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In recent years, much attention has been given to the decoding of linear block codes by means of trellis decoding algorithms, such as the Bahl-Cocke-Jelinek-Raviv (BCJR) and Viterbi algorithms. Not only do these algorithms support soft in. put decoding, but also the application of channel state information for improved decoding performances in fading channel environments. This paper presents a performance evaluation, based on an extensive simulation study, of Viterbi decoded binary Hamming and non-binary Reed-Solomon block codes under flat fading channel conditions with varying Doppler frequencies and line-of-sight signal strengths. Special attention is given to the influence of channel state information on the bit error rate performance.