Optimal and Suboptimal Noises Enhancing Mutual Information in Threshold System

Abstract

In this paper, we investigate the efficacy of noise enhancing information transmission in a threshold system. At first, in the frame of stochastic resonance (SR), optimal noise (Opt N) is derived to maximize mutual information (MI) of this nonlinear system. When input signal is discrete (binary), the optimal SR noise is found to have a finite distribution. In contrast, when input signal is continuous, the optimal SR noise is a constant one. In addition, suboptimal SR noises are explored as well with optimization methods when the types of noise added into the system are predetermined. We find that for small thresholds, suboptimal noises do not exist. Only when thresholds reach some level, do suboptimal noises come into effect. Meanwhile, we have discussed the impact of tails in noise distribution on SR effect. Finally, this paper extends the single-threshold system to an array of multi-threshold devices and presents the corresponding efficacy of information transmission produced by optimal and suboptimal SR noises. These results may be beneficial to quantization and coding.