  Lattice reduction-aided decoding features reduced decoding complexity and
near-optimum performance in multi-input multi-output communications. In this
paper, a quantitative analysis of lattice reduction-aided decoding is
presented. To this aim, the proximity factors are defined to measure the
worst-case losses in distances relative to closest point search (in an infinite
lattice). Upper bounds on the proximity factors are derived, which are
functions of the dimension $n$ of the lattice alone. The study is then extended
to the dual-basis reduction. It is found that the bounds for dual basis
reduction may be smaller. Reasonably good bounds are derived in many cases. The
constant bounds on proximity factors not only imply the same diversity order in
fading channels, but also relate the error probabilities of (infinite) lattice
decoding and lattice reduction-aided decoding.
