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A forbidden rate region for generalized cross constellations

Publication ,  Journal Article
Gelblum, EA; Calderbank, AR
Published in: IEEE Transactions on Information Theory
December 1, 1997

An analysis of the Generalized Cross Constellation (GCC) is presented and a new perspective on its coding algorithm is described. We show how the GCC can be used to address generic sets of symbol points in any multidimensional space through an example based on the matched spectral null coding used in magnetic recording devices. We also prove that there is a forbidden rate region of fractional coding rates that are practically unrealizable using the GCC construction. We introduce the idea of a constellation tree and show how its decomposition can be used to design GCC's matching desired parameters. Following this analysis, an algorithm to design the optimal rate GCC from a restriction on the maximum size of its constellation signal set is given, and a formula for determining the size of the GCC achieving a desired coding rate is derived. We finish with an upper bound on the size of the constellation expansion ratio. © 1997 IEEE.

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Published In

IEEE Transactions on Information Theory

DOI

ISSN

0018-9448

Publication Date

December 1, 1997

Volume

43

Issue

1

Start / End Page

335 / 341

Related Subject Headings

  • Networking & Telecommunications
  • 1005 Communications Technologies
  • 0906 Electrical and Electronic Engineering
  • 0801 Artificial Intelligence and Image Processing
 

Citation

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Gelblum, E. A., & Calderbank, A. R. (1997). A forbidden rate region for generalized cross constellations. IEEE Transactions on Information Theory, 43(1), 335–341. https://doi.org/10.1109/18.567754
Gelblum, E. A., and A. R. Calderbank. “A forbidden rate region for generalized cross constellations.” IEEE Transactions on Information Theory 43, no. 1 (December 1, 1997): 335–41. https://doi.org/10.1109/18.567754.
Gelblum EA, Calderbank AR. A forbidden rate region for generalized cross constellations. IEEE Transactions on Information Theory. 1997 Dec 1;43(1):335–41.
Gelblum, E. A., and A. R. Calderbank. “A forbidden rate region for generalized cross constellations.” IEEE Transactions on Information Theory, vol. 43, no. 1, Dec. 1997, pp. 335–41. Scopus, doi:10.1109/18.567754.
Gelblum EA, Calderbank AR. A forbidden rate region for generalized cross constellations. IEEE Transactions on Information Theory. 1997 Dec 1;43(1):335–341.

Published In

IEEE Transactions on Information Theory

DOI

ISSN

0018-9448

Publication Date

December 1, 1997

Volume

43

Issue

1

Start / End Page

335 / 341

Related Subject Headings

  • Networking & Telecommunications
  • 1005 Communications Technologies
  • 0906 Electrical and Electronic Engineering
  • 0801 Artificial Intelligence and Image Processing