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

Published online by Cambridge University Press:  21 July 2009

Matthias Löwe  and
Franck Vermet
Matthias Löwe
Affiliation:
Fachbereich Mathematik und Informatik, Universität Münster, Einsteinstrasse 62, 48149 Münster, Germany; [email protected]
Franck Vermet
Affiliation:
Laboratoire de Mathématiques, UMR CNRS 6205, Université de Bretagne Occidentale, 6 avenue Victor Le Gorgeu CS 93837, 29238 Brest Cedex 3, France; [email protected]
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Abstract

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.

Keywords

Moderate deviationslarge deviationsneural networksstorage capacityHopfield modelcode division multiple access (CDMA) systemsparallel interference cancellation
Type
Research Article
Information
ESAIM: Probability and Statistics , Volume 13 , July 2009 , pp. 343 - 362
Copyright
© EDP Sciences, SMAI, 2009

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