We design nonlinear functions for the transmission of a small signal with non-Gaussian noise and perform experiments to characterize their responses. Using statistical design theory [A. Ichiki and Y. Tadokoro, Phys. Rev. E 87, 012124 (2013)], a static nonlinear function is estimated from the probability density function of the given noise in order to maximize the signal-to-noise ratio of the ou...

Random or incoherent noise is an important type of seismic noise, which can seriously affect the quality of the data. Therefore, decreasing the level of this category of noises is necessary for increasing the signal-to-noise ratio (SNR) of seismic records. Random noises and other events overlap each other in time domain, which makes it difficult to attenuate them from seismic records. In this r...

The feedback capacity of the stationary Gaussian additive noise channel has been open, except for the case where the noise is white. Here we obtain the closed-form feedback capacity of the first-order moving average additive Gaussian noise channel. Specifically, the channel is given by Yi = Xi +Zi, i = 1, 2, . . . , where the input {Xi} satisfies a power constraint and the noise {Zi} is a first...

We solve stochastic differential equations involving the Malliavin derivative and the fractional Malliavin derivative by means of a chaos expansion on a general white noise space (Gaussian, Poissonian, fractional Gaussian and fractional Poissonian white noise space). There exist unitary mappings between the Gaussian and Poissonian white noise spaces, which can be applied in solving SDEs.