Towards Optimality in Multiterminal Transform Coding
This paper is concerned with transform coding of correlated sources in conjunction with variable rate quantization at high resolution. The approach builds on our prior work on optimality conditions for transform coding in the point-to-point setting. The first contribution involves transform coding with decoder side information. In this setting, side information is only available to the decoder, whereas the encoder knows the joint statistics. The necessary and sufficient condition for optimality of a unitary transform in the side information setting is derived, namely, such transform minimizes a conditional divergence-based measure of inter-dependence of the transform coefficients, given the side information. This optimality result subsumes prior, known results that were restricted to the Gaussian case, where the conditional Karhunen-Loeve transform is optimal. The second contribution involves distributed transform coding, where two correlated sources are to be transform coded separately, but decoded jointly. The necessary and sufficient condition for optimality of unitary transforms in the distributed coding setting is derived. It is then specialized to produce closed form optimal transforms for specific source densities, including the case of jointly Gaussian sources.