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The art of signaling: fifty years of coding theory

Publication ,  Journal Article
Calderbank, AR
Published in: IEEE Transactions on Information Theory
December 1, 1998

In 1948 Shannon developed fundamental limits on the efficiency of communication over noisy channels. The coding theorem asserts that there are block codes with code rates arbitrarily close to channel capacity and probabilities of error arbitrarily close to zero. Fifty years later, codes for the Gaussian channel have been discovered that come close to these fundamental limits. There is now a substantial algebraic theory of error-correcting codes with as many connections to mathematics as to engineering practice, and the last 20 years have seen the construction of algebraic-geometry codes that can be encoded and decoded in polynomial time, and that beat the Gilbert-Varshamov bound. Given the size of coding theory as a subject, this review is of necessity a personal perspective, and the focus is reliable communication, and not source coding or cryptography. The emphasis is on connecting coding theories for Hamming and Euclidean space and on future challenges, specifically in data networking, wireless communication, and quantum information theory. © 1998 IEEE.

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Published In

IEEE Transactions on Information Theory

DOI

ISSN

0018-9448

Publication Date

December 1, 1998

Volume

44

Issue

6

Start / End Page

2561 / 2595

Related Subject Headings

  • Networking & Telecommunications
  • 4613 Theory of computation
  • 4006 Communications engineering
  • 1005 Communications Technologies
  • 0906 Electrical and Electronic Engineering
  • 0801 Artificial Intelligence and Image Processing
 

Citation

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Calderbank, A. R. (1998). The art of signaling: fifty years of coding theory. IEEE Transactions on Information Theory, 44(6), 2561–2595. https://doi.org/10.1109/18.720549
Calderbank, A. R. “The art of signaling: fifty years of coding theory.” IEEE Transactions on Information Theory 44, no. 6 (December 1, 1998): 2561–95. https://doi.org/10.1109/18.720549.
Calderbank AR. The art of signaling: fifty years of coding theory. IEEE Transactions on Information Theory. 1998 Dec 1;44(6):2561–95.
Calderbank, A. R. “The art of signaling: fifty years of coding theory.” IEEE Transactions on Information Theory, vol. 44, no. 6, Dec. 1998, pp. 2561–95. Scopus, doi:10.1109/18.720549.
Calderbank AR. The art of signaling: fifty years of coding theory. IEEE Transactions on Information Theory. 1998 Dec 1;44(6):2561–2595.

Published In

IEEE Transactions on Information Theory

DOI

ISSN

0018-9448

Publication Date

December 1, 1998

Volume

44

Issue

6

Start / End Page

2561 / 2595

Related Subject Headings

  • Networking & Telecommunications
  • 4613 Theory of computation
  • 4006 Communications engineering
  • 1005 Communications Technologies
  • 0906 Electrical and Electronic Engineering
  • 0801 Artificial Intelligence and Image Processing