  In multiple-input multiple-output (MIMO) fading channels, the design
criterion for full-diversity space-time block codes (STBCs) is primarily
determined by the decoding method at the receiver. Although constructions of
STBCs have predominantly matched the maximum-likelihood (ML) decoder, design
criteria and constructions of full-diversity STBCs have also been reported for
low-complexity linear receivers. A new receiver architecture called
Integer-Forcing (IF) linear receiver has been proposed to MIMO channels by Zhan
et al. which showed promising results for the high-rate V-BLAST encoding
scheme. In this paper, we address the design of full-diversity STBCs for IF
linear receivers. In particular, we are interested in characterizing the
structure of STBCs that provide full-diversity with the IF receiver. Along that
direction, we derive an upper bound on the probability of decoding error, and
show that STBCs that satisfy the restricted non-vanishing singular value (RNVS)
property provide full-diversity for the IF receiver. Furthermore, we prove that
all known STBCs with the non-vanishing determinant property provide
full-diversity with IF receivers, as they guarantee the RNVS property. By using
the formulation of RNVS property, we also prove the existence of a
full-diversity STBC outside the class of perfect STBCs, thereby adding
significant insights compared to the existing works on STBCs with IF decoding.
Finally, we present extensive simulation results to demonstrate that linear
designs with RNVS property provide full-diversity for IF receiver.
