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2006.20: Mutual information and capacity of a linear digital channel

2006.20: D. S. Broomhead and Nikita Sidorov (2004) Mutual information and capacity of a linear digital channel. Nonlinearity, 17 (6). pp. 2203-2223. ISSN 1361-6544

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DOI: 10.1088/0951-7715/17/6/010

Abstract

In this paper we analyse a simple model of a digital communications channel. This model proves to be closely related to an iterated function system (IFS) related to the well-known Bernoulli convolution. We derive it from a randomly forced first-order ordinary differential equation. This allows the parameter of the Bernoulli convolution—the contraction rate, λ—to be related to the rate at which symbols are input to the channel. It is shown that for a channel with equiprobable binary inputs the mutual information between input and output distributions is the stationary measure of the complement of the overlap region of the IFS. We show that the mutual information is Hölder continuous with respect to λ and decreases hyper-exponentially as λ → 1. We also study the case of non-equiprobable binary inputs and show that the maximum of the mutual information—the channel capacity—does not always correspond to equiprobable inputs.

Item Type:Article
Uncontrolled Keywords:Digital channel, capacity, IFS, Bernoulli convolution
Subjects:MSC 2000 > 60 Probability theory and stochastic processes
MSC 2000 > 68 Computer science
MSC 2000 > 94 Information and communication, circuits
MIMS number:2006.20
Deposited By:Dr Mark Muldoon
Deposited On:02 March 2006

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