This work considers the achievable diversity for coded systems appropriately characterized by a block-fading channel model. We are primarily interested in cases where the number of uncorrelated fading channel realizations(blocks) F, is small, so that ideal interleaving assumptions do not hold. This is usually the case in mobile radio systems which employ coded slow frequency-hopping such as the GSM system and its derivatives. We show that the diversity order is limited to a value less than or equal to F which depends on the code rate and the size of the signaling constellation. We report on the results of code searches for rate 1 convolutional codes for simple AM constellations, which show the minimum complexity needed to achieve maximum diversity. We also present computer simulations of some codes in order to determine the effect of code complexity on the frame and bit error-rate performance.
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