Advancing over up-to-date information theoreticresults that assume symmetric correlation models, in this workwe consider the problem of lossy binary source coding withside information, where the correlation is expressed by a genericbinary asymmetric channel. Specifically, we present an in-depthanalysis of rate distortion with side information available to boththe encoder and decoder (conventional predictive), as well as theWyner-Ziv problem for this particular setup. Prompted by ourrecent results for the Z-channel correlation case, we evaluate therate loss between the Wyner-Ziv and the conventional predictivecoding, as a function of the parameters of the binary asymmetriccorrelation channel.