  Two new rate-one full-diversity space-time block codes (STBC) are proposed.
They are characterized by the \emph{lowest decoding complexity} among the known
rate-one STBC, arising due to the complete separability of the transmitted
symbols into four groups for maximum likelihood detection. The first and the
second codes are delay-optimal if the number of transmit antennas is a power of
2 and even, respectively. The exact pair-wise error probability is derived to
allow for the performance optimization of the two codes. Compared with existing
low-decoding complexity STBC, the two new codes offer several advantages such
as higher code rate, lower encoding/decoding delay and complexity, lower
peak-to-average power ratio, and better performance.
