Improved Upper Bounds for Approximate Lattice Decoding With Dual-Basis Reduction

Lattice reduction-aided decoding enables significant complexity saving and near-optimum performance in digital communications. Its performance can be characterized by the proximity factors that measure the worst-case gap to exact lattice decoding in terms of the signal-to-noise ratio for given error rate. The proximity factors have been derived in literature for both primal and dual basis reduction, and it has been found that in some cases reducing the dual basis can result in asymptotically smaller proximity factors. In this paper, improved upper bounds on the proximity factors for dual-basis reduction are derived, which are uniformly smaller than those for primal basis reduction.