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We consider the problem of data collection in a two-layer network consisting of (1) noisy links between N distributed agents and a remote sink node; (2) a noisy sparse network formed by these distributed agents. We jointly consider the design of the optimal graph topology for the inter-agent network and the in-network computing scheme under the sparsity constraint and the energy constraint, and study the effect of inter-agent communications on the overall energy consumption. Despite the sparse connections between agents, we provide an in-network coding scheme that reduces the overall energy consumption by a factor of &#x0398;(logN) compared to a naive scheme based on direct agent-to-sink communications only. By providing lower bounds on both the energy consumption and the sparseness (number of links) of the network, we show that the proposed scheme is energy-optimal except for a factor of &#x0398;(log logN). The proposed scheme extends a previous work of Gallager [2] on noisy broadcasting from a complete graph to a sparse graph, while bringing in new techniques from error control coding and noisy circuits.

Energy efficient distributed coding for data collection in a noisy sparse network