Capacity bounds for the CDMA system and a neural network: a moderate deviations approach

Abstract

Abstract. We study two systems that are based on sums of weakly dependent Bernoulli random variables that take values ±1 with equal probabilities. We show that already one step of the so-called soft decision parallel interference cancellation, used in the third generation of mobile telecommunication CDMA, is able to considerably increase the number of users such a system can host. We also consider a variant of the well-known Hopfield model of neural networks. We show that this variant proposed by Amari and Yanai [2] has a larger storage capacity than the original model. Both situations lead to the question of the moderate deviations behavior of a sum of weakly dependent Bernoulli random variables. We prove a moderate deviations principle for such a sum on the appropriate scale. Mathematics Subject Classification. 82C32, 82B44, 60K35, 94A05, 94A15. Résumé. Nousétudions deux systèmes basés sur des sommes de variables aléatoires de