  When the Channel State Information (CSI) is known by both the transmitter and
the receiver, beamforming techniques employing Singular Value Decomposition
(SVD) are commonly used in Multiple-Input Multiple-Output (MIMO) systems.
Without channel coding, there is a trade-off between full diversity and full
multiplexing. When channel coding is added, both of them can be achieved as
long as the code rate Rc and the number of employed subchannels S satisfy the
condition RcS<=1. By adding a properly designed constellation precoder, both
full diversity and full multiplexing can be achieved for both uncoded and coded
systems with the trade-off of a higher decoding complexity, e.g., Fully
Precoded Multiple Beamforming (FPMB) and Bit-Interleaved Coded Multiple
Beamforming with Full Precoding (BICMB-FP) without the condition RcS<=1.
Recently discovered Perfect Space-Time Block Code (PSTBC) is a full-rate
full-diversity space-time code, which achieves efficient shaping and high
coding gain for MIMO systems. In this paper, a new technique, Bit-Interleaved
Coded Multiple Beamforming with Perfect Coding (BICMB-PC), is introduced.
BICMB-PC transmits PSTBCs through convolutional coded SVD systems. Similar to
BICMB-FP, BICMB-PC achieves both full diversity and full multiplexing, and its
performance is almost the same as BICMB-FP. The advantage of BICMB-PC is that
it can provide a much lower decoding complexity than BICMB-FP, since the real
and imaginary parts of the received signal can be separated for BICMB-PC of
dimensions 2 and 4, and only the part corresponding to the coded bit is
required to acquire one bit metric for the Viterbi decoder.
