On zero-delay lossy source coding with side information at the decoder

We consider real-time, variable-rate lossy source coding in the presence of side information (SI) at the decoder. We show that time-sharing at most two scalar encoder-decoder pairs achieves optimal performance. We further demonstrate that in this setting, increasing the number of quantization levels can reduce the minimum average rate. Finally, two structure theorems, pertaining to source- or SI look-ahead are given.