Multiple description quantization by deterministic annealing

The design of vector quantizers for diversity-based communication over two or more channels of possibly differing capacities and failure probabilities, is considered. The crucial dependence of current design techniques on initialization, especially of index assignment, is well recognized. Instead, we propose to pursue a deterministic annealing approach which is independent of initialization, does not assume any prior knowledge of the source density, and avoids many poor local minima of the cost surface. The approach consists of iterative optimization of a random encoder at gradually decreasing levels of randomness as measured by the Shannon entropy. At the limit of zero entropy, a hard multiple description (MD) quantizer is obtained. This process is directly analogous to annealing processes in statistical physics. Via an alternative derivation, we show that it may also be interpreted as approximating the minimum rate sums among points on the convex hull of the MD achievable rate-distortion region of El Gamal and Cover, subject to constraints on the sizes of the reproduction alphabets. To illustrate the potential of our approach, we present simulation results that show substantial performance gains over existing design techniques.