The No-Rate-Loss Property of Wyner-Ziv Coding in the Z-Channel Correlation Case

In this letter, we present the exact Wyner-Ziv limit for binary source coding with side information correlated by a Z-channel and with the Hamming-distance as distortion metric. A surprising discovery is that, unlike the general case, Wyner-Ziv coding under this setup does not suffer a rate loss compared to source coding with side information available at both the encoder and the decoder. Highlighting the significance of our finding, we note that this is an additional case for which Wyner-Ziv coding is shown not to suffer a rate loss apart from the quadratic Gaussian case, proven by Wyner and Ziv, and its generalization by Pradhan et al.