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Computable Bounds for Rate Distortion With Feed Forward for Stationary and Ergodic Sources

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2 Author(s)
Naiss, I. ; Dept. of Electr. & Comput. Eng., Ben-Gurion Univ. of the Negev, Beer-Sheva, Israel ; Permuter, H.H.

In this paper, we 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. We show that for ergodic and stationary sources, the rate Rn(D) = 1/n min IX̂n → Xn) is achievable for any n, where the minimization is performed over the transition conditioning probability p(x̂n|xn) such that E [d(Xn, X̂n] ≤ D. We also show that the limit of Rn(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 Rn(D) using the alternating minimization procedure and present several numerical examples. We also present a dual form for the optimization of Rn(D) and transform it into a geometric programming problem.

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Information Theory, IEEE Transactions on  (Volume:59 ,  Issue: 2 )