Book contents
- Frontmatter
- Contents
- List of contributors
- Preface
- Bibliography of J. F. C. Kingman
- 1 A fragment of autobiography, 1957–1967
- 2 More uses of exchangeability: representations of complex random structures
- 3 Perfect simulation using dominated coupling from the past with application to area-interaction point processes and wavelet thresholding
- 4 Assessing molecular variability in cancer genomes
- 5 Branching out
- 6 Kingman, category and combinatorics
- 7 Long-range dependence in a Cox process directed by an alternating renewal process
- 8 Kernel methods and minimum contrast estimators for empirical deconvolution
- 9 The coalescent and its descendants
- 10 Kingman and mathematical population genetics
- 11 Characterizations of exchangeable partitions and random discrete distributions by deletion properties
- 12 Applying coupon-collecting theory to computer-aided assessments
- 13 Colouring and breaking sticks: random distributions and heterogeneous clustering
- 14 The associated random walk and martingales in random walks with stationary increments
- 15 Diffusion processes and coalescent trees
- 16 Three problems for the clairvoyant demon
- 17 Homogenization for advection-diffusion in a perforated domain
- 18 Heavy traffic on a controlled motorway
- 19 Coupling time distribution asymptotics for some couplings of the Lévy stochastic area
- 20 Queueing with neighbours
- 21 Optimal information feed
- 22 A dynamical-system picture of a simple branching-process phase transition
- Index
21 - Optimal information feed
Published online by Cambridge University Press: 07 September 2011
- Frontmatter
- Contents
- List of contributors
- Preface
- Bibliography of J. F. C. Kingman
- 1 A fragment of autobiography, 1957–1967
- 2 More uses of exchangeability: representations of complex random structures
- 3 Perfect simulation using dominated coupling from the past with application to area-interaction point processes and wavelet thresholding
- 4 Assessing molecular variability in cancer genomes
- 5 Branching out
- 6 Kingman, category and combinatorics
- 7 Long-range dependence in a Cox process directed by an alternating renewal process
- 8 Kernel methods and minimum contrast estimators for empirical deconvolution
- 9 The coalescent and its descendants
- 10 Kingman and mathematical population genetics
- 11 Characterizations of exchangeable partitions and random discrete distributions by deletion properties
- 12 Applying coupon-collecting theory to computer-aided assessments
- 13 Colouring and breaking sticks: random distributions and heterogeneous clustering
- 14 The associated random walk and martingales in random walks with stationary increments
- 15 Diffusion processes and coalescent trees
- 16 Three problems for the clairvoyant demon
- 17 Homogenization for advection-diffusion in a perforated domain
- 18 Heavy traffic on a controlled motorway
- 19 Coupling time distribution asymptotics for some couplings of the Lévy stochastic area
- 20 Queueing with neighbours
- 21 Optimal information feed
- 22 A dynamical-system picture of a simple branching-process phase transition
- Index
Summary
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.
- Type
- Chapter
- Information
- Probability and Mathematical GeneticsPapers in Honour of Sir John Kingman, pp. 483 - 490Publisher: Cambridge University PressPrint publication year: 2010