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Distributed averaging, or distributed average consensus, is a common methodfor computing the sample mean of the data dispersed among the nodes of anetwork in a decentralized manner. By iteratively exchanging messages withneighbors, the nodes of the network can converge to an agreement on the samplemean of their initial states. In real-world scenarios, these messages aresubject to bandwidth and power constraints, which motivates the design of alossy compression strategy. Few prior works consider the rate allocationproblem from the perspective of constrained optimization, which provides aprincipled method for the design of lossy compression schemes, allows for therelaxation of certain assumptions, and offers performance guarantees. We showfor Gaussian-distributed initial states with entropy-coded scalar quantizationand vector quantization that the coding rates for distributed averaging can beoptimized through generalized geometric programming. In the absence of sideinformation from past states, this approach finds a rate allocation over nodesand iterations that minimizes the aggregate coding rate required to achieve atarget mean square error within a finite run time. Our rate allocation iscompared to some of the prior art through numerical simulations. The resultsmotivate the incorporation of side-information through differential orpredictive coding to improve rate-distortion performance.

Generalized Geometric Programming for Rate Allocation in Consensus