3 research outputs found
Distributed Function Computation in Asymmetric Communication Scenarios
We consider the distributed function computation problem in asymmetric
communication scenarios, where the sink computes some deterministic function of
the data split among N correlated informants. The distributed function
computation problem is addressed as a generalization of distributed source
coding (DSC) problem. We are mainly interested in minimizing the number of
informant bits required, in the worst-case, to allow the sink to exactly
compute the function. We provide a constructive solution for this in terms of
an interactive communication protocol and prove its optimality. The proposed
protocol also allows us to compute the worst-case achievable rate-region for
the computation of any function. We define two classes of functions: lossy and
lossless. We show that, in general, the lossy functions can be computed at the
sink with fewer number of informant bits than the DSC problem, while
computation of the lossless functions requires as many informant bits as the
DSC problem.Comment: 10 pages, 6 figures, 2 table
Worst-case Compressibility of Discrete and Finite Distributions
In the worst-case distributed source coding (DSC) problem of [1], the smaller
cardinality of the support-set describing the correlation in informant data,
may neither imply that fewer informant bits are required nor that fewer
informants need to be queried, to finish the data-gathering at the sink. It is
important to formally address these observations for two reasons: first, to
develop good worst-case information measures and second, to perform meaningful
worst-case information-theoretic analysis of various distributed data-gathering
problems. Towards this goal, we introduce the notions of bit-compressibility
and informant-compressibility of support-sets. We consider DSC and distributed
function computation problems and provide results on computing the bit- and
informant- compressibilities regions of the support-sets as a function of their
cardinality.Comment: 5 pages, 3 figure