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We propose a tool for the analysis of the finite-length iterative turbo decoding algorithm. The proposed tool is a generalized EXIT (extrinsic information transfer) chart based on the mutual information transfer characteristics of the extrinsic information in the iterative turbo decoding algorithm. The proposed tool can describe the probabilistic convergence behavior of the iterative decoding algorithm. By using this tool, we obtain the BER estimates of the finite-length turbo codes in the form of a lower bound, which shows a gentle waterfall over a wide waterfall region. The obtained lower bound is in reasonable agreement with the BER obtained by simulations of the iterative decoding algorithm.