1A Formula for the Capacity of the General Gel’fand-Pinsker Channel

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 spec-trum 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. Index Terms—Gel’fand-Pinsker, Information spectrum, Gen-eral channels, General source