TY - JOUR
T1 - Construction methods for asymmetric and multiblock space-time codes
AU - Hollanti, Camilla
AU - Lu, Hsiao-Feng
PY - 2009/3/26
Y1 - 2009/3/26
N2 - 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.
AB - 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.
KW - Asymmetric space-time block codes (ASTBCs)
KW - Cyclic division algebras (CDAs)
KW - Dense lattices
KW - Discriminants
KW - Diversity-multiplexing tradeoff (DMT)
KW - Maximal orders
KW - Multiblock codes
KW - Multiple-input multiple-output (MIMO) channels
KW - Normalized minimum determinant
UR - http://www.scopus.com/inward/record.url?scp=62749084523&partnerID=8YFLogxK
U2 - 10.1109/TIT.2008.2011449
DO - 10.1109/TIT.2008.2011449
M3 - Article
AN - SCOPUS:62749084523
SN - 0018-9448
VL - 55
SP - 1086
EP - 1103
JO - IEEE Transactions on Information Theory
JF - IEEE Transactions on Information Theory
IS - 3
ER -