[IEEE Trans. on Information Theory, March 1996, pp. 480-487]
On the Cost of Finite Block Length in Quantizing Unbounded
Memoryless Sources
Tamás Linder and Kenneth Zeger
Abstract
The problem of fixed-rate block quantization of an unbounded real memoryless
source is studied. It is proved that if the source has a finite sixth moment,
then there exists a sequence of quantizers $Q_n$ of increasing dimension n
and fixed rate R such that the mean squared distortion $\Delta(Q_n)$ is
bounded as $\Delta(Q_n)\leq D(R)+ O(\sqrt{\log n/n})$, where D(R) is the
distortion-rate function of the source. Applications of this result include
the evaluation of the distortion redundancy of fixed-rate universal quantizers,
and the generalization to the non-Gaussian case of a result of Wyner on the
transmission of a quantized Gaussian source over a memoryless channel.