Noise effect on signal quantization in an array of binary quantizers

The effect of noise is examined in both the uniform quantizer and a stochastic quantizer. The stochastic quantizer is an array of identical binary quantizers combined with a linear decoder. In uniform quantization scenario, we find that noise cannot help decrease mean square error (MSE) distortion. However, in the array of binary quantizers with identical thresholds, noise may play a positive role, and stochastic resonance (SR) can be observed. First, based on MSE distortion, the optimal noise in the array is derived by Gateaux differential, which is shown to be a uniform noise. And then, some other noises, including uniform noise with zero mean, Gaussian noise, Laplacian noise, and discrete noise, are considered for comparison. In the case that the granular region is fixed, the quantization performances induced by those noises are shown, and the SR effects are discussed. Furthermore, when the granular region is adjustable, quantization performance may be better. Especially, the MSE distortion, in the optimal noise case, will approximate zero as the rate becomes high. At last, some further studies are discussed, which may extend our results.