New approach to optimal approximation of tanh rule for LDPC codes under the Gaussian approximation

In this paper, a new approach is presented for optimizing the approximation of tanh rule based on Minimum Mean Square Error (MMSE) criterion under the Gaussian approximation. New concepts of anti-symmetric distribution and isomorphic generalized symmetric distribution are introduced. Under the isomorphic generalized symmetric distribution, several useful conclusions are drawn, by which a practical method for computing the optimal approximation is also presented. In comparison with the conventional approximation presented by Hagenauer, simulation results for several (3,6) regular Low-Density Parity-Check (LDPC) codes on the Additive White Gaussian Noise (AWGN) channel show that the approach can improve the decoding performance with a little increase in decoding complexity.