On the asymptotic spectrum of the error probability of composite networks

This paper investigates composite multiterminal networks which consist of a set of multiterminal channels indexed or parametrized by a vector of channel parameters θ. The channel in operation is drawn from the sample set with probability P_θ. Instead of finding the maximum achievable rate subject to a -asymptotically- small error probability (EP), we look at the behavior of the error probability for a fixed coding rate. The asymptotic spectrum of error probability (ASEP) is then introduced as a novel and more general performance measure for composite networks. Indeed, the ASEP is defined as the smallest probability that the EP exceeds a desirable error ε for a coding rate r. It is shown that the ASEP is directly related to the ε-capacity of the network and assuming memoryless channels the ASEP can be bounded by a new region referred to as the full error region. Moreover, every code with a rate belonging to this region yields asymptotic EP equal to one.