Fast-group-decodable STBCs via codes over GF(4)

Abstract

Abstract-In this paper we construct low ML decoding complexity STBCs by using the Pauli matrices as linear dispersion matrices. In this case the Hurwitz-Radon orthogonality condition is shown to be easily checked by transferring the problem to F4 domain. The problem of constructing low ML decoding complexity STBCs is shown to be equivalent to finding certain codes over F4. It is shown that almost all known low ML decoding complexity STBCs can be obtained by this approach. New classes of codes are given that have the least known ML decoding complexity in some ranges of rate.

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

“…LOW ML DECODING COMPLEXITY DESIGNS VIA CODES OVER F 4 In this section, we briefly review the framework given in [1] to construct low ML decoding complexity designs via codes over F 4 . Using this framework, new codes with fulldiversity, cubic shaping and low ML decoding complexity are constructed in Section IV.…”

“…We first review the construction of rate 5 4 cspcu FGD designs given in [1]. Using these designs, we then construct new full-diversity STBCs with cubic shaping property and low ML decoding complexity for N = 2 m , m > 1, antennas and rates R > 1.…”

“…New FD and FGD codes were constructed using this framework and it was shown that almost all known multigroup ML decodable STBCs can be obtained via codes over F 4 . It was also shown in [1] that the FGD STBC of [3] is a specific example of STBCs obtainable via codes over F 4 .…”

“…In [1], a framework was given to construct full-diversity, low ML decoding complexity STBCs via codes over F 4 . New FD and FGD codes were constructed using this framework and it was shown that almost all known multigroup ML decodable STBCs can be obtained via codes over F 4 .…”

“…• We give a sufficient condition for a design to give rise to a full-diversity STBC when the real symbols of the design are encoded pairwise using rotated square QAM constellations (Section II). In Section III, we briefly review the framework given in [1] for constructing low ML decoding complexity STBCs via codes over F 4 . Concluding remarks and directions for future work are discussed in Section V.…”