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

TL;DR

This paper investigates a Binary Symmetric Channel where the transition probability varies according to a Poisson distribution, providing error rate analysis and capacity bounds, motivated by impulse noise models and extending to Gaussian channels.

Contribution

It introduces a novel BSC model with Poisson-distributed transition probabilities and derives error rates and capacity bounds, extending to Gaussian channels.

Findings

Error rate for the Poisson-based BSC is derived

Bounds for channel capacity are established

Model extension to Gaussian channels with Poisson noise variance

Abstract

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.