Algebraic identification for optimal nonorthogonality 4 × 4 complex space-time block codes using tensor product on quaternions

Ming Yang Chen, Hua Chieh Li, Soo Chang Pei

Research output: Contribution to journalArticle

12 Citations (Scopus)


The design potential of using quaternionic numbers to identify a 4 × 4 real orthogonal space-time block code has been exploited in various communication articles. Although it has been shown that orthogonal codes in full-rate exist only for 2 Tx-antennas in complex constellations, a series of complex quasi-orthogonal codes for 4 Tx-antennas is still proposed to have good performance recently. This quasi-orthogonal scheme enables the codes to reach the optimal nonorthogonality, which can be measured by taking the expectation over all transmit signals of the ratios between the powers of the off-diagonal and diagonal components. This correspondence extends the quaternionic identification to the above encoding methods. Based upon tensor product for giving the quaternionic space a linear extension, a complete necessary and sufficient condition for identifying any given complex quasi-orthogonal code with the extended space is generalized by considering every possible two-dimensional ℝ-algebra.

Original languageEnglish
Pages (from-to)324-330
Number of pages7
JournalIEEE Transactions on Information Theory
Issue number1
Publication statusPublished - 2005 Jan 1



  • Algebraic codes
  • Division algebras
  • Quasi-orthogonal space-time block code (STBC)
  • Quaternions
  • R-algebras
  • Representations of finite groups
  • Tensor product

ASJC Scopus subject areas

  • Information Systems
  • Computer Science Applications
  • Library and Information Sciences

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