Noise-Enhanced Hamming Code Transmission over an Additive Gaussian Mixture Noise Channel with One-Bit ADCs

Abstract

Random noise may have a positive effect on the transmission and reception of signals in some nonlinear communication systems, which is termed as stochastic resonance (SR) or noise-enhanced effect. In this paper, we investigate the performance of signals transmitted over an additive Gaussian mixture noise channel. At the receiving end, before detection by a maximum likelihood (ML) detector, signals are injected with an intentionally added Gaussian noise and quantized by one-bit analog-to-digital converters (ADCs). How the injected Gaussian noise affects the transmission performance and whether the SR effect exists are explored. For both the uncoded signal and Hamming-coded signal, the error probabilities of transmission are derived. The corresponding performance is shown theoretically and by simulation. We find that under certain conditions, the injected Gaussian noise may improve the performance of the signal transmission, which indicates that SR exists in this communication system. In particular, the optimal noise intensity is determined and the minimum error probability is achieved. Moreover, the transmission of a speech signal is presented as a specific example, in which the noise-enhanced effect is demonstrated as well.