A mathematical theory of communication

@article{Shannon2001AMT,
  title={A mathematical theory of communication},
  author={Claude E. Shannon},
  journal={Bell Syst. Tech. J.},
  year={2001},
  volume={27},
  pages={379-423}
}
  • 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… 
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References

SHOWING 1-3 OF 3 REFERENCES
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