Improved union bounds on turbo codes performance

Abstract

An improved union bound on the performance of turbo codes is evaluated, extending the preliminary results presented by Viterbi and Viterbi (1998) in conjunction with the input-binary AWGN channel. Since, in an increasing number of important applications, the AWGN channel provides an entirely inappropriate model of the propagation environment, the analytical expression of the previously derived improved union bound is extended to provide a characterisation of turbo code performance in a more general case, namely when considering the multiplicative fast-fading fully-interleaved channel. A uniform interleaver is assumed; this strategy allows one to derive the average performance of the turbo coding scheme by analysis. Of interest is the improvement of the bound for values of Eb/N0 near and below R0 (i.e. the ‘computational cutoff rate’), a region where the conventional union bound becomes useless. This improvement allows a better estimate of turbo code performance in conjunction with the fast-fading fully-interleaved channel and with the AWGN channel, which can be treated as a particular case. Moreover, it allows one to determine a tighter bound to the actual code performance as far as the slow fading Rician channel is concerned.