The binary regenerative channel

The nature of the errors in a regenerative digital transmission system is such that a memoryless channel is a poor model for predicting the error phenomena. In this paper we present a model which provides a reasonable approximation to observed error phenomena. The memory of the channel is represented by a Markov model. This model is similar to the model developed by E. N. Gilbert, but several important modifications greatly simplify the estimation of parameters, and make the model correspond more closely to the physical phenomena involved. Bounds for the channel capacity of the binary regenerative channel are obtained. Error separation, block error, and burst statistics are derived. Error model parameters are derived from available experimental data on the T1 digital transmission line and the switched telephone network. The Markov model is shown to provide a good representation of the observed error phenomena.