Statistical mechanics of optimal networked source coding,” preprint. 24 T. Mutayama, “Statistical mechanics of the data compression theorem

Abstract — We consider a large scale network of autonomous sensors each equipped with a local encoder and a local decoder. The nodes collaborate to reproduce a distributed source using a multiple description code (MDC). Each local encoder is a side encoder of MDC, producing one of the many descriptions and broadcasts its encoding to all its neighbors via an unreliable network. Each local decoder reconstructs the source using descriptions received from its neighbors along with the locally encoded description. Since duplicate descriptions arrived at a node will benefit it less, side MDC encoders should be assigned to nodes in such a way that, in an average sense, nodes receive the most number of distinct descriptions. This optimization problem is particularly challenging if the assignment has to be determined locally without central knowledge of the network. For simple network topologies, we consider the global orchestration of the nodes using a family of stochastic optimization algorithms, namely simulated annealing. Analogies to statistical mechanical models such as the antiferromagnetic Ising models are drawn which allow us to analytically derive the average distortion at steady state and characterize the ordering (and lack of it) in the assignments as a function of protocol parameters. I