Nonsystematic Turbo Codes

Abstract

In this paper, we introduce the concept of nonsystematic turbo codes and compare them with classical systematic turbo codes. Nonsystematic turbo codes can achieve lower error floors than systematic turbo codes because of their superior effective free distance properties. Moreover, they can achieve comparable performance in the waterfall region if the nonsystematic constituent encoder has a low-weight feedforward inverse. A uniform interleaver analysis is used to show that rate R=1/3 turbo codes using nonsystematic constituent encoders have larger effective free distances than when systematic constituent encoders are used. Also, mutual information-based transfer characteristics and extrinsic information transfer charts are used to show that rate R=1/3 turbo codes with nonsystematic constituent encoders having low-weight feedforward inverses achieve convergence thresholds comparable to those achieved with systematic constituent encoders. Catastrophic encoders, which do not possess a feedforward inverse, are shown to be capable of achieving low convergence thresholds by doping the code with a small fraction of systematic bits. Finally, we give tables of good nonsystematic turbo codes and present simulation results comparing the performance of systematic and nonsystematic turbo codes.