Multiple parallel concatenated codes with optimal puncturing and energy distribution

In this paper we show how to find optimal energy distribution together with optimal puncturing ratios for parallel concatenated codes with two or more constituent codes. The energy distribution and the puncturing ratios are optimal in terms of minimizing the average signal-to-noise ratio convergence threshold. The extrinsic information transfer functions of the constituent codes are used for the optimization. Using this technique we obtain additional degrees of freedom for constructing codes with low convergence thresholds over a large range of code rates.