On the Proximity Factors of Lattice Reduction-Aided Decoding

TL;DR

This paper provides a quantitative analysis of lattice reduction-aided decoding in MIMO systems, introducing proximity factors to measure worst-case performance loss and deriving bounds that relate to error probabilities.

Contribution

It introduces the concept of proximity factors for lattice reduction-aided decoding and derives bounds based solely on lattice dimension, extending analysis to dual-basis reduction.

Findings

Proximity factors are bounded functions of lattice dimension.

Bounds for dual basis reduction can be smaller than for primal basis.

Constant bounds imply the same diversity order and relate error probabilities.

Abstract

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.