The zero-delay Wyner-Ziv problem

We consider the zero-delay version of the Wyner-Ziv problem. The zero-delay constraint translates into causal (sequential) encoder and decoder pairs as well as the use of instantaneous codes. We show that optimal performance is attained by time sharing at most two scalar encoder-decoder pairs, that use zero-error side information codes. Side information lookahead is shown to be useless in this setting. We show that the restriction to causal encoding functions is the one that causes the performance degradation, compared to unrestricted systems, and not the sequential decoders or instantaneous codes.