On function computation over a cascade network

Abstract

A transmitter has access to X, a relay has access to Y, and a receiver has access to Z and wants to compute a given function f(X, Y, Z). How many bits must be transmitted from the transmitter to the relay and from the relay to the receiver so that the latter can reliably recover f(X, Y, Z)? The main result is an inner bound to the rate region of this problem which is tight when X - Y - Z forms a Markov chain.