Analysis of packet errors in Gilbert-Elliott channels

50 years ago, Gilbert and Elliott introduced 2-state Markov channels to characterize bursty error processes in data transmission. The focus of this work is on the analysis of the effect of bit errors on higher layer blocks or packets. Starting from 2-state bit error channels in an extended Gilbert-Elliott format, packet errors again result in a 2-state process of the same type. The parameters of the packet error process are explicitly derived from those of the underlying bit error process. The solution for main performance measures is based on a superposition of two geometrical functions for the distributions of packet error bursts and gaps and the second order statistics. Knowledge about the solution for 2-state channels is implicitly present in solutions for N-state Markov models by Turin et al, but which require a more complex factorization approach. The latter involves root finding algorithms for eigenvalues and eigenvectors and NxN linear boundary equations, going far beyond what is needed for a 2-state analysis. Conversely, analysis of Markov processes is excluded in other work on packet error evaluation due to the lack of simple solutions. Therefore the authors think it worthwhile to summarize the simple approach for popular 2-state channels.