Construction methods for asymmetric and multiblock space-time codes

Camilla Hollanti*, Hsiao-Feng Lu

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

22 Scopus citations


In this paper, the need for the construction of asymmetric and multiblock space-time codes is discussed. Above the trivial puncturing method, i.e., switching off the extra layers in the symmetric multiple-input multiple-output (MIMO) setting, two more sophisticated asymmetric construction methods are proposed. The first method, called the block diagonal method (BDM), can be converted to produce multiblock space-time codes that achieve the diversity-multiplexing tradeoff (DMT). It is also shown that maximizing the density of the newly proposed block diagonal asymmetric space-time (AST) codes is equivalent to minimizing the discriminant of a certain order, a result that also holds as such for the multiblock codes. An implicit lower bound for the density is provided and made explicit for an important special case that contains e.g., the systems equipped with 4Tx +2Rx antennas. Further, an explicit scheme achieving the bound is given. Another method proposed here is the Smart Puncturing Method (SPM) that generalizes the subfield construction method proposed in earlier work by Hollanti and Ranto and applies to any number of transmitting and lesser receiving antennas. The use of the general methods is demonstrated by building explicit, sphere decodable codes using different cyclic division algebras (CDAs). Computer simulations verify that the newly proposed methods can compete with the trivial puncturing method, and in some cases clearly outperform it. The conquering construction exploiting maximal orders improves upon the punctured perfect code and the DjABBA code as well as the Icosian code. Also extensive DMT analysis is provided.

Original languageAmerican English
Pages (from-to)1086-1103
Number of pages18
JournalIEEE Transactions on Information Theory
Issue number3
StatePublished - 26 Mar 2009


  • Asymmetric space-time block codes (ASTBCs)
  • Cyclic division algebras (CDAs)
  • Dense lattices
  • Discriminants
  • Diversity-multiplexing tradeoff (DMT)
  • Maximal orders
  • Multiblock codes
  • Multiple-input multiple-output (MIMO) channels
  • Normalized minimum determinant


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