In this work we consider asymmetric correlation channels and focus on the achievability of the rate-distortion function when the source is binary uniform. This lies in contrast with conventional symmetric correlation channel models employed in the literature. The rate-distortion function for binary source coding with correlated side information is expressed as a function of an auxiliary random variable with an alphabet size smaller or equal to three. Complementing our recent findings on the problem, we propose a numerical analysis of the differences between assuming binary and ternary auxiliary variables in the derivation of the rate distortion bound. We also show that, even if the proposed bound does not admit an analytical expression, it always admits a unique solution.