Summary form only given. Motivated by the correlation channel modeling problem in practical applications, such as distributed video coding, we study the binary source coding of a uniform source with side information, under asymmetric correlation channel assumptions. First, we consider the case where side information is available to both the encoder and decoder, and give an analytical formula for the rate-distortion bound. Then, we consider the side information to be available only to the decoder and present the derivation of the associated Wyner-Ziv rate-distortion bound. Most importantly, we characterize the evolution of the rate-loss suffered by Wyner-Ziv coding, for all possible binary asymmetric correlation channels.

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. First, we derive for the first time the rate-distortion function for conventional predictive coding in the binary-asymmetric-correlation-channel scenario. Second, 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 corresponds 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 with 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.