The final case of the decoding delay problem for maximum rate complex orthogonal designs

Authors:
Sarah Spence Adams;Nathaniel Karst;Mathav Kishore Murugan
Affiliations:
Franklin W. Olin College of Engineering, Needham, MA;Center for Applied Mathematics, Cornell University, Ithaca, NY;Morgan Stanley, Mumbai and Indian Institute of Technology, Kharagpur, India
Venue:
IEEE Transactions on Information Theory
Year:
2010

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Abstract

Complex orthogonal space-time block codes (COSTBCs) based on generalized complex orthogonal designs (CODs) have been successfully implemented in wireless systems with multiple transmit antennas and single or multiple receive antennas. It has been shown that for a maximum rate COD with 2m - 1 or 2m columns, a lower bound on decoding delay is (2m m-1) and this delay is achievable when the number of columns is congruent to 0, 1, or 3 modulo 4. In this paper, the final case is addressed, and it is shown that when the number of columns is congruent to 2 modulo 4, the lower bound on decoding delay cannot be achieved. In this case, the shortest decoding delay a maximum rate COD can achieve is twice the lower bound. New techniques for analyzing CODs are introduced with connections to binary vector spaces.