Functional Epsilon Entropy
Information Theory
2019-10-21 v1 math.IT
Abstract
We consider the problem of coding for computing with maximal distortion, where the sender communicates with a receiver, which has its own private data and wants to compute a function of their combined data with some fidelity constraint known to both agents. We show that the minimum rate for this problem is equal to the conditional entropy of a hypergraph and design practical codes for the problem. Further, the minimum rate of this problem may be a discontinuous function of the fidelity constraint. We also consider the case when the exact function is not known to the sender, but some approximate function or a class to which the function belongs is known and provide efficient achievable schemes.
Keywords
Cite
@article{arxiv.1910.08276,
title = {Functional Epsilon Entropy},
author = {Sourya Basu and Daewon Seo and Lav R. Varshney},
journal= {arXiv preprint arXiv:1910.08276},
year = {2019}
}