Abstract
We consider the rate distortion problem with side information at the decoder posed and investigated by Wyner and Ziv. Using side information and encoded original data, the decoder must reconstruct the original data with an arbitrary prescribed distortion level. The rate distortion region indicating the trade-off between a data compression rate R and a prescribed distortion level was determined by Wyner and Ziv. In this paper, we study the error probability of decoding for pairs of outside the rate distortion region. We evaluate the probability of decoding such that the estimation of source outputs by the decoder has a distortion not exceeding a prescribed distortion level . We prove that, when is outside the rate distortion region, this probability goes to zero exponentially and derive an explicit lower bound of this exponent function. On the Wyner–Ziv source coding problem the strong converse coding theorem has not been established yet. We prove this as a simple corollary of our result.
Highlights
For single or multi terminal source coding systems, the converse coding theorems state that at any data compression rates below the fundamental theoretical limit of the system the error probability of decoding cannot go to zero when the block length n of the codes tends to infinity
We study the strong converse theorem for the rate distortion problem with side information at the decoder posed and investigated by Wyner and Ziv [1]
For the WZ system, we prove that if ( R, ∆) is out side the rate distortion region RWZ ( p XY ), we have that for any sequence {( φ(n), ψ(n) )}∞
Summary
For single or multi terminal source coding systems, the converse coding theorems state that at any data compression rates below the fundamental theoretical limit of the system the error probability of decoding cannot go to zero when the block length n of the codes tends to infinity. The strong converse theorems state that, at any transmission rates exceeding the fundamental theoretical limit, the error probability of decoding must go to one when n tends to infinity. For the WZ system, we prove that if ( R, ∆) is out side the rate distortion region RWZ ( p XY ), we have that for any sequence {( φ(n) , ψ(n) )}∞. Goes to zero exponentially and derive an explicit lower bound of this exponent function We use a new method called the recursive method This method is a general powerful tool to prove strong converse theorems for several coding problems in information theory. The recursive method plays important roles in deriving exponential strong converse exponent for communication systems treated in [5,6,7,8]
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