  The Lenstra-Lenstra-Lovasz (LLL) reduction has wide applications in digital
communications. It can greatly improve the speed of the sphere decoding (SD)
algorithms for solving an integer least squares (ILS) problem and the
performance of the Babai integer point, a suboptimal solution to the ILS
problem. Recently Ling and Howgrave-Graham proposed the so-called effective LLL
(ELLL) reduction. It has less computational complexity than LLL, while it has
the same effect on the performance of the Babai integer point as LLL. In this
paper we propose a partial LLL (PLLL) reduction. PLLL avoids the numerical
stability problem with ELLL, which may result in very poor performance of the
Babai integer point. Furthermore, numerical simulations indicated that it is
faster than ELLL. We also show that in theory PLLL and ELLL have the same
effect on the search speed of a typical SD algorithm as LLL.
