In this paper, we derive a formula for calculating the throughput efficienc
y of the Go-Back-N (GBN) protocol when error sources in the forward and bac
kward channels are modeled by a hidden Markov model. The result is presente
d in the matrix form which makes it applicable to models with any number of
states, We consider also the relationship between bit-level and block-leve
l models and obtain the probability distribution of the time that a message
spends in the system.