An approximation method for SNR soft information for a transmitter of a communications system includes obtaining a conditional probability density function (PDF) corresponding to a response message of a transmitted packet, obtaining a PDF of a probability distribution model, and a mean and a variance of the PDF, by approximating the conditional PDF corresponding to the response message with the probability distribution model, and calculating a second mean and a second variance of a second PDF approximated to a conditional PDF of SNR corresponding to the transmitted packet according to the mean and the variance of the PDF, and a first mean and a first variance of a first PDF approximated to a conditional PDF of SNR corresponding to another transmitted packet immediately preceding the transmitted packet.