Optimal quantization and suprathreshold stochastic resonance

Abstract

It is shown that Suprathreshold Stochastic Resonance (SSR) is effectively a way of using noise to perform quantization or lossy signal compression with a population of identical threshold-based devices. Quantization of an analog signal is a fundamental requirement for its efficient storage or compression in a digital system. This process will always result in a loss of quality, known as distortion, in a reproduction of the original signal. The distortion can be decreased by increasing the number of states available for encoding the signal (measured by the rate, or mutual information). Hence, designing a quantizer requires a tradeoff between distortion and rate. Quantization theory has recently been applied to the analysis of neural coding and here we examine the possibility that SSR is a possible mechanism used by populations of sensory neurons to quantize signals. In particular, we analyze the rate-distortion performance of SSR for a range of input SNR’s and show that both the optimal distortion and optimal rate occurs for an input SNR of about 0 dB, which is a biologically plausible situation. Furthermore, we relax the constraint that all thresholds are identical, and find the optimal threshold values for a range of input SNRs. We find that for sufficiently small input SNRs, the optimal quantizer is one in which all thresholds are identical, that is, the SSR situation is optimal in this case.