Explicit space-time codes achieving the diversity-multiplexing gain tradeoff

Elia, P. ; Kumar, K. R. ; Pawar, S. A. ; Kumar, P. V. ; Lu, H.-F. (2006) Explicit space-time codes achieving the diversity-multiplexing gain tradeoff IEEE Transactions on Information Theory, 52 (9). pp. 3869-3884. ISSN 0018-9448

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Official URL: http://ieeexplore.ieee.org/document/1683914/

Related URL: http://dx.doi.org/10.1109/TIT.2006.880037

Abstract

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) code. This tradeoff is precisely known in the case of independent and identically distributed (i.i.d.) Rayleigh fading, for Tgesnt+nr-1 where T is the number of time slots over which coding takes place and nt,nr are the number of transmit and receive antennas, respectively. For T<nt+nr-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=nt=n, cyclic-division-algebra (CDA)-based ST codes having the nonvanishing 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>nt 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 Tgesnt is the same as that previously known to hold for Tgesnt+n r-1.

Item Type:Article
Source:Copyright of this article belongs to Institute of Electrical and Electronic Engineers.
Keywords:Space-Time Codes; Cyclic Division Algebra; Diversity-Multiplexing Gain Tradeoff; Explicit Construction
ID Code:110087
Deposited On:31 Jan 2018 10:15
Last Modified:31 Jan 2018 10:15

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