Optimal multiple description transform coding of Gaussian vectors

Multiple description coding (MDC) is source coding for multiple channels such that a decoder which receives an arbitrary subset of the channels may produce a useful reconstruction. Orchard et. a. [1] proposed a transform coding method for MDC of pairs of independent Gaussian random variables. This paper provides a general framework which extends multiple description transforms coding (MDTC) to any number of variables and expands the set of transforms which are considered. Analysis of the general case is provided, which can be used to numerically design optimal MDTC systems. The case of two variables sent over two channels is analytically optimized in the most general setting where channel failures need not have equal probability or be independent. It is shown that when channel failures are equally probable and independent, the transforms used in [1] are in the optimal set, but many other choices are possible. A cascade structure is presented which facilitates low-complexity design, coding, and decoding for a system with a large number of variables.