A mathematical theory of communication

  title={A mathematical theory of communication},
  author={Claude E. Shannon},
  journal={Bell Syst. Tech. J.},
  • C. Shannon
  • Published 1 July 1948
  • Mathematics
  • Bell Syst. Tech. J.
In this final installment of the paper we consider the case where the signals or the messages or both are continuously variable, in contrast with the discrete nature assumed until now. To a considerable extent the continuous case can be obtained through a limiting process from the discrete case by dividing the continuum of messages and signals into a large but finite number of small regions and calculating the various parameters involved on a discrete basis. As the size of the regions is… 
On a quantitative definition of information and its impact on the field of communications
The authors consider the overhead information in such a communication network that is necessary to protect the messages against unauthorised use, and to make sure that messages are delivered at the proper address.
Bounds on communication
This paper describes the boundary between compatible and incompatible sets of parameter values and assumes that the disturbance is additive Gaussian noise with constant power density spectrum in the transmission band.
Communication in the presence of noise
  • C. Shannon
  • Computer Science
    Proceedings of the IEEE
  • 1984
A method is developed for representing any communication system geometrically and a number of results in communication theory are deduced concerning expansion and compression of bandwidth and the threshold effect.
Theoretical Aspects of Asynchronous Multiplexing
  • W.D. White
  • Computer Science
    Proceedings of the IRE
  • 1950
An examination of the case where isolated transmitters share a common channel without synchronization is examined, and general observations on the efficiency of asynchronous multiplex systems are presented.
Taxonomy and Information
The greatest average transmission rate is achieved if the length L i of the ith message is set equal to the expected value of a random variable which has the value log k (1/p i ).
Theoretical Limitations on the Rate of Transmission of Information
A review of early work on the theory of the transmission of information is followed by a critical survey of this work and a refutation of the point that, in the absence of noise, there is a finite
Basic Principles of Communication Engineering
The reception of a binary signal in the presence of noise is given special emphasis, and it is examined how constraints linking the symbols, thus introducing redundancy, can endow a sequence with resilience to the errors which may individually affect its symbols.
Information theory and inverse probability in telecommunication
The foundations of information theory are presented as an extension of the theory of inverse probability. By postulating that information is additive and taking suitable averages, all the essential
On the role of dynamic programming in statistical communication theory
It is shown by Kelly that under certain conditions, the rate of transmission, as defined by Shannon, can be obtained from a certain multistage decision process with an economic criterion.


Transmission of information
A quantitative measure of “information” is developed which is based on physical as contrasted with psychological considerations. How the rate of transmission of this information over a system is
Certain factors affecting telegraph speed
In considering methods for increasing the speed of telegraph circuits, the engineer is confronted by the problem of transmitting over a circuit the maximum amount of intelligence using a given
In order to obtain the maximum power transfer from a generator to a load, a transformer must in general be introduced so that the generator as seen from the load has the load resistance
  • The situation here is roughly analogous. The transducer which does the encoding should match the source to the channel in a statistical sense. The source as seen from the channel through the transducer should have the same statistical structure 9Technical Report No. 65, The Research Laboratory of El
  • 1949