Distributed Functional Compression through Graph Coloring

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,...

• Type: Conference
• Year: 2007
• Where: DCC
• Authors: Devavrat Shah, Muriel Médard, Sidharth Jaggi, Vishal Doshi
• Keywords: Computer Graphics, Correlation Coding, DCC 2007, Function Coding, Minimal Joint Rate