Locally optimal block quantizer design

Abstract

Several properties are developed for a recently proposed algorithm for the design of block quantizers based either on a probabilistic source model or on a long training sequence of data. Conditions on the source and general distortion measures under which the algorithm is well defined and converges to a local minimum are provided. A variation of the ergodic theorem is used to show that if the source is block stationary and ergodic, then in the limit as n → ∝, the algorithm run on a sample distribution of a training sequence of length n will produce the same result as if the algorithm were run on the “true” underlying distribution.