Error probability analyses of maximum a posteriori probability decoding by moment techniques

The error probability performance of convolutional codes are mostly evaluated by computer simulations, and few studies have been made for exact error probability of convolutional codes. In [1], the moments of decision variable are derived by a recurrence relation for maximum a-posteriori probability (MAP) decoding of 4-state convolutional code. However, due to the convergence problem of moment techniques, the error probability is shown only for a modified MAP decoding, which employs Jth root of branch metrics. In this paper, the generalized Gram-Charlier expansion is introduced to obtain the good convergence property. The root normal distribution is found to be appropriate as a reference distribution in the expansion. The techniques are also applied to MAP decoding in Middleton's class A impulsive noise channels, and the exact error probability is demonstrated.