  It is well known that Space-Time Block Codes (STBCs) from orthogonal designs
(ODs) are single-symbol decodable/symbol-by-symbol decodable (SSD) and are
obtainable from unitary matrix representations of Clifford algebras. However,
SSD codes are obtainable from designs that are not orthogonal also. Recently,
two such classes of SSD codes have been studied: (i) Coordinate Interleaved
Orthogonal Designs (CIODs) and (ii) Minimum-Decoding-Complexity (MDC) STBCs
from Quasi-ODs (QODs). Codes from ODs, CIODs and MDC-QODs are mutually
non-intersecting classes of codes. The class of CIODs have {\it non-unitary
weight matrices} when written as a Linear Dispersion Code (LDC) proposed by
Hassibi and Hochwald, whereas several known SSD codes including CODs have {\it
unitary weight matrices}. In this paper, we obtain SSD codes with unitary
weight matrices (that are not CODs) called Clifford Unitary Weight SSDs
(CUW-SSDs) from matrix representations of Clifford algebras. A main result of
this paper is the derivation of an achievable upper bound on the rate of any
unitary weight SSD code as $\frac{a}{2^{a-1}}$ for $2^a$ antennas which is
larger than that of the CODs which is $\frac{a+1}{2^a}$. It is shown that
several known classes of SSD codes are CUW-SSD codes and CUW-SSD codes meet
this upper bound. Also, for the codes of this paper conditions on the signal
sets which ensure full-diversity and expressions for the coding gain are
presented. A large class of SSD codes with non-unitary weight matrices are
obtained which include CIODs as a proper subclass.
