Universal lattice decoding: principle and recent advances

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Abstract
The idea of formulating the detection of a lattice‐type modulation, such as M‐PAM and M‐QAM, transmitted over a linear channel as the so‐called universal lattice decoding problem dates back to at least the early 1990s. The applications of such lattice decoders have proliferated in the last few years because of the growing importance of some linear channel models such as multiple‐antenna fading channels and multi‐user CDMA channels. The principle of universal lattice decoding can trace its roots back to the theory and algorithms developed for solving the shortest/closest lattice vector problem for integer programming and cryptoanalysis applications. In this semi‐tutorial paper, such a principle as well as some related recent advances will be reviewed and extended. It will be shown that the lattice basis reduction algorithm of Lenstra, Lenstra and Lovász (LLL) can significantly improve the performance of suboptimal lattice decoders such as the zero‐forcing and VBLAST detectors. In addition, new implementation of the optimal lattice decoder that is particularly efficient at moderate signal‐to‐noise ratios will also be presented. Copyright © 2003 John Wiley & Sons, Ltd.