Multiple description quantization by deterministic annealing

We consider the design of vector quantizers for diversity-based communication over two channels of capacities R₁ and R₂ with possibly differing failure probabilities. A multiple description vector quantizer (MDVQ) maps an n-dimensional source vector x to n-dimensional code vectors x_ij⁰, x_i¹ and x_j² from the code books χ⁰, χ¹ and χ² respectively. Let d(x,y) be a single-letter distortion measure, and random vectors X and X^m, m=0,1,2 represent the source and decoder outputs respectively. For given values of R₁, R₂ , λ1 and λ2 we then wish to find an MDVQ which minimizes the average distortion cost