We study two systems that are based on sums of weakly dependentBernoulli random variables that take values ± 1 with equalprobabilities. We show that already one step of the so-calledsoft decision parallel interference cancellation, used in the thirdgeneration of mobile telecommunication CDMA, is able to considerablyincrease the number of users such a system can host. We alsoconsider a variant of the well-known Hopfield model of neuralnetworks. We show that this variant proposed by Amari and Yanai[CITE] has a larger storage capacity than the original model. Both situations lead to the question of the moderatedeviations behavior of a sum of weakly dependent Bernoulli randomvariables. We prove a moderate deviations principle for such a sumon the appropriate scale.
