When Shannon Meets Nonstochastic Information: Communication and Estimation

Abstract

This note focuses on the issue of whether or not the state of a plant can be estimated when the inputs of communication channel involve noise and disturbance simultaneously. It turns out to calculate the maximum capacity of stationary memoryless M-MQAC under nonstochastic information theory. It is shown that the maximum information rate over such a channel is determined by a convex hull spanned by the zero-error capacities, which are specified on the underlying sample spaces. Moreover, the state of a plant could be estimated provided that the maximal information rate is strictly greater than the topology entropy.