Improved upper bounds on the performance of parallel and serial concatenated turbo codes via their ensemble distance spectrum

The ensemble performance of parallel and serial concatenated turbo codes (TC) is considered for a binary-input AWGN channel and maximum likelihood (ML) decoding. Following the derivation of the ensemble distance spectrum of parallel and serial concatenated codes, improved upper bounds on the bit and block error probabilities of these ensembles of codes are derived and the influence of the interleaver length N and the memory length of the component codes m are investigated. The improved bounding technique, based on the tangential sphere bound, is compared to the conventional union bound and to an alternative bounding technique by Duman and Salehi (see Proceedings of 1997 Global Communications Conference (GLOBECOM'97), Phoenix, Arizona, USA, p.634-8, 1997). The advantage of the bounds is demonstrated for a variety of parallel and serial concatenated coding schemes with either fixed or random component codes, and it is especially pronounced in the region above the cutoff rate, where the performance of TC is most appealing.