Information dissipation in noiseless lossy in-network function computation

We consider the problem of distributed lossy linear function computation in a tree network. We examine two cases: (i) data aggregation (only one sink node computes) and (ii) consensus (all nodes compute the same function). By quantifying the information dissipation in distributed computing, we obtain fundamental limits on network computation rate as a function of incremental distortions (and hence incremental information dissipation) along the edges of the network, and not just the overall distortions used classically. Combining this observation with an inequality on the dominance of mean-square measures over relative-entropy measures, we obtain lower bounds on the rate-distortion function that are tighter than classical cut-set bounds by a difference which can be arbitrarily large in both data aggregation and consensus.