Optimal pairwise correlating transforms for multiple description coding

Multiple description coding (MDC) addresses the problem of encoding a source into two (or more) bitstreams such that a high-quality reconstruction is decodable from the two bitstreams together, while a lower, but still acceptable, quality reconstructions is decodable if either of the two bitstreams is lost. Recent research [1] has proposed using transforms to introduce a controlled amount of correlation between the two bitstreams in order to achieve MDC objectives. This paper considers several optimality issues related to such transform-based MDC methods. Redundancy rate-distortion (RRD) performance of a general class of transforms is derived and used to identify the optimal transform for achieving any given amount of redundancy. Then, the paper introduces a more general transform-based MDC framework incorporating both the transform mode of redundancy and a second mode of redundancy. The optimal allocation of redundancy among these two modes is analyzed.