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Recently, Guo and Xia gave sufficient conditions for an STBC to achieve fulldiversity when a PIC (Partial Interference Cancellation) or a PIC-SIC (PIC withSuccessive Interference Cancellation) decoder is used at the receiver. In thispaper, we give alternative conditions for an STBC to achieve full diversitywith PIC and PIC-SIC decoders, which are equivalent to Guo and Xia'sconditions, but are much easier to check. Using these conditions, we constructa new class of full diversity PIC-SIC decodable codes, which contain theToeplitz codes and a family of codes recently proposed by Zhang, Xu et. al. asproper subclasses. With the help of the new criteria, we also show that a classof PIC-SIC decodable codes recently proposed by Zhang, Shi et. al. can bedecoded with much lower complexity than what is reported, without compromisingon full diversity.

A New Full-diversity Criterion and Low-complexity STBCs with Partial Interference Cancellation Decoding