Boosting quantization for L<inf>p</inf> norm distortion measure

Abstract

Quantization is a widely used technique in signal processing. The purpose of many quantization schemes is to faithfully reproduce the input signals. However, in many situations, one is more interested in comparison of different classes of signals in order to classify them into different categories. The classification criterion is based on comparing distances under certain metric. For classical quantizers, although the individual quantized signal may show high fidelity to its original signals, the distance features characterizing different categories may not be well reserved, which results in poor performance of classification in spite of relatively good reproduction of individual signals. In this paper, we propose a special optimal quantization under the L p norm distortion measure called Boosting Quantization. The quantization is guaranteed to preserve the distances of different classes. We provide a quantization algorithm to generate the quantizer. We also derive several theoretical properties for the proposed quantization. Finally, we provide numerical examples to illustrate our proposed boosting quantization.

Decision-Oriented Communications: Application to Energy-Efficient Resource Allocation

“…distortion. Concerning the problem of quantization, there exist some works (e.g., [2]) where the performance criterion is not distortion (as originally proposed in [3]) but a more general Lp-norm. But the approach developed in the present paper is not only more general because it concerns arbitrary utility functions but also corresponds to a new approach of designing a communication system.…”

Payoff-oriented quantization and application to power control

“…However, almost always, the performance criterion is the distortion. There exist some other works where a different performance criterion is considered such as [9] where the L p´n orm is considered (instead of the Euclidean norm) or some specific performance criterion such as in [10] where the goal is to obtain a quantized beamforming vector. More generally, in [11], the author considers the problem of minimizing an arbitrary function of the difference between the actual vector of parameters and its quantized version but, again, this problem does not correspond to the framework of payoff-oriented quantization we propose here.…”