On Optimal Bit Allocation Algorithm for Quantizing a Random Vector

It is shown that the use of the allocation algorithm for a specified number of bits for quantizing independent components of a random vector, known earlier for the case of convex functions of minimum mean quantization error for individual components, can ensure minimum overall mean quantization error for all components even in the convex case, if some condition of quasiconvexity is satisfied with respect to the result of this algorithm. In the opposite situation, the resultant solution simplifies the search for the optimal allocation in terms of a dynamic programming algorithm.