noise over information flows between the directed links connecting transmitters, switches (relays), and receivers. We unveil that there yet exist closed-form relations for the gradient of the mutual information with respect to different components of the system matrix M. On the one hand, this result opens a new class of problems casting further insights into effects of the network topology, topological changes when nodes are mobile, and the impact of errors and delays in certain links into the network capacity which can be further studied in scenarios where one source multi-sinks multicasts and multi-source multicast where the invertibility and the rank of matrix M plays a significant role in the decoding process and therefore, on the network capacity. On the other hand, it opens further research questions of finding precoding solutions adapted to the network level.