NDLI: Distributed Functional Compression through Graph Coloring

Content Provider	IEEE Xplore Digital Library
Author	Doshi, V. Shah, D. Medard, M. Jaggi, S.
Copyright Year	2007
Description	Author affiliation: Lab. for Inf. & Decision Syst., Massachusetts Inst. of Technol., MA (Doshi, V.; Shah, D.; Medard, M.; Jaggi, S.)
Abstract	We consider the distributed computation of a function of random sources with minimal communication. Specifically, given two discrete memoryless sources, X and Y, a receiver wishes to compute f(X, Y) based on (encoded) information sent from X and Y in a distributed manner. A special case, f(X, Y) = (X, Y), is the classical question of distributed source coding considered by Slepian and Wolf (1973). Orlitsky and Roche (2001) considered a somewhat restricted setup when Y is available as side information at the receiver. They characterized the minimal rate at which X needs to transmit data to the receiver as the conditional graph entropy of the characteristic graph of X based on f. In our recent work (2006), we further established that this minimal rate can be achieved by means of graph coloring and distributed source coding (e.g. Slepian-Wolf coding). This characterization allows for the separation between "function coding" and "correlation coding." In this paper, we consider a more general setup where X and Y are both encoded (separately). This is a significantly harder setup for which to give a single-letter characterization for the complete rate region. We find that under a certain condition on the support set of X and Y (called the zigzag condition), it is possible to characterize the rate region based on graph colorings at X and Y separately. That is, any achievable pair of rates can be realized by means of first coloring graphs at X and Y separately (function coding) and then using Slepian-Wolf coding for these colors (correlation coding). We also obtain a single-letter characterization of the minimal joint rate. Finally, we provide simulation results based on graph coloring to establish the rate gains on real sequences
Starting Page	93
Ending Page	102
File Size	211433
Page Count	10
File Format	PDF
ISBN	0769527914
ISSN	10680314
DOI	10.1109/DCC.2007.34
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2007-03-27
Publisher Place	USA
Access Restriction	Subscribed
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Source coding Decoding Distributed computing Sensor phenomena and characterization Data compression Laboratories Entropy Computational modeling Relays Encoding
Content Type	Text
Resource Type	Article
Subject	Computer Networks and Communications

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