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Grassmannian packings from operator ReedMuller codes

Publication ,  Journal Article
Ashikhmin, A; Calderbank, AR
Published in: IEEE Transactions on Information Theory
November 1, 2010

This paper introduces multidimensional generalizations of binary Reed-Muller codes where the codewords are projection operators, and the corresponding subspaces are widely separated with respect to the chordal distance on Grassmannian space. Parameters of these Grassmannian packings are derived and a low complexity decoding algorithm is developed by modifying standard decoding algorithms for binary Reed-Muller codes. The subspaces are associated with projection operators determined by Pauli matrices appearing in the theory of quantum error correction and this connection with quantum stabilizer codes may be of independent interest. The Grassmannian packings constructed here find application in noncoherent wireless communication with multiple antennas, where separation with respect to the chordal distance on Grassmannian space guarantees closeness to the channel capacity. It is shown that the capacity of the noncoherent multiple-inputmultiple-output (MIMO) channel at both low and moderate signal-to-noise ratio (SNR) (under the constraint that only isotropically distributed unitary matrices are used for information transmission) is closely approximated by these packings. © 2006 IEEE.

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Published In

IEEE Transactions on Information Theory

DOI

ISSN

0018-9448

Publication Date

November 1, 2010

Volume

56

Issue

11

Start / End Page

5689 / 5714

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
 

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Ashikhmin, A., & Calderbank, A. R. (2010). Grassmannian packings from operator ReedMuller codes. IEEE Transactions on Information Theory, 56(11), 5689–5714. https://doi.org/10.1109/TIT.2010.2070192
Ashikhmin, A., and A. R. Calderbank. “Grassmannian packings from operator ReedMuller codes.” IEEE Transactions on Information Theory 56, no. 11 (November 1, 2010): 5689–5714. https://doi.org/10.1109/TIT.2010.2070192.
Ashikhmin A, Calderbank AR. Grassmannian packings from operator ReedMuller codes. IEEE Transactions on Information Theory. 2010 Nov 1;56(11):5689–714.
Ashikhmin, A., and A. R. Calderbank. “Grassmannian packings from operator ReedMuller codes.” IEEE Transactions on Information Theory, vol. 56, no. 11, Nov. 2010, pp. 5689–714. Scopus, doi:10.1109/TIT.2010.2070192.
Ashikhmin A, Calderbank AR. Grassmannian packings from operator ReedMuller codes. IEEE Transactions on Information Theory. 2010 Nov 1;56(11):5689–5714.

Published In

IEEE Transactions on Information Theory

DOI

ISSN

0018-9448

Publication Date

November 1, 2010

Volume

56

Issue

11

Start / End Page

5689 / 5714

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