Fast-Decodable Asymmetric Space-Time Codes from Division Algebras

TL;DR

This paper introduces a new family of division algebra-based 4x4 MIDO space-time codes that significantly reduce decoding complexity while maintaining full diversity and NVD, suitable for modern wireless channels.

Contribution

It presents a general class of fast-decodable 4x4 MIDO codes with guaranteed complexity reduction and full diversity, based on division algebra constructions.

Findings

At least 37.5% worst-case complexity reduction.

Codes maintain full diversity and non-vanishing determinant.

Explicit constructions demonstrate excellent performance.

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 x 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 x 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. Several explicit constructions are presented and shown to have excellent performance through computer simulations.