Recently, lattice reduction aided (LRA) detectors have been introduced into Vertical Bell-Labs Layered Space-Time (V-BLAST) systems to obtain nearly optimal bit error rate (BER) performance for only small additional complexity. In this paper, the layer error characteristics of LRA-V-BLAST detectors are investigated and compared with those of conventional V-BLAST ones. Two important conclusions are drawn for the LRA-V-BLAST detectors. First, the variation of their mean square error (MSE) within each detection iteration is not as large as in conventional V-BLAST detectors. Second, thanks to lattice reduction there exists an inherent sub-optimal detection order from the last to the first layer. These conclusions allow LRA-V-BLAST detectors to avoid optimal ordering to further reduce the complexity. LRA-V-BLAST detectors without optimal ordering are shown to obtain almost the same BER performance of LRA-V-BLAST detector with optimal ordering.

We review public-key cryptosystems from lattice problems, which are inspired by Ajtai's remarkable result, and consider their security from the point of view of both theory and practice. We also survey recent results on the power of the lattice reduction algorithm in cryptanalysis.