Optimal subband filter banks for multiple description coding

Multiple description coding refers to the encoding of an information source into multiple bit streams, in a manner that each bit stream independently represents a "coarse" description of the source, while multiple descriptions jointly convey a higher fidelity source representation. Thus multiple description coding allows enhanced resilience to loss of individual descriptions, and can be viewed as a form of source-based diversity coding. This paper addresses the design of subband filter banks to optimize the rate-distortion performance of multiple description subband coding. The problem is formulated in a Lagrangian optimization framework, and is solved directly in the frequency domain to produce the optimal filter spectral responses. By varying the Lagrangian parameter, our design obtains all points on the redundancy-distortion curve for Gaussian wide-sense stationary input processes. We consider the cases of both orthonormal and more general biorthogonal filter banks. We also analyze the connections between these two solutions, and quantify the gap in their optimal performance. Application of the proposed methods to the popular first-order autoregressive (AR(1)) model yields very interesting and insightful results. In the two extreme cases of maximum and minimum redundancy, our solutions degenerate to previously known results. Finally, comparisons with popularly deployed filter banks reveal large gaps from the theoretical performance bound.