  There exist two issues among popular lattice reduction (LR) algorithms that
should cause our concern. The first one is Korkine-Zolotarev (KZ) and
Lenstra-Lenstra-Lovasz (LLL) algorithms may increase the lengths of basis
vectors. The other is KZ reduction suffers much worse performance than
Minkowski reduction in terms of providing short basis vectors, despite its
superior theoretical upper bounds. To address these limitations, we improve the
size reduction steps in KZ and LLL to set up two new efficient algorithms,
referred to as boosted KZ and LLL, for solving the shortest basis problem (SBP)
with exponential and polynomial complexity, respectively. Both of them offer
better actual performance than their classic counterparts, and the performance
bounds for KZ are also improved. We apply them to designing integer-forcing
(IF) linear receivers for multi-input multi-output (MIMO) communications. Our
simulations confirm their rate and complexity advantages.
