The performance of fingerprinting codes has been studied under the well-known marking assumption. In a realistic environment, however, a pirated copy will be distorted by an additional attack. Under the assumption that the distortion is modeled as AWGN, a soft decision method for a tracing algorithm has been proposed and the traceability has been experimentally evaluated. However, the previous soft decision method works directly with a received signal without considering the communication theory. In this study, we calculate the likelihood of received signal considering a posterior probability, and propose a soft decision tracing algorithm considering the characteristic of Gaussian channel. For the estimation of channel, we employ the expectation-maximization algorithm by giving constraints under the possible collusion strategies. We also propose an equalizer to give a proper weighting parameter for calculating a correlation score.