Bounds on rate distortion with feed forward for stationary and ergodic sources

Abstract

THIS PAPER IS ELIGIBLE FOR THE STUDENT PAPER AWARD. Consider the rate distortion problem of discrete-time, ergodic, and stationary sources with feed forward at the receiver. We derive a sequence of achievable and computable rates that converge to the feed forward rate distortion. For ergodic and stationary sources, we show that for any n, the rate equation is achievable, where the minimization is taken over the transition conditioning probability p(xn∣xn) such that equation. The limit of R n (D) exists and is the feed forward rate distortion. We follow Gallager's proof where there is no feed forward, and, with appropriate modification, obtain our result. We provide an algorithm for calculating R n (D) using the alternating minimization procedure, and present several numerical examples.