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The performance of different soft decision decoding algorithms for linear block codes applied to fading channels is studied in this paper. All the algorithms achieve either the performance of maximum-likelihood-decoding (MLD) or approximate that. One class of the algorithms is a simplified scheme for correlation decoding by selecting certain codewords using erasure information setting a suitable threshold value at the received sequence. This algorithm achieves nearly the performance of correlation decoding for a certain value of threshold. The other class includes the algorithms which use a maximum likelihood metric as a decision criterion for the codeword which is chosen and achieve MLD. This metric is based on the estimation of the probability of one bit to have been sent given the received energy level. Computer simulation results are derived for different terrestrial and satellite channel models. The models which have been used are the well known Rayleigh, the combined Rayleigh-Lognormal and Rice-Lognormal one, and a model for satellite channels including time factor A. All the algorithms and channels are compared for three different BCH codes (15,11,3), (15,7,5) and (15,5,7) with the same block length and different correction capability. The results show that the performance of decoding algorithms which are MLD is always superior to those which approximate MLD.-115-