On The Statistical Analysis Based Waterfall Region Performance Evaluation For Turbo Codes

Turbo codes have been widely uitlized because of their outstanding performance. Meanwhile, the iterative decoding convergence analysis and performance analysis of Turbo codes are always the core challenges since its invention. Basically, the performance of Turbo codes can be sub-divided into two characteristic regions, namley the waterfall region and the error floor region. The performance of error floor region can be evaluated by using Union Bound or the free distance asymptote, while little progress has been made for the analysis of waterfall region behavior. Based on the statistical analysis of LLR (Log-Likelihood Ratio) out of the Turbo decoders, the iterative decoding convergence and waterfall region performance are investigated in this thesis.After a brief introduction of the Turbo encoding and decoding principle, some existing methods for decoding convergence analysis and performance evaluation are reviewed and compared with each other. A statistical analysis model of LLR based on all-ones information sequence assumption is presented in this thesis. And our analysis results indicate that, with the increase in the iteration numbers, the statistical distribution of LLR within waterfall region can be well approximated with Gaussian mixture models. Moreover, it is shown through simulations that the Gaussian mixture distirbution provides a general model to characterize the stochastic distribution of different information bits with different information length at different SNR.Based on the Gaussian mixture stochastic modeling of the LLRs, the connection between the LLR distribution models and the achieved iterative decoding convergence as well as the final decoding reliability are explicated. It is shown that, the iterative Turbo decoding within waterfall region is to move the LLR values from the ambiguious decision zone to more reliable decision zone. By examining the area values of both the left LLR side-lope and the right ones around the convergence threshold, it is unveiled that the convergence threshold SNR value almost corresponds to the area reversion point in between the left sidelobe and the right one. Further simulation results and analysis demonstrate that, the achieved reliability performance of Turbo decoding within waterfall region can be well approximated by the left side-lope distribution characteristics of the Gaussian mixture models as well.The sthochastic modeling of the LLR distribution out of iterative Turbo decoding in this thesis provides some interesting hints for next step work on the waterfall region performance formulation and more accurate analysis efforts.