[IEEE Trans. on Information Theory, January 2004, pp. 62-77]
Quantizers with Uniform Encoders and Channel Optimized Decoders
Benjamin Farber and Kenneth Zeger
Abstract
Scalar quantizers with uniform encoders and channel optimized decoders are
studied for uniform sources and binary symmetric channels. It is shown that
the Natural Binary Code and Folded Binary Code induce point density functions
that are uniform on proper subintervals of the source support, whereas the Gray
Code does not induce a point density function. The mean squared errors for the
Natural Binary Code, Folded Binary Code, Gray Code, and for randomly chosen
index assignments are calculated and the Natural Binary Code is shown to be
mean squared optimal among all possible index assignments. In contrast, it is
shown that almost all index assignments perform poorly and have degenerate
codebooks.