By using the equations derived from extrinsic information transfer (EXIT) functions, we propose a new performance-analysis method for belief propagation (BP) decoding of regular and irregular low-density parity-check (LDPC) codes. By means of the derived so-called EXIT equations, the problem of finding the convergence threshold for a given regular or irregular LDPC code can be described as a minimizing optimization. On the additive white Gaussian noise (AWGN) channel, the achieved convergence threshold values by our proposed optimization for the enumerated regular and irregular codes have error to those from density evolution about 0.01 dB and 0.05 dB, respectively. Furthermore, the proposed method in contrast with density evolution is more convenient since no iterations and no computations for Fourier and inverse Fourier transforms are required during the performance analysis.
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