Analysis of random and burst error codes in 2-state Markov channels

Markov chains are a popular means to capture correlated random processes for characterization and analysis of error pattern or bursty traffic in data transmission. The performance evaluation of communication protocols based on Markov models is tractable with limited state space and often depends on efficient implementation. Simulation or other methods have to be adopted for system of higher complexity. We study the effect of bit errors on transmitted packets for Markov error processes in the presence of error detecting or error correcting codes. We show that the evaluation for 2-state Markov channels leads the same 2-state channel characteristics also for packet errors, where parameters are determined by a recursive and closed form solution depending on the parameters of the bit error channel. Computation schemes are derived for random and burst error detecting and correcting codes whose computation effort is shown to be moderate and generally tractable for usual packet sizes in telecommunication.