We numerically study the effect of additive Gaussian white noise in the dynamics of a time-delayed feedback system. The system is a semiconductor laser with optical feedback from a distant reflector. For moderate feedback levels the system presents several coexisting attractors, and noise levels above a threshold value induce jumps among these attractors. Based on the residence times probabilit...

Error correction techniques traditionally focus on the co-design of restricted code-structures in tandem with code-specific decoders that are computationally efficient when decoding long codes hardware. Modern applications are, however, driving demand for ultra-reliable low-latency communications (URLLC), rekindling interest performance shorter, higher-rate error correcting codes, and raising p...

We consider the nonparametric estimation of a periodic function that is observed in additive Gaussian white noise after convolution with a “boxcar,” the indicator function of an interval. This is an idealized model for the problem of recovery of noisy signals and images observed with “motion blur.” If the length of the boxcar is rational, then certain frequencies are irretreviably lost in the p...

We show that a nonequilibrium first-order phase transition can be induced by additive noise. As a model system to study this phenomenon, we consider a nonlinear lattice of overdamped oscillators with both additive and multiplicative noise terms. Predictions from mean field theory are successfully confirmed by numerical simulations. A physical explanation for the mechanism of the transition is g...

Hamiltonian systems with additive noise possess the property of preserving symplectic structure. Numerical methods with the same property are constructed for such systems. Special attention is paid to systems with separable Hamiltonians and to second-order differential equations with additive noise. Some numerical tests are presented.

We provide a counterexample to Cover’s conjecture that the feedback capacity CFB of an additive Gaussian noise channel under power constraint P be no greater than the nonfeedback capacity C of the same channel under power constraint 2P , i.e., CFB(P ) C(2P ). Index Terms|Additive Gaussian noise channels, channel capacity, conjecture, counterexample, feedback.