  In this paper, collocated and distributed space-time block codes (DSTBCs)
which admit multi-group maximum likelihood (ML) decoding are studied. First the
collocated case is considered and the problem of constructing space-time block
codes (STBCs) which optimally tradeoff rate and ML decoding complexity is
posed. Recently, sufficient conditions for multi-group ML decodability have
been provided in the literature and codes meeting these sufficient conditions
were called Clifford Unitary Weight (CUW) STBCs. An algebraic framework based
on extended Clifford algebras is proposed to study CUW STBCs and using this
framework, the optimal tradeoff between rate and ML decoding complexity of CUW
STBCs is obtained for few specific cases. Code constructions meeting this
tradeoff optimally are also provided. The paper then focuses on multi-group ML
decodable DSTBCs for application in synchronous wireless relay networks and
three constructions of four-group ML decodable DSTBCs are provided. Finally,
the OFDM based Alamouti space-time coded scheme proposed by Li-Xia for a 2
relay asynchronous relay network is extended to a more general transmission
scheme that can achieve full asynchronous cooperative diversity for arbitrary
number of relays. It is then shown how differential encoding at the source can
be combined with the proposed transmission scheme to arrive at a new
transmission scheme that can achieve full cooperative diversity in asynchronous
wireless relay networks with no channel information and also no timing error
knowledge at the destination node. Four-group decodable DSTBCs applicable in
the proposed OFDM based transmission scheme are also given.
