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 et al. proposed a design for 2 transmit antennas, which achieves capacity for any number of receive antennas, calling the resulting STBC when used with a signal set an informationlossless STBC. In this paper, using crossed-product central simple algebras, we construct STBCs for arbitrary number of transmit antennas over an apriori 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 fullrank. 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 QAM symbols as input.

Cyclic Division Algebras: A Tool for Space-Time Coding

“…In [7,44] and then in [21], perfect codes were presented as division algebra codes which furthermore satisfy a shaping property and have a non-vanishing determinant. In [53], information lossless codes from crossed product algebras, a new family of division algebras, are presented. In [31], codes from maximal orders of division algebras are investigated.…”

MMSE optimal algebraic space-time codes

“…For instance, MMSE optimal STBCs can also be constructed from tensor products of division algebras and Brauer division algebras. We refer the readers to [12] for more details on these constructions.…”

“…In this subsection, using Theorem 1, we identify an existing STBC construction [12], [13] based on cyclic algebras to be MMSE optimal.…”

On Improving 4 � 4 Space-Time Codes

“…Note that in order to have information lossless code [5], the matrix R has to be unitary and γ of complex modulus 1. In other words, those conditions also guarantee an efficient encoding, since the encoding does not change the energy at the transmitter.…”

“…They also benefit of an efficient encoding, which consists in putting the information symbols into the layer of the spacetime code using a lattice structure, that does not increase the energy of the system. This property is also called information lossless [5], and guarantees that there is no loss of capacity compared to uncoded systems.…”