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Published online by Cambridge University Press: 07 September 2011
Abstract
The paper considers the situation of transmission over a memoryless noisy channel with feedback, which can be given a number of interpretations. The criteria for achieving the maximal rate of information transfer are well known, but examples of a simple and meaningful coding meeting these are few. Such a one is found for the Gaussian channel.
Keywords feedback channel, Gaussian channel
AMS subject classification (MSC2010) 94A24
Interrogation, transmission and coding
In this section we set out material which is classic in high degree, harking back to Shannon's seminal paper (1948), and presented in some form in texts such as those of Blahut (1987), Cover and Thomas (1991) and MacKay (2003). However, some exposition is necessary if we are to distinguish clearly between three versions of the model.
Suppose that an experimenter wishes to determine the value of a random variable U of which he knows only the probability distribution P(U). The formal argument is conveyed well enough for the moment if we suppose all distributions discrete and use the notation P(·) generically for such distributions. We may also abuse this convention by occasionally using P(U) to denote the function of U defined by the distribution.
The outcome of the experiment, if errorless, might be written x(U), where the form of the function x(U) reflects the design of the experiment. The experimenter will choose this, subject to practical constraints, so as to make the experiment as informative as possible.
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