Turbo Codes Performance Optimization over Block Fading Channels

Abstract

In this paper, the best achievable performance of a turbo coded system on a block fading channel is obtained, assuming binary antipodal modulation. A rate 1/3 turbo code is considered, obtained by concatenating, through a random interleaver, an 8-states rate 1/2 and a rate 1 convolutional codes (CC). The block fading channel model is motivated by the fact that in many wireless systems the coherence time of the channel is much longer than one symbol interval, resulting in adjacent symbols being affected by the same fading value. The fading blocks will experience independent fades, assuming a sufficient separation in time, in frequency, or both in time and in frequency. This channel model is suitable for analyzing, for instance, wireless communication systems employing techniques such as slow frequency-hopping, as is done in the Global System for Mobile communications (GSM). In such systems, coded information is transmitted over a small number of fading channels in order to achieve diversity. The best coded information allocations over a certain number of fading channels are evaluated, using the Eades-McKay algorithm to generate distinct permutations of a multiset. Bounds on the achievable performance due to coding are derived using information-theoretic techniques. In particular, in the paper an analytical method is proposed, based on the sphere-packing bounding technique, to assess the achievable performance. Moreover, simulation results are obtained and compared with the theoretical ones.