A mutual information-maximizing quantizer based on the noise-injected threshold array.

Channel quantization, particularly designing optimal quantizers maximizing the mutual information between channel input and quantizer output, plays a great role in communications. This paper focuses on the mutual information-maximizing quantizer and explores stochastic resonance (SR) effect on quantization performance when the channel is constructed by a noise-injected threshold array. First, we present the structure of an optimal quantizer. Such a quantizer is determined by using optimal boundaries to partition the set of channel output into disjoint subsets consisting of consecutive integers. Next, the optimal binary quantizer is examined and the optimal noise in the array is derived. For non-optimal Gaussian noise, we find that noise helps to improve mutual information when the threshold is greater than the amplitude of input signal. This means SR occurs in subthreshold case. Moreover, optimal non-binary quantizers are obtained based on dynamic programming. In this case, the Gaussian noise's effect on enhancing mutual information is also demonstrated. At the same time, the impact of the number of threshold units or the quantization levels is explored. Finally, a non-Gaussian noise, i.e., Cauchy noise, is considered, and its SR effect is displayed as well. These results in this paper may be useful for channel coding. [ABSTRACT FROM AUTHOR]