The Aladdin-Pythagoras space-time code

  • Authors:
  • Joseph J. Boutros;Hugues Randriambololona

  • Affiliations:
  • Texas A&M University, Department of Electrical Engineering, Education City, Doha, Qatar;TELECOM ParisTech, LTCI, CNRS UMR, Computer Science and Networks Department, Paris, France

  • Venue:
  • ISIT'09 Proceedings of the 2009 IEEE international conference on Symposium on Information Theory - Volume 4
  • Year:
  • 2009

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Abstract

Our motivation is the design of space-time coding which is optimal under both maximum likelihood and iterative decoding. We describe the construction of new full-rate space-time codes with non-vanishing determinant that satisfy the genie conditions for iterative probabilistic decoding. The problem combining the genie conditions and the rank criterion is rewritten in terms of a quadratic form. The construction over Z[i] (the cubic lattice) yields a family of codes defined by Pythagorean triples. The space-time code built over Z[i] and involving the quaternion algebra (i, 5/Q(i)) is referred to as the Aladdin-Pythagoras code. The construction over Z[j] (the hexagonal lattice) also yields a full-rate non-vanishing determinant code that is suitable for iterative decoding on multiple antenna channels.