Hsiao-feng Lu

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) 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 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

A unified construction of space-time codes with optimal rate-diversity tradeoff

The problem of constructing space-time (ST) block codes over a fixed, desired signal constellation is considered. In this situation, there is a tradeoff between the transmission rate as measured in constellation symbols per channel use and the transmit diversity gain achieved by the code. The transmit diversity is a measure of the rate of polynomial decay of pairwise error probability of the code with increase in the signal-to-noise ratio (SNR). In the setting of a quasi-static channel model, let n/sub t/ denote the number of transmit antennas and T the block interval. For any n/sub t/ /spl les/ T, a unified construction of (n/sub t/ /spl times/ T) ST codes is provided here, for a class of signal constellations that includes the familiar pulse-amplitude (PAM), quadrature-amplitude (QAM), and 2/sup K/-ary phase-shift-keying (PSK) modulations as special cases. The construction is optimal as measured by the rate-diversity tradeoff and can achieve any given integer point on the rate-diversity tradeoff curve. An estimate of the coding gain realized is given. Other results presented here include i) an extension of the optimal unified construction to the multiple fading block case, ii) a version of the optimal unified construction in which the underlying binary block codes are replaced by trellis codes, iii) the providing of a linear dispersion form for the underlying binary block codes, iv) a Gray-mapped version of the unified construction, and v) a generalization of construction of the -ary case corresponding to constellations of size /sup K/. Items ii) and iii) are aimed at simplifying the decoding of this class of ST codes.

Rate-diversity tradeoff of space-time codes with fixed alphabet and optimal constructions for PSK modulation

We show that for any (Q/spl times/M) space-time code S having a fixed, finite signal constellation, there is a tradeoff between the transmission rate R and the transmit diversity gain /spl nu/ achieved by the code. The tradeoff is characterized by R/spl les/Q-/spl nu/+1, where Q is the number of transmit antennas. When either binary phase-shift keying (BPSK) or quaternary phase-shift keying (QPSK) is used as the signal constellation, a systematic construction is presented to achieve the maximum possible rate for every possible value of transmit diversity gain.

Remarks on space-time codes including a new lower bound and an improved code

This article presents a new asymptotically exact lower bound on pairwise error probability of a space-time code as well as an example code that outperforms the comparable orthogonal-design-based space-time (ODST) code. Also contained in the article are an exact expression for pairwise error probability (PEP), signal design guidelines, and some observations relating to the reception of ODST codes.

Explicit space-time codes that achieve the diversity-multiplexing gain tradeoff

In the recent landmark paper of Zheng and Tse it is shown for the quasi-static, Rayleigh-fading MIMO channel with nt transmit and nr receive antennas, that there exists a fundamental tradeoff between diversity gain and multiplexing gain, referred to as the diversity-multiplexing gain (D-MG) tradeoff. This paper presents the first explicit construction of space-time (ST) codes for an arbitrary number of transmit and/or receive antennas that achieve the D-MG tradeoff. It is shown here that ST codes constructed from cyclic-division-algebras (CDA) and satisfying a certain non-vanishing determinant (NVD) property, are optimal under the D-MG tradeoff for any nt,nr. Furthermore, this optimality is achieved with minimum possible value of the delay or block-length parameter T = n t. CDA-based ST codes with NVD have previously been constructed for restricted values of nt. A unified construction of D-MG optimal CDA-based ST codes with NVD is given here, for any number nt of transmit antennas. The CDA-based constructions are also extended to provide D-MG optimal codes for all T ges nt, again for any number nt of transmit antennas. This extension thus presents rectangular D-MG optimal space-time codes that achieve the D-MG tradeoff. Taken together, the above constructions also extend the region of T for which the D-MG tradeoff is precisely known from T ges nt + nr - 1 to T ges nt

Constructions of Multiblock Space–Time Coding Schemes That Achieve the Diversity–Multiplexing Tradeoff

Constructions of multiblock space-time coding schemes that are optimal with respect to diversity-multiplexing (D-M) tradeoff when coding is applied over any number of fading blocks are presented in this correspondence. The constructions are based on a left-regular representation of elements in some cyclic division algebra. In particular, the main construction applies to the case when the quasi-static fading interval equals the number of transmit antennas, hence the resulting scheme is termed a minimal delay multiblock space-time coding scheme. Constructions corresponding to the cases of nonminimal delay are also provided. As the number of coded blocks approaches infinity, coding schemes derived from the proposed constructions can be used to provide a reliable multiple-input multiple-output (MIMO) communication with vanishing error probability.

Explicit Constructions of Multi-Block Space-Time Codes That Achieve The Diversity-Multiplexing Tradeoff

Constructions of multi-block space-time coding schemes that are optimal with respect to the diversity-multiplexing tradeoff when coding is applied over any number of independent fading blocks are presented in this paper. The constructions are based on the left-regular representation of elements of some cyclic division algebra. In particular, the main construction applies to the case when the quasi-static fading interval equals the number of transmit antennas, and the resultant scheme is termed minimal delay multi-block space-time coding scheme. Variations of this construction corresponding to the cases of non-minimal delay are also provided. As the number of coded blocks approaches infinity, coding schemes derived from the proposed constructions can be used to provide a reliable MIMO communication with vanishing error probability

Construction Methods for Asymmetric and Multiblock Space–Time Codes

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.

A Generalized Bose-Chowla Family of Optical Orthogonal Codes and Distinct Difference Sets

A new construction of optical orthogonal codes is provided in this correspondence which is a generalization of the well-known construction of distinct difference set (DDS) by Bose and Chowla. This construction is optimal with respect to the Johnson bound and has parameters n=qa-1, omega=q, and lambda=1

New Space–Time Code Constructions for Two-User Multiple Access Channels

This paper addresses the problem of constructing multiuser multiple-input multiple-output (MU-MIMO) codes for two users. The users are assumed to be equipped with nt transmit antennas, and there are nr antennas available at the receiving end. A general scheme is proposed and shown to achieve the optimal diversity-multiplexing gain tradeoff (DMT). Moreover, an explicit construction for the special case of nt = 2 and nr = 2 is given, based on the optimization of the code shape and density. All the proposed constructions are based on cyclic division algebras and their orders and take advantage of the multi-block structure. Computer simulations show that both the proposed schemes yield codes with excellent performance improving upon the best previously known codes. Finally, it is shown that the previously proposed design criteria for DMT optimal MU-MIMO codes are sufficient but in general too strict and impossible to fulfill. Relaxed alternative design criteria are then proposed and shown to be still sufficient for achieving the multiple-access channel diversity-multiplexing tradeoff.