How to use noise to reduce complexity in quantization

Abstract

Consider a quantization scheme which has the aim of quantizing a signal into N+1 discrete output states. The specification of such a scheme has two parts. Firstly, in the encoding stage, the specification of N unique threshold values is required. Secondly, the decoding stage requires specification of N+1 unique reproduction values. Thus, in general, 2N+1 unique values are required for a complete specification. We show in this paper how noise can be used to reduce the number of unique values required in the encoding stage. This is achieved by allowing the noise to effectively make all thresholds independent random variables, the end result being a stochastic quantization. This idea originates from a form of stochastic resonance known as suprathreshold stochastic resonance. Stochastic resonance occurs when noise in a system is essential for that system to provide its optimal output and can only occur in nonlinear systems--one prime example being neurons. The use of noise requires a tradeoff in performance, however, we show that even very low signal-to-noise ratios can provide a reasonable average performance for a substantial reduction in complexity, and that high signal-to-noise ratios can also provide a reduction in complexity for only a negligible degradation in performance.