On Optimal Overcomplete Subband Expansions for Multiple Description Coding

We study the use of overcomplete (also known as oversampled) subband expansions for multiple description coding. The system proposed uses an overcomplete subband expansion (a subband expansion in which the number of subbands is larger than the down sampling factor of each subband) followed by independent coding (quantization and coding) of each of the subbands. The entire coding of each of the subbands is entirely contained within a single description. Using analysis in the polyphase domain, we study finding frequency responses of optimal filterbanks and the rate allocation across the subbands to minimize the end-to-end reconstruction error subject to a transmission rate constraint when a distribution over channel states is known. A general analysis of the problem is given and results are shown for a 3×2 expansion of a first-order autoregressive process.