Network Information Flow with Correlated Sources

TL;DR

This paper demonstrates that in a network with correlated sources and point-to-point channels, source and channel coding can be separated, with information flow behaving like classical network flow, enabling layered protocol implementation.

Contribution

It proves a source/channel separation theorem for correlated sources over networks with point-to-point channels, showing information flow parallels classical network flow.

Findings

Perfect reconstruction condition based on network cuts and entropy

Separation theorem holds under specified network conditions

Information flow analogy supports layered protocol design

Abstract

In this paper, we consider a network communications problem in which multiple correlated sources must be delivered to a single data collector node, over a network of noisy independent point-to-point channels. We prove that perfect reconstruction of all the sources at the sink is possible if and only if, for all partitions of the network nodes into two subsets S and S^c such that the sink is always in S^c, we have that H(U_S|U_{S^c}) < \sum_{i\in S,j\in S^c} C_{ij}. Our main finding is that in this setup a general source/channel separation theorem holds, and that Shannon information behaves as a classical network flow, identical in nature to the flow of water in pipes. At first glance, it might seem surprising that separation holds in a fairly general network situation like the one we study. A closer look, however, reveals that the reason for this is that our model allows only for independent point-to-point channels between pairs of nodes, and not multiple-access and/or broadcast channels, for which separation is well known not to hold. This ``information as flow'' view provides an algorithmic interpretation for our results, among which perhaps the most important one is the optimality of implementing codes using a layered protocol stack.