On two or more dimensional optimum quantizers

It is hard to compute the performance of an N-level K-dimensional optimum quantizer <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Q̂N</tex> directly. In this paper the performance of <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Q̂N</tex> is studied more closely from the performance of Q' <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N</inf> , a class of stationary quantizers. An analytical derivation of the algorithm for generating Q' <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N</inf> quantizers and a computer experimental study on the performance of Q' <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N</inf> for two dimensional case are given. The results show that it is possible to bound the performance of <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Q̂N</tex> more closely from Q' <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N</inf> .