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In multiple-input multiple-output (MIMO) fading channels, the designcriterion for full-diversity space-time block codes (STBCs) is primarilydetermined by the decoding method at the receiver. Although constructions ofSTBCs have predominantly matched the maximum-likelihood (ML) decoder, designcriteria and constructions of full-diversity STBCs have also been reported forlow-complexity linear receivers. A new receiver architecture calledInteger-Forcing (IF) linear receiver has been proposed to MIMO channels by Zhanet al. which showed promising results for the high-rate V-BLAST encodingscheme. In this work we address the design of full-diversity STBCs for IFlinear receivers. We derive an upper bound on the probability of decodingerror, and show that STBCs that satisfy the non-vanishing singular value (NVS)property provide full-diversity for the IF receiver. We also present simulationresults to demonstrate that linear designs with NVS property provide fulldiversity for IF receiver. As a special case of our analysis on STBCs, wepresent an upper bound on the error probability for the V-BLAST architecturepresented by Zhan \emph{et al.}, and demonstrate that the IF linear receiversprovide full receive diversity. Our results supplement the existing outageprobability based results for the IF receiver.

Integer-Forcing Linear Receivers: A Design Criterion for Full-Diversity STBCs