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

Multi-group ML Decodable Collocated and Distributed Space Time Block Codes