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

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 R_n(D)=1/n min I(X̂ⁿ →Xⁿ) is achievable, where the minimization is taken over the transition conditioning probability p(x̂ⁿ|xⁿ) such that E[d(Xⁿ, X̂ⁿ)] ≤ D. 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.