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Abstract: We study the limits of communication efficiency for function computation incollocated networks within the framework of multi-terminal block source codingtheory. With the goal of computing a desired function of sources at a sink,nodes interact with each other through a sequence of error-free, network-widebroadcasts of finite-rate messages. For any function of independent sources, wederive a computable characterization of the set of all feasible message codingrates - the rate region - in terms of single-letter information measures. Weshow that when computing symmetric functions of binary sources, the sink willinevitably learn certain additional information which is not demanded incomputing the function. This conceptual understanding leads to new improvedbounds for the minimum sum-rate. The new bounds are shown to be orderwisebetter than those based on cut-sets as the network scales. The scaling law ofthe minimum sum-rate is explored for different classes of symmetric functionsand source parameters.



Autor: Nan Ma, Prakash Ishwar, Piyush Gupta

Fuente: https://arxiv.org/







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