Quantization in the Presence of Large Amplitude Threshold Noise

Signal quantization in the presence of independent, identically distributed, large amplitude threshold noise is examined. It has previously been shown that when all quantization thresholds are set to the same value, this situation exhibits a form of stochastic resonance known as suprathreshold stochastic resonance. This means the optimal quantizer performance occurs for a small input signal-to-noise ratio. Here we examine the performance of this stochastic quantization in terms of both mutual information and mean square error distortion. It is also shown that for low input signal-to-noise ratios that the case of all thresholds being identical provides the optimal mean square error distortion performance for the given noise conditions.