Noise-assisted transmission of binary information: theory and experiment

Noise enhances information transfer in hierarchical networks

We study the influence of noise on information transmission in the form of packages shipped between nodes of hierarchical networks. Numerical simulations are performed for artificial tree networks, scale-free Ravasz-Barabási networks as well for a real network formed by email addresses of former Enron employees. Two types of noise are considered. One is related to packet dynamics and is responsible for a random part of packets paths. The second one originates from random changes in initial network topology. We find that the information transfer can be enhanced by the noise. The system possesses optimal performance when both kinds of noise are tuned to specific values, this corresponds to the Stochastic Resonance phenomenon. There is a non-trivial synergy present for both noisy components. We found also that hierarchical networks built of nodes of various degrees are more efficient in information transfer than trees with a fixed branching factor.

Numerical implementation of a VCSEL-based stochastic logic gate via polarization bistability

We study the interplay of polarization bistability, spontaneous emission noise and aperiodic current modulation in vertical cavity surface emitting lasers (VCSELs). We demonstrate the phenomenon of logic stochastic resonance (LSR), by which the laser gives robust and reliable logic response to two logic inputs encoded in an aperiodic signal directly modulating the laser bias current. The probability of a correct response is controlled by the noise strength, and is equal to 1 in a wide region of noise strengths. LSR is associated with optimal noise-activated polarization switchings (the so-called "inter-well" dynamics if one considers the VCSEL as a bistable system described by a double-well potential) and optimal sensitivity to spontaneous emission in each polarization (the "intra-well" dynamics in the double-well potential picture). The robust nature of LSR in VCSELs offers interesting perspectives for novel applications and provides yet another example of a driven nonlinear optical system where noise can be employed constructively.

Vibrational resonance and the detection of aperiodic binary signals

We present the experimental and numerical study of a method for detecting aperiodic binary signals in a bistable, vertical cavity surface emitting laser (VCSEL). The method uses the phenomenon of vibrational resonance, in presence of a fixed level of noise. We show that the addition of a periodic signal with a period much shorter than the bit duration of the aperiodic input signal allows one to significantly increase the cross-correlation coefficient between the input and the output, as well as to substantially decrease the bit error rate. The experimental observation of a time lag between the input and the output of the VCSEL due the high-frequency modulation is reported. The effect of an asymmetry of the bistable quasipotential on the detection is also analyzed. The numerical results of simulations in a simple model are in qualitative agreement with the experiment.

Stochastic resonance of electrochemical aperiodic spike trains

Aperiodic stochastic resonance in an electrochemical system with excitable dynamics is characterized in experiments and simulations. Two different spike trains, one with stochastic and the other with chaotic interspike intervals, are imposed on the system as subthreshold aperiodic signals. Information transmission is quantified by the cross correlation between the subthreshold input signal and the noise induced system response. A maximum is exhibited in the input-output correlation as a function of the noise amplitude. Numerical simulations with an electrochemical model are in excellent agreement with the experimental observations.

Residual aperiodic stochastic resonance in a bistable dynamic system transmitting a suprathreshold binary signal

Conventional stochastic resonance can be viewed as an amplitude effect, in which a small (subthreshold) input signal receives assistance from noise to trigger a stronger response from a nonlinear system. We demonstrate another mechanism of improvement by the noise, which is more of a temporal effect. An intrinsically slow system has difficulty to respond to a fast (suprathreshold) input, and the noise plays a constructive role by spurring the system for a more efficient response. The possibility of this form of stochastic resonance is established and studied here in a double-well bistable dynamic system, driven by a suprathreshold random binary signal, with the noise accelerating the switching between wells.

Experimental study of noise-induced phase synchronization in vertical-cavity lasers

We report the experimental evidence of noise-induced phase synchronization in a vertical-cavity laser. The polarized laser emission is entrained with the input periodic pump modulation when an optimal amount of white, Gaussian noise is applied. We characterize the phenomenon, evaluating the average frequency of the output signal and the diffusion coefficient of the phase difference variable. Their values are roughly independent of the different wave forms of periodic input, provided that a simple condition for the amplitudes is satisfied. The experimental results are compared with numerical simulations of a Langevin model.

Information gain in an optical bistable system by stochastic resonance

We have shown an experimental demonstration of information gain due to the stochastic resonance in an optical bistable system, that is, information hidden in the input wave form appears in the output of a nonlinear system when the input noise amplitude is adequate. The optical bistable system is a hybrid type comprising a LiNbO3 crystal with an electric feedback loop, and the input of the system is the sum of a binary bit series and a Gaussian colored noise. The information gain is proved to be prominent when the noise cutoff frequency is larger than the bit rate.