Simple Bounds for Lossless Source Coding in A Two-Hop Network

We describe new upper bounds on the lower convex hull of the lossless source coding region for a simple three-node network. While the given bound may not be tight, its advantage lies in its simplicity. Precisely, it allows us to easily calculate meaningful numerical bounds for all possible source distributions. This property contrasts markedly with earlier results where solutions characterized in terms of auxiliary random variables make it difficult to quantify results for a given distribution. The given result represents a first step in developing techniques for finding loose, calculable bounds for network source coding performance. Such techniques are likely to play a critical role in the advancement of this difficult field.