Methods and systems for demodulating a multiuser signal using channel decoders for a multiple-access communication system are disclosed. According to one method, a signal containing information for a plurality of users in a multiple-access communication system employing spreading sequences is received. The received signal is despread using a signature sequence for each user to produce individual user signals having multiple-access interference (MAI). Channel estimates associated with each of the individual user received signals are determined. Each of the individual user signals are decoded using a channel decoder with a log-likelihood ratio (LLR) that accounts for the time-varying variance of the MAI in the individual user signals based on a model of the MAI including the channel estimates of the received signals of other users.