Infinite series of interference variables with Cantor-type distributions

The sum of an infinite series of weighted binary random variables arises in communications problems involving intersymbol and adjacent-channel interference. If the weighting decays asymptotically at least exponentially and if the decay is not too slow, the sum has an unusual distribution which has neither a density nor a discrete mass function, and therefore cannot be manipulated with usual techniques. The distribution of the sum is given, and the calculus for dealing with the distribution is presented. It is shown that these Cantor-type random variables arise in a range of digital communications models, and exact explicit expressions for performance measures, such as the probability of error, may be obtained. Several examples are given.<
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