[IEEE Trans. on Information Theory, March 1997, pp. 612-637]
Empirical Quantizer Design in the Presence of
Source Noise or Channel Noise
Tamás Linder, Gábor Lugosi, and Kenneth Zeger
Abstract
The problem of vector quantizer empirical design for noisy channels or
for noisy sources is studied. It is shown that the average squared
distortion of a vector quantizer designed optimally from observing
clean i.i.d. training vectors converges in expectation, as the
training set size grows, to the minimum possible mean-squared error
obtainable for quantizing the clean source and transmitting across a
discrete memoryless noisy channel. Similarly, it is shown that if the
source is corrupted by additive noise, then the average squared
distortion of a vector quantizer designed optimally from observing
i.i.d. noisy training vectors converges in expectation, as the
training set size grows, to the minimum possible mean-squared error
obtainable for quantizing the noisy source and transmitting across a
noiseless channel. Rates of convergence are also provided.