On Bit Number Distribution upon Quantization of a Multivariate Random Variable

The article considers a numerical solution algorithm for the problem of optimum distribution of a specified number of bits among the independent components of a random vector so as to obtain minimum overall quantization error for all components using the number of bits allotted for each component. Special attention is given to the case in which the minimum mean quantization error for each component, as a function of the number of bits allotted for this component, is convex.