Radial compression function for vector quantizer of Laplacian source with high dynamic variance range

Abstract

In this paper, our aim is to define a high dynamic range vector quantization model for an i.i.d. Laplacian source. In order to do this we use a geometric approach and lattice quantization. As a result, we achieve symmetry in distribution of code vectors and introduce the radial scalar compression function for lattice cell side determination. This enables derivation of a sophisticated creation for a condition which the radial compression function should satisfy in order to make the SQNR non-dependent on variance. It is interesting that the obtained solution represents the generalisation of solution in the case of high dynamic range scalar quantization. Because of that, in the second part of the paper, the well-known semilogarithmic A-law compression characteristic is utilized as radial scalar compression function of geometric vector quantizer. It is shown that such a model has very good performances over a very wide variance range. The proper choice of compression parameter A and dimension n enables the constant SQNR to sustain over much wider variance range than in case of log-scalar quantization. Particularly, the high dimension makes it possible to broaden the variance range over which SQNR remains constant by increasing the A value simultaneously holding the SQNR level unchanged. In comparison with the widely used log-scalar quantization, the presented solution for dimensions from 10 to 140 gives a quality improvement of 7–9 dB, while comparison of maximal SQNR value to that of optimal scalar quantization shows the SQNR growth of 3–5 dB. Furthermore, for dimension 40 the SQNR maximum is only for 0.5 dB lower than that of optimal vector quantization, while dynamic range characteristic broadening is considerable. The cited benefits of high dynamic range vector quantization make it possible to realize a high quality signal compression. Besides, in comparison with the adaptive quantization, our proposal has a smaller implementation complexity. Copyright © 2010 John Wiley & Sons, Ltd.