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15 - Network Functional Compression

Published online by Cambridge University Press:  22 March 2021

By
Soheil Feizi  and
Muriel Mérd
Edited by
Miguel R. D. Rodrigues  and
Yonina C. Eldar
Miguel R. D. Rodrigues
Affiliation:
University College London
Yonina C. Eldar
Affiliation:
Weizmann Institute of Science, Israel
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Summary

We study compression for function computation of sources at nodes in a network at receiver(s). The rate region of this problem has been considered under restrictive assumptions. We present results that significantly relax these assumptions. For a one-stage tree network, we characterize a rate region by a necessary and sufficient condition for any achievable coloring-based coding scheme, the coloring connectivity condition. We propose a modularized coding scheme based on graph colorings to perform arbitrarily closely to derived rate lower bounds. For a general tree network, we provide a rate lower bound based on graph entropies and show that it is tight for independent sources. We show that, in a general tree network case with independent sources, to achieve the rate lower bound, intermediate nodes should perform computations, but for a family of functions and random variables, which we call chain-rule proper sets, it suffices to have no computations at intermediate nodes to perform arbitrarily closely to the rate lower bound. We consider practicalities of coloring-based coding schemes and propose an efficient algorithm to compute a minimum-entropy coloring of a characteristic graph.

Keywords

compressionnetwork functional compressionnetwork coding
Type
Chapter
Information
Information-Theoretic Methods in Data Science , pp. 455 - 486
Publisher: Cambridge University Press
Print publication year: 2021

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