Fast-Group-Decodable STBCs via Codes over GF(4): Further Results

Abstract

Recently in [1], a framework was given to construct low ML decoding complexity Space-Time Block Codes (STBCs) via codes over the finite field F 4. In this paper, we construct new full-diversity STBCs with cubic shaping property and low ML decoding complexity via codes over F 4 for number of transmit antennas N = 2 m , m > 1, and rates R > 1 complex symbols per channel use. The new codes have the least ML decoding complexity among all known codes for a large set of (N, R) pairs. The new full-rate codes of this paper (R = N ) are not only information-lossless and fully diverse but also have the least known ML decoding complexity in the literature. For N ≥ 4, the new full-rate codes are the first instances of full-diversity, information-lossless STBCs with low ML decoding complexity. We also give a sufficient condition for STBCs obtainable from codes over F 4 to have cubic shaping property, and a sufficient condition for any design to give rise to a full-diversity STBC when the symbols are encoded using rotated square QAM constellations.

Iterated Space-Time Code Constructions From Cyclic Algebras

“…Analysis of conditions under which a code satisfies fast decodability can be found in e.g. [3]- [5], where the notions of fast decodable, group decodable and conditionally group decodable are detailed.…”

The nonassociative algebras used to build fast-decodable space-time block codes

“…One current goal in space-time block coding is to construct space-time block codes which are fast-decodable in the sense of [4], [7], [8] also when there are less receive than transmit antennas, support high data rates and have the potential to be systematically built for given numbers of transmit and receive antennas.…”

A class of iterated fast decodable space-time codes for 2ⁿ Tx antennas

“…While supplying full diversity, these codes also possess a lattice structure which incurs a high complexity of Maximum Likelihood (ML) decoding, typically implemented with a sphere decoder [2]. A line of research on fast-decodable codes initiated in [3] yielded several families of codes with reduced ML decoding complexity, notably in [4]- [6], where different notions of fast-decodability are studied and categorized. Codes for the Multiple Input Double Output (MIDO) channel have been of special interest due to their potential application to digital video broadcasting, where the number of receive antennas is limited by the size of the user's portable device.…”