### Abstract

Our motivation is the design of space-time coding which is optimal under both maxim um likelihood and iterative decoding. We describe the construction of new full-rate spacetime 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[iJ and involving the quaternion algebra (i5/(Qi)) is referred to as the Aladdin-Pythagoras code. The construction over Z[j] (the hexagonal lattice) also yields a fullrate non-vanishing determinant code that is suitable for iterative decoding on multiple antenna channels.

Original language | English |
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Title of host publication | 2009 IEEE International Symposium on Information Theory, ISIT 2009 |

Pages | 2823-2827 |

Number of pages | 5 |

DOIs | |

Publication status | Published - 19 Nov 2009 |

Event | 2009 IEEE International Symposium on Information Theory, ISIT 2009 - Seoul, Korea, Republic of Duration: 28 Jun 2009 → 3 Jul 2009 |

### Other

Other | 2009 IEEE International Symposium on Information Theory, ISIT 2009 |
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Country | Korea, Republic of |

City | Seoul |

Period | 28/6/09 → 3/7/09 |

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### ASJC Scopus subject areas

- Theoretical Computer Science
- Information Systems
- Modelling and Simulation
- Applied Mathematics

### Cite this

*2009 IEEE International Symposium on Information Theory, ISIT 2009*(pp. 2823-2827). [5205763] https://doi.org/10.1109/ISIT.2009.5205763