Computation Over Gaussian Networks With Orthogonal Components

Function computation over Gaussian networks with orthogonal components is studied for arbitrarily correlated discrete memoryless sources. Two classes of functions are considered: 1) the arithmetic sum function and 2) the type function. The arithmetic sum function in this paper is defined as a set of multiple weighted arithmetic sums, which includes averaging of the sources and estimating each of the sources as special cases. The type or frequency histogram function counts the number of occurrences of each argument, which yields various fundamental statistics, such as mean, variance, maximum, minimum, median, and so on. The proposed computation coding first abstracts Gaussian networks into the corresponding modulo sum multiple-access channels via nested lattice codes and linear network coding and then computes the desired function using linear Slepian-Wolf source coding. For orthogonal Gaussian networks (with no broadcast and multiple-access components), the computation capacity is characterized for a class of networks. For Gaussian networks with multiple-access components (but no broadcast), an approximate computation capacity is characterized for a class of networks.


Published in:
IEEE Transactions on Information Theory, 60, 12, 7841-7861
Year:
2014
Publisher:
Piscataway, Institute of Electrical and Electronics Engineers
ISSN:
0018-9448
Keywords:
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 Record created 2014-11-21, last modified 2018-09-13

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