  Space-Time Block Codes (STBCs) suffer from a prohibitively high decoding
complexity unless the low-complexity decodability property is taken into
consideration in the STBC design. For this purpose, several families of STBCs
that involve a reduced decoding complexity have been proposed, notably the
multi-group decodable and the fast decodable (FD) codes. Recently, a new family
of codes that combines both of these families namely the fast group decodable
(FGD) codes was proposed. In this paper, we propose a new construction scheme
for rate-1 FGD codes for 2^a transmit antennas. The proposed scheme is then
applied to the case of four transmit antennas and we show that the new rate-1
FGD code has the lowest worst-case decoding complexity among existing
comparable STBCs. The coding gain of the new rate-1 code is optimized through
constellation stretching and proved to be constant irrespective of the
underlying QAM constellation prior to normalization. Next, we propose a new
rate-2 FD STBC by multiplexing two of our rate-1 codes by the means of a
unitary matrix. Also a compromise between rate and complexity is obtained
through puncturing our rate-2 FD code giving rise to a new rate-3/2 FD code.
The proposed codes are compared to existing codes in the literature and
simulation results show that our rate-3/2 code has a lower average decoding
complexity while our rate-2 code maintains its lower average decoding
complexity in the low SNR region. If a time-out sphere decoder is employed, our
proposed codes outperform existing codes at high SNR region thanks to their
lower worst-case decoding complexity.
