On the Existence of Universally Decodable Matrices

  • Authors:
  • A. Ganesan;P. O. Vontobel

  • Affiliations:
  • Univ. of Wisconsin-Madison, Madison;-

  • Venue:
  • IEEE Transactions on Information Theory
  • Year:
  • 2007

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Abstract

Universally decodable matrices (UDMs) can be used for coding purposes when transmitting over slow fading channels. These matrices are parameterized by positive integers L and N and a prime power q. The main result of this correspondence is that the simple condition L = q + 1 is both necessary and sufficient for (L, N, q)-VDMs to exist. The existence proof is constructive and yields a coding scheme that is equivalent to a class of codes that was proposed by Rosenbloom and Tsfasman. Our work resolves an open problem posed recently in the literature.