On the Binary Symmetric Channel with a Transition Probability Determined by a Poisson Distribution

The classical Binary Symmetric Channel has a fixed transition probability. We discuss the Binary Symmetric Channel with a variable transition probability that depends on a Poisson distribution. The error rate for this channel is determined and we also give bounds for the channel capacity. We give a motivation for the model based on the Class-A impulse noise model, as given by Middleton. The channel model can be extended to the Additive White Gaussian Channel model, where the noise variance also depends on a Poisson distribution.