Stopping Set Analysis of 3-Dimensional Turbo Code Ensembles

In this paper, we analyze the asymptotic stopping set distribution of 3-dimensional turbo code (3D-TC) ensembles, consisting of a parallel turbo code concatenated in series with an inner accumulator which encodes only a fraction lambda of the turbo code parity bits. We show that, for certain parameters, the stopping distance of 3D-TC ensembles asymptotically grows linearly with the block length, i.e., 3D-TCs are good for the binary erasure channel. We also consider random puncturing of non-systematic bits and show that higher (or some) linear growth rate is obtained for decreasing values of lambda, contrary to the asymptotic minimum distance, whose growth rate decreases with decreasing values of lambda. Finally, iterative convergence thresholds of 3D-TC ensembles are analyzed by means of extrinsic information transfer charts.