On the cost of finite block length in quantizing unbounded memoryless sources

Author

Linder, Tamás ; Zeger, Kenneth

Author_Institution

Dept. of Math. & Comput. Sci., Tech. Univ. Budapest, Hungary

Volume

42

Issue

2

fYear

1996

fDate

3/1/1996 12:00:00 AM

Firstpage

480

Lastpage

487

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 Δ(Q_n) is bounded as Δ(Q_n)⩽D(R)+O(√(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

Keywords

memoryless systems; quantisation (signal); rate distortion theory; redundancy; source coding; distortion redundancy; distortion-rate function; finite block length cost; finite sixth moment; fixed-rate block quantization; mean squared distortion; memoryless channel; nonGaussian case; quantized Gaussian source; quantizing unbounded memoryless sources; sequence of quantizers; source coding; universal quantizers; Convergence; Costs; Laplace equations; Memoryless systems; Performance analysis; Propagation losses; Quantization; Rate distortion theory; Redundancy; Source coding;

fLanguage

English

Journal_Title

Information Theory, IEEE Transactions on

Publisher

ieee

ISSN

0018-9448

Type

jour

DOI

10.1109/18.485718

Filename

485718