Information structures of capacity achieving distribution for channels with memory and feedback

Abstract

The information structures of the optimal channel input distributions P[0,n] t {PAi|Ai-1,Bi-1 : i = 0,1.,n}, which correspond to the extremum problem of feedback capacity equation are identified, for any class of channel distributions {PBi|Bi-1,Ai : i = 0,1.,n} and equation, where Bn t {Bj : j = 0,1.,n} are the channel output RVs, An t {Aj : j = 0,1.,n} are the channel inputs RVs, and M is a finite nonnegative integer. The methodology utilizes stochastic optimal control theory, to identify the control process, the controlled process, and a variational equality of directed information, to derive upper bounds on I(An → Bn) t Σi=0 nI(Ai;Bi|Bi-1), which are achievable over specific subsets of P[0,n], which satisfy conditional independence. The main theorem states, that for any channel with memory M, the optimal channel input conditional distribution occur in the subset equation, and the corresponding extremum problem simplifies to the following characterization. equation. © 2016 IEEE.