A Formula for the Capacity of the General Gel'fand-Pinsker Channel

TL;DR

This paper derives a general formula for the capacity of the Gel'fand-Pinsker channel using the information spectrum method, applicable to non-stationary, non-memoryless, and non-ergodic channels, extending previous results.

Contribution

It introduces a new capacity formula for the general Gel'fand-Pinsker channel using spectral inf- and sup-mutual information rates, broadening the scope beyond classical assumptions.

Findings

Capacity expressed as an optimization over spectral inf- and sup-mutual information rates.

Applicable to channels that are non-stationary, non-memoryless, and non-ergodic.

Special cases include memoryless but non-stationary channels.

Abstract

We consider the Gel'fand-Pinsker problem in which the channel and state are general, i.e., possibly non-stationary, non-memoryless and non-ergodic. Using the information spectrum method and a non-trivial modification of the piggyback coding lemma by Wyner, we prove that the capacity can be expressed as an optimization over the difference of a spectral inf- and a spectral sup-mutual information rate. We consider various specializations including the case where the channel and state are memoryless but not necessarily stationary.