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.
Sechelea, A, Munteanu, A, Cheng, S & Deligiannis, N 2016, 'On the rate-distortion function for binary source coding with side information', IEEE Transactions on Communications, vol. 64, no. 12, pp. 5203-5216. https://doi.org/10.1109/TCOMM.2016.2607745
Sechelea, A., Munteanu, A., Cheng, S., & Deligiannis, N. (2016). On the rate-distortion function for binary source coding with side information. IEEE Transactions on Communications, 64(12), 5203-5216. https://doi.org/10.1109/TCOMM.2016.2607745
@article{9356f186eb5b4c3ba58af3328998692a,
title = "On the rate-distortion function for binary source coding with side information",
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.",
keywords = "Information theory, Source coding, Rate distortion theory",
author = "Andrei Sechelea and Adrian Munteanu and Samuel Cheng and Nikolaos Deligiannis",
year = "2016",
month = dec,
doi = "10.1109/TCOMM.2016.2607745",
language = "English",
volume = "64",
pages = "5203--5216",
journal = "IEEE Transactions on Communications",
issn = "0090-6778",
publisher = "Institute of Electrical and Electronics Engineers Inc.",
number = "12",
}