Analysis of 3-dimensional turbo code ensembles

In this work, we analyze the 3-dimensional turbo codes (3D-TCs) recently introduced by Berrou et al. from an ensemble perspective, both in the waterfall region, by means of an extrinsic information transfer charts analysis, and in the error floor region, by means of a minimum distance analysis. The minimum distance analysis is performed both in the finite-length regime and in the asymptotic case of large block lengths. Here, we consider binary 3D-TCs while the original work of Berrou et al. considered double-binary codes. In particular, we analyze the asymptotic weight distribution of 3D-TCs and show that their typical minimum distance may, depending on the specific parameters, asymptotically grow linearly with the block length, i.e., the 3D-TC ensemble is asymptotically good for some parameters.