Modulo-q Sum Consensus Via Compressed Data

The goal of n nodes, each measuring a component of a source and communicating via broadcast compressed messages, is to ultimately achieve consensus, with high reliability, on the modulo-q sum of the measured data. We provide an example (specifically, a joint probability mass function for the source) for which we characterize the "K-rate region" the rates necessary and sufficient for consensus. For our example, when there are two nodes in the network, the K-rate region coincides with the Slepian-Wolf rate region. However, for more than 2 nodes, compressing for consensus can result in lower rates than compressing, as in the Slepian-Wolf formulation, for the entire data sequences in the network. We quantify the savings in rate that are obtained, when compressing for K in comparison to the Slepian-Wolf rates, as the number of nodes in the network grows.