On improved bounds on the decoding error probability of block codes over interleaved fading channels, with applications to turbo-like codes

We derive here improved upper bounds on the error probability of block codes which are transmitted over fully interleaved Rician fading channels, coherently detected and maximum likelihood decoded. We assume that the fading coefficients during each symbol are statistically independent (due to a perfect channel interleaver), and that perfect estimates of these fading coefficients are provided to the receiver. The improved upper bounds on the block and bit error probabilities are derived for fully interleaved fading channels with various orders of space diversity, and are found by generalizing some recently introduced upper bounds for the binary-input AWGN channel. The advantage of these bounds over the ubiquitous union bound is demonstrated for some ensembles of turbo codes and low-density parity check codes, and it is especially pronounced in a portion of the rate region exceeding the cutoff rate. Our generalization of the Duman and Salehi bound which is based on certain variations of Gallager’s bounding technique, is demonstrated to be the tightest reported upper bound. We therefore apply it to calculate numerically upper bounds on the thresholds of some ensembles of turbo-like codes, referring to the optimal maximum likelihood decoding. For certain ensembles of uniformly interleaved turbo codes, the upper bounds derived here also indicate good match with computer simulation results of efficient iterative decoding algorithms.