Convergence Analysis and BER Performance of Finite-Length Turbo Codes

We propose the signal-to-noise ratio (SNR) transfer characteristic band (TCB) chart of extrinsic information (EI) as a basic tool for the probabilistic convergence analysis of iterative decoding. The proposed SNR TCB chart is a general version of the widely used SNR transfer chart, and it can model the behavior of EI in iterative decoding with any blocklength. We propose an algorithm using the SNR TCB chart to obtain the information, which is both quantitative and qualitative, on the probabilistic convergence behavior of iterative decoding. We also propose the bit-error rate (BER) estimate, in the form of a lower bound, of turbo codes over an additive white Gaussian noise channel. The proposed estimate is especially useful in estimating the BER of finite-length turbo codes in a waterfall region, while it is meaningful for all blocklengths and all E_b/N₀