  Distributed Orthogonal Space-Time Block Codes (DOSTBCs) achieving full
diversity order and single-symbol ML decodability have been introduced recently
for cooperative networks and an upper-bound on the maximal rate of such codes
along with code constructions has been presented. In this report, we introduce
a new class of Distributed STBCs called Semi-orthogonal Precoded Distributed
Single-Symbol Decodable STBCs (S-PDSSDC) wherein, the source performs
co-ordinate interleaving of information symbols appropriately before
transmitting it to all the relays. It is shown that DOSTBCs are a special case
of S-PDSSDCs. A special class of S-PDSSDCs having diagonal covariance matrix at
the destination is studied and an upper bound on the maximal rate of such codes
is derived. The bounds obtained are approximately twice larger than that of the
DOSTBCs. A systematic construction of S-PDSSDCs is presented when the number of
relays $K \geq 4$. The constructed codes are shown to achieve the upper-bound
on the rate when $K$ is of the form 0 modulo 4 or 3 modulo 4. For the rest of
the values of $K$, the constructed codes are shown to have rates higher than
that of DOSTBCs. It is also shown that S-PDSSDCs cannot be constructed with any
form of linear processing at the relays when the source doesn't perform
co-ordinate interleaving of the information symbols.
