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On the rate-distortion function for binary source coding with side information This publication appears in: IEEE Transactions on Communications Authors: A. Sechelea, A. Munteanu, S. Cheng and N. Deligiannis Volume: 64 Issue: 12 Pages: 5203-5216 Publication Date: Dec. 2016
Abstract: We present an in-depth analysis of the problem of lossy compression of binary sources in the presence of correlated side information, where the correlation is given by a generic binary asymmetric channel and the Hamming distance is the distortion metric. Our analysis is motivated by systematic rate-distortion gains observed when applying asymmetric correlation models in Wyner-Ziv video coding. Firstly, we derive for the first time the rate-distortion function for conventional predictive coding in the binary-asymmetric-correlation-channel scenario. Secondly, we propose a new bound for the case where the side information is only available at the decoder - Wyner-Ziv coding. We conjecture this bound to be tight. We show that the maximum rate needed to encode as well as the maximum rate-loss of Wyner-Ziv coding relative to predictive coding correspond to uniform sources and symmetric correlations. Importantly, we show that the upper bound on the rate-loss established by Zamir is not tight and that the maximum value is actually significantly lower. Moreover, we prove that the only binary correlation channel that incurs no rate-loss for Wyner-Ziv coding compared to predictive coding is the Z-channel. Finally, we complement our analysis with new compression performance results obtained with our state-of-the-art Wyner-Ziv video coding system.
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