Analysis of three-dimensional turbo codes

Our paper presents a detailed study of the three-dimensional turbo code (3D TC). This code which combines both parallel and serial concatenation is derived from the classical TC by concatenating a rate-1 post-encoder at its output. The 3D TC provides very low error rates for a wide range of block lengths and coding rates, at the expense of an increase in complexity and a loss in convergence. This paper deals with the performance improvement of the 3D TC. First, we optimize the distance spectrum of the 3D TC by means of the adoption of a non regular post-encoding pattern. This allows us to increase the minimum hamming distance (MHD) and thereby to improve the performance at very low error rates. Then, we propose a time varying construction of the post-encoded parity in order to reduce the observable loss of convergence at high error rates. Performance comparisons are made between the 3GPP2 standardized TC and the corresponding 3D code. The different improvement stages are illustrated with simulation results, asymptotical bounds, and EXIT charts.