Two-Party Zero-Error Function Computation with Asymmetric Priors

Abstract

Abstract:We consider a two party network where each party wishes to compute a function of two correlated sources. Each source is observed by one of the parties. The true joint distribution of the sources is known to one party. The other party, on the other hand, assumes a distribution for which the set of source pairs that have a positive probability is only a subset of those that may appear in the true distribution. In that sense, this party has only partial information about the true distribution from which the sources are generated. We study the impact of this asymmetry on the worst-case message length for zero-error function computation, by identifying the conditions under which reconciling the missing information prior to communication is better than not reconciling it but instead using an interactive protocol that ensures zero-error communication without reconciliation. Accordingly, we provide upper and lower bounds on the minimum worst-case message length for the communication strategies with and without reconciliation. Through specializing the proposed model to certain distribution classes, we show that partially reconciling the true distribution by allowing a certain degree of ambiguity can perform better than the strategies with perfect reconciliation as well as strategies that do not start with an explicit reconciliation step. As such, our results demonstrate a tradeoff between the reconciliation and communication rates, and that the worst-case message length is a result of the interplay between the two factors.