The Kaspi Rate-Distortion Problem with Encoder Side-Information: Binary Erasure Case

We consider the problem of compressing a binary symmetric i.i.d. source stream for two decoders, one of which has access to side-information. Kaspi found the rate-distortion tradeoff for this problem for general discrete memoryless sources for the two cases with and without encoder side-information. We focus on the case in which the encoder has access to side-information. We assume that the source has a symmetric Bernoulli distribution and that the side-information is the output of an erasure channel whose input is the source stream. We explicitly solve the optimization problem for this setup. We also show that the Wyner-Ziv rate-distortion function and the conditional rate-distortion function coincide for general discrete memoryless sources when the side-information is of the erasure type.