Performance estimation for concatenated coding schemes

Asymptotical analysis of concatenated codes with EXIT charts (ten Brink, S., 1999) or the AMCA (Huettinger, S. and Huber, J., 2002) has proven to be a powerful tool for the design of power-efficient communication systems. However, the result of the asymptotical analysis is usually a binary decision, whether convergence of iterative decoding is possible at the chosen signal-to-noise ratio, or not. We show how to obtain the information processing characteristic (IPC) introduced by Huettinger et al. for concatenated coding schemes (see Proc. 39th Allerton Conf. on Commun., Control and Computing, 2001). If asymptotical analysis is performed under the assumption of infinite interleaving and infinitely many iterations, this IPC is a lower bound. Furthermore, it is also possible to estimate the performance of realistic coding schemes by restricting the number of iterations. Finally, the IPC can be used to estimate the resulting bit error ratio for the concatenated coding scheme. As an upper and a lower bound on the bit error ratio for a given IPC exist, we are able to lower bound the performance of any concatenated coding scheme and give an achievability bound, i.e. it is possible to determine a performance that can surely be achieved if sufficiently many iterations are performed and a large interleaver is used.