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We consider the rate distortion problem with side information at the decoderposed and investigated by Wyner and Ziv. The rate distortion functionindicating the trade-off between the rate on the data compression and thequality of data obtained at the decoder was determined by Wyner and Ziv. Inthis paper, we study the error probability of decoding at rates below the ratedistortion function. We evaluate the probability of decoding such that theestimation of source outputs by the decoder has a distortion not exceeding aprescribed distortion level. We prove that when the rate of the datacompression is below the rate distortion function this probability goes to zeroexponentially and derive an explicit lower bound of this exponent function. Onthe Wyner-Ziv source coding problem the strong converse coding theorem has notbeen established yet. We prove this as a simple corollary of our result.

Exponent Function for Source Coding with Side Information at the Decoder at Rates below the Rate Distortion Function