Explicit Space-Time Codes Achieving The Diversity-Multiplexing Gain Tradeoff
<|reference_start|>Explicit Space-Time Codes Achieving The Diversity-Multiplexing Gain Tradeoff: A recent result of Zheng and Tse states that over a quasi-static channel, there exists a fundamental tradeoff, referred to as the diversity-multiplexing gain (D-MG) tradeoff, between the spatial multiplexing gain and the diversity gain that can be simultaneously achieved by a space-time (ST) block code. This tradeoff is precisely known in the case of i.i.d. Rayleigh-fading, for T>= n_t+n_r-1 where T is the number of time slots over which coding takes place and n_t,n_r are the number of transmit and receive antennas respectively. For T < n_t+n_r-1, only upper and lower bounds on the D-MG tradeoff are available.   In this paper, we present a complete solution to the problem of explicitly constructing D-MG optimal ST codes, i.e., codes that achieve the D-MG tradeoff for any number of receive antennas. We do this by showing that for the square minimum-delay case when T=n_t=n, cyclic-division-algebra (CDA) based ST codes having the non-vanishing determinant property are D-MG optimal. While constructions of such codes were previously known for restricted values of n, we provide here a construction for such codes that is valid for all n.   For the rectangular, T > n_t case, we present two general techniques for building D-MG-optimal rectangular ST codes from their square counterparts. A byproduct of our results establishes that the D-MG tradeoff for all T>= n_t is the same as that previously known to hold for T >= n_t + n_r -1.<|reference_end|>
@article{elia2006explicit,
    title={Explicit Space-Time Codes Achieving The Diversity-Multiplexing Gain
  Tradeoff},
    author={Petros Elia, K. Raj Kumar, Sameer A. Pawar, P. Vijay Kumar and
  Hsiao-feng Lu},
    journal={arXiv preprint arXiv:cs/0602054},
    year={2006},
    archivePrefix={arXiv},
    eprint={cs/0602054},
    primaryClass={cs.IT math.IT}
}