## Abstract

Recently, a family of full-rate, full-diversity spacetime block codes (STBCs) for 2 × 2 multiple-input multipleoutput (MIMO) channels was proposed in [1], [2], [3], [4] using a combination of Clifford algebra and Alamouti structures, namely twisted space-time transmit diversity code. This family was recently rediscovered by Paredes et al., and they pointed out that such STBCs enable reduced-complexity maximum-likelihood (ML) decoding. Independently, the same STBCs were found in [8], and named multi-strata space-time codes. In this paper we show how this code can be constructed algebraically from a particular cyclic division algebra (CDA). This formulation enables to prove that the code has the nonvanishing determinant (NVD) property and hence achieves the diversity-multiplexing tradeoff (DMT) optimality. The fact that the normalized minimum determinant is 1/√7 places this code in the second position with respect to the Golden code, which exhibits a minimum determinant of 1/√5, and motivates the name Silver code.

Original language | English |
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Title of host publication | 2008 IEEE Information Theory Workshop, ITW |

Publisher | IEEE |

Pages | 91-94 |

Number of pages | 4 |

ISBN (Electronic) | 978-1-4244-2270-8 |

ISBN (Print) | 978-1-4244-2269-2 |

DOIs | |

Publication status | Published - 2008 |

MoE publication type | A4 Article in a conference publication |

Event | IEEE Information Theory Workshop - Porto, Portugal Duration: 5 May 2008 → 8 May 2008 |

### Workshop

Workshop | IEEE Information Theory Workshop |
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Abbreviated title | ITW |

Country | Portugal |

City | Porto |

Period | 05/05/2008 → 08/05/2008 |

## Keywords

- DIVERSITY