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This work develops finite state channel (FSC) models for a discrete communication channel with flat fading and analyzes the throughput efficiency of the Go-Back-N (GBN) scheme of the automatic repeat request protocol on FSC models. This protocol performance measure is then applied to determine the range of parameters of the communication system in which the binary error sequence generated by the discrete channel can be approximated by two classes of FSC models: First-order Markov and Gilbert-Elliott channel. The influence of the various parameters of the communication system on the throughput of the GBN protocol is evaluated. I. INTRODUCTIONFinite state channel (FSC) models have been used to describe the bursty nature of the binary error sequence that represents the successes and the failures of symbols transmitted over correlated flat fading channels [1] - [5]. Accurate models allow the performance assessment of coding schemes over fading channels with arbitrary fading rates [3], [4], [6], [7]. This paper concerns on the analysis of the throughput efficiency of the Go-Back-N (GBN) scheme of the ARQ protocol on FSC models. The majority of the previous throughput analysis of classic ARQ protocols, such as GBN and Selective Repeat, on channels with correlated errors have assumed a first-order Markov model representation of the error sequence [8]-[6]. This model is adequate for packet error sequences [6], [12], however, its parameterization depends on parameters of the code used, e.g., codeword length, error correcting/detecting capabilities. The accurate characterization of the bit error sequence requires more complex models [4], [5]. Moreover formulas of the throughput efficiency of ARQ protocols have been derived for channels modeled as higher order Markov [13], and general FSC models [14]. The effect of feedback channel errors have been considered in [10], [6], [12], [14].We herein aim at the study of the accuracy of bit-level FSC models to calculate the throughput of the GBN scheme in correlated fading channels. Firstly, we employ a generating function approach to develop an alternative closed-form formula for the throughput efficiency of the GBN protocol over general FSC models. We then carry out a numerical study to identify the range of fading parameters for which some specific models, e.g. first-order Markov and Gilbert-Elliott channel (GEC), are valid. The effectiveness of a particular model to approximate the fading channel is generally confirmed by comparing certain statistics of the model (autocorrelation function, packed error rate) with those obtained by simulations [3], [4], [5], [7]. The

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