Fast-Decodable Asymmetric Space-Time Codes From Division Algebras

Abstract

Multiple-input double-output (MIDO) codes are important in the near-future wireless communications, where the portable end-user device is physically small and will typically contain at most two receive antennas. Especially tempting is the 4 × 2 channel due to its immediate applicability in the digital video broadcasting (DVB). Such channels optimally employ rate-two space-time (ST) codes consisting of (4 × 4) matrices. Unfortunately, such codes are in general very complex to decode, hence setting forth a call for constructions with reduced complexity.Recently, some reduced complexity constructions have been proposed, but they have mainly been based on different ad hoc methods and have resulted in isolated examples rather than in a more general class of codes. In this paper, it will be shown that a family of division algebra based MIDO codes will always result in at least 37.5% worst-case complexity reduction, while maintaining full diversity and, for the first time, the non-vanishing determinant (NVD) property. The reduction follows from the fact that, similarly to the Alamouti code, the codes will be subsets of matrix rings of the Hamiltonian quaternions, hence allowing simplified decoding. At the moment, such reductions are among the best known for rate-two MIDO codes [4], [5]. Several explicit constructions are presented and shown to have excellent performance through computer simulations. Index Terms-Coding gain, cyclic division algebra, digital video broadcasting next generation handheld (DVB-NGH), fast maximum-likelihood (ML) sphere decoding, Hamiltonian quaternions, Hasse invariants, lattices, lowcomplexity space-time block codes (STBCs), multiple-input single/double/multiple-output (MISO/MIDO/MIMO), nonvanishing determinant (NVD), orders.

Fast-Decodable MIDO Codes With Large Coding Gain

“…£ The exact minimum determinant of this STBC has not been calculated, but it has been shown that the STBC has the NVD property [1]. ¥ These STBCs are not available explicitly in [1].…”

“…Such a scenario occurs, for example, in the downlink transmission from a base station to a mobile phone, and in digital video broadcasting (DVB) where communication is between a TV broadcasting station and a portable TV device (see, for example, [14]). Of particular interest is the 4 × 2 MIDO system for which a slew of rate-2 STBCs have been developed [1], [2], [15]- [20], with the particular aim of allowing fast-decodability (see Definition 7), a term that was first coined in [15]. Among these codes, those in [1], [16]- [20] have been shown to have a minimum determinant that is bounded away from zero irrespective of the size of the signal constellation and hence STBC-schemes that consist of these codes have the NVD property and are DMToptimal for the 4 × 2 MIDO system [21].…”

“…Among these codes, those in [1], [16]- [20] have been shown to have a minimum determinant that is bounded away from zero irrespective of the size of the signal constellation and hence STBC-schemes that consist of these codes have the NVD property and are DMToptimal for the 4 × 2 MIDO system [21]. A generalization of fast-decodable STBC construction for higher number of transmit antennas has been proposed in [1]. STBCs from nonassociative division algebras have also been proposed in [22].…”

Fast-decodable MIDO codes from non-associative algebras

“…Fast-decodable codes are treated by Biglieri, Hong and Viterbo [15], Vehkalahti, Hollanti and Oggier [16], [17], Luzzi and Oggier [18], Markin and Oggier [19], and in [13], [14] and [9], to name just a few.…”

Minimizing the complexity of fast sphere decoding of STBCs

“…Fast decodable codes (codes that admit FSD) have reduced SD complexity owing to the fact that a few of the variables can be decoded as single symbols or in groups if we condition them with respect to the other variables. Fast decodable codes for asymmetric systems using division algebras have been recently reported [11]. Golden code and Silver code are also examples of fast decodable codes as shown in [12] and [13].…”