B.A. Sethuraman

Bio: B.A. Sethuraman is an academic researcher from California State University, Northridge. The author has contributed to research in topics: Division algebra & Block code. The author has an hindex of 14, co-authored 50 publications receiving 1264 citations. Previous affiliations of B.A. Sethuraman include California State University & University of Southern California.

Full-diversity, high-rate space-time block codes from division algebras

Abstract: We present some general techniques for constructing full-rank, minimal-delay, rate at least one space-time block codes (STBCs) over a variety of signal sets for arbitrary number of transmit antennas using commutative division algebras (field extensions) as well as using noncommutative division algebras of the rational field /spl Qopf/ embedded in matrix rings. The first half of the paper deals with constructions using field extensions of /spl Qopf/. Working with cyclotomic field extensions, we construct several families of STBCs over a wide range of signal sets that are of full rank, minimal delay, and rate at least one appropriate for any number of transmit antennas. We study the coding gain and capacity of these codes. Using transcendental extensions we construct arbitrary rate codes that are full rank for arbitrary number of antennas. We also present a method of constructing STBCs using noncyclotomic field extensions. In the later half of the paper, we discuss two ways of embedding noncommutative division algebras into matrices: left regular representation, and representation over maximal cyclic subfields. The 4/spl times/4 real orthogonal design is obtained by the left regular representation of quaternions. Alamouti's (1998) code is just a special case of the construction using representation over maximal cyclic subfields and we observe certain algebraic uniqueness characteristics of it. Also, we discuss a general principle for constructing cyclic division algebras using the nth root of a transcendental element and study the capacity of the STBCs obtained from this construction. Another family of cyclic division algebras discovered by Brauer (1933) is discussed and several examples of STBCs derived from each of these constructions are presented.

Perfect Space–Time Codes for Any Number of Antennas

Abstract: In a recent paper, perfect (n times n) space-time codes were introduced as the class of linear dispersion space-time (ST) codes having full rate, nonvanishing determinant, a signal constellation isomorphic to either the rectangular or hexagonal lattices in 2n 2 dimensions, and uniform average transmitted energy per antenna. Consequence of these conditions include optimality of perfect codes with respect to the Zheng-Tse diversity-multiplexing gain tradeoff (DMT), as well as excellent low signal-to-noise ratio (SNR) performance. Yet perfect space-time codes have been constructed only for two, three, four, and six transmit antennas. In this paper, we construct perfect codes for all channel dimensions, present some additional attributes of this class of ST codes, and extend the notion of a perfect code to the rectangular case.

Perfect space-time codes with minimum and non-minimum delay for any number of antennas

Abstract: We here introduce explicit constructions of minimum-delay perfect space-time codes for any number n/sub t/ of transmit antennas and any number n/sub t/ of receive antennas. We also proceed to construct non-minimal delay perfect space-time codes for any n/sub t/, n/sub r/ and any block length T /spl ges/ n/sub t/. Perfect space-time codes were first introduced in F. Oggier et al. (2004) for dimensions of 2 /spl times/ 2, 3 /spl times/ 3, 4 /spl times/ 4 and 6 /spl times/ 6, to be the space-time codes that have full rate, full diversity-gain, non-vanishing determinant for increasing spectral efficiency, uniform average transmitted energy per antenna and good shaping of the constellation. The term perfect corresponds to the fact that the code simultaneously satisfies all the above mentioned important criteria. As a result, perfect codes have proven to have extraordinary performance. Finally, we point out that the set of criteria in F. Oggier et al. (2004) of non-vanishing determinant, full diversity, and full rate, is a subset of the more general and more strict set of criteria for optimally in the diversity-multiplexing gain (D-MG) tradeoff [Elias, P. et al., 2004], [Kumar, K.R. et al., 2005], an approach that takes special significance when constructing non-minimal delay perfect codes. Both minimum and non-minimum delay perfect codes are shown to be D-MG optimal.

Information-Lossless Space–Time Block Codes From Crossed-Product Algebras

Abstract: It is known that the Alamouti code is the only complex orthogonal design (COD) which achieves capacity and that too for the case of two transmit and one receive antenna only. Damen proposed a design for two transmit antennas, which achieves capacity for any number of receive antennas, calling the resulting space-time block code (STBC) when used with a signal set an information-lossless STBC. In this paper, using crossed-product central simple algebras, we construct STBCs for arbitrary number of transmit antennas over an a priori specified signal set. Alamouti code and quasi-orthogonal designs are the simplest special cases of our constructions. We obtain a condition under which these STBCs from crossed-product algebras are information-lossless. We give some classes of crossed-product algebras, from which the STBCs obtained are information-lossless and also of full rank. We present some simulation results for two, three, and four transmit antennas to show that our STBCs perform better than some of the best known STBCs and also that these STBCs are approximately 1 dB away from the capacity of the channel with quadrature amplitude modulation (QAM) symbols as input

The Book of Involutions

Abstract: This monograph yields a comprehensive exposition of the theory of central simple algebras with involution, in relation with linear algebraic groups It aims to provide the algebra-theoretic foundations for much of the recent work on linear algebraic groups over arbitrary fields Involutions are viewed as twisted forms of similarity classes of hermitian or bilinear forms, leading to new developments on the model of the algebraic theory of quadratic forms Besides classical groups, phenomena related to triality are also discussed, as well as groups of type F_4 or G_2 arising from exceptional Jordan or composition algebras Several results and notions appear here for the first time, notably the discriminant algebra of an algebra with unitary involution and the algebra-theoretic counterpart to linear groups of type D_4 For research mathematicians and graduate students working in central simple algebras, algebraic groups, nonabelian Galois cohomology or Jordan algebras

The golden code: a 2/spl times/2 full-rate space-time code with nonvanishing determinants

Abstract: In this paper, the Golden code for a 2/spl times/2 multiple-input multiple-output (MIMO) system is presented. This is a full-rate 2/spl times/2 linear dispersion algebraic space-time code with unprecedented performance based on the Golden number 1+/spl radic/5/2.

The golden code: a 2 x 2 full-rate space-time code with non-vanishing determinants

Abstract: In this paper we present the Golden code for a 2times2 MIMO system. This is a full-rate 2times2 linear dispersion algebraic space-time code with unprecedented performance based on the Golden number 1+radic5/2