This paper presents the first silicon-proven implementation of a lattice reduction (LR) algorithm, which achieves maximum likelihood diversity. The implementation is based on a novel hardware-optimized due to the Lenstra, Lenstra, and Lovász (LLL) algorithm, which significantly reduces its complexity by replacing all the computationally intensive LLL operations (multiplication, division, and sq...

The credit on reduction theory goes back to the work of Lagrange, Gauss, Hermite, Korkin, Zolotarev, and Minkowski. Modern reduction theory is voluminous and includes the work of A. Lenstra, H. Lenstra and L. Lovasz who created the well known LLL algorithm, and many other researchers such as L. Babai and C. P. Schnorr who created significant new variants of basis reduction algorithms. In this p...

We consider the recent works of [3, 31, 2] that provide tools for analyzing focused stochastic local search algorithms that arise from algorithmizations of the Lovász Local Lemma [17] (LLL) in general probability spaces. These are algorithms which search a state space probabilistically by repeatedly selecting a “flaw” that is currently present and moving to a random nearby state in an effort to...

Full diversity high-rate Space Time Block Codes (STBCs) based on cyclotomic field extensions Q(ωl), where ωl is the complex lth root of unity, can be decoded by Lenstra-Lenstra-Lovász (LLL) lattice reduction-aided linear equalization followed by appropriate zero forcing. LLL lattice reduction-aided linear equalization enables lower complexity decoding compared to sphere decoding, while resultin...

Lattice reduction is a hard problem of interest to both publickey cryptography and cryptanalysis. Despite its importance, extremely few algorithms are known. The best algorithm known in high dimension is due to Schnorr, proposed in 1987 as a block generalization of the famous LLL algorithm. This paper deals with Schnorr’s algorithm and potential improvements. We prove that Schnorr’s algorithm o...

We devise an algorithm, e L, with the following specifications: It takes as input an arbitrary basis B = (bi)i ∈ Zd×d of a Euclidean lattice L; It computes a basis of L which is reduced for a mild modification of the Lenstra-Lenstra-Lovász reduction; It terminates in time O(dβ + dβ) where β = log max ‖bi‖ (for any ε > 0 and ω is a valid exponent for matrix multiplication). This is the first LLL...

In this paper we introduce an improved variant of the LLL algorithm. Using the Gram matrix to avoid expensive correction steps necessary in the Schnorr-Euchner algorithm and introducing the use of buffered transformations allows us to obtain a major improvement in reduction time. Unlike previous work, we are able to achieve the improvement while obtaining a strong reduction result and maintaini...

Recently, lattice theory has been widely used for integer ambiguity resolution in the Global Navigation Satellite System (GNSS). When using to deal with ambiguity, we need reduce correlation between bases ensure efficiency of solution. Lattice reduction is divided into scale and basis vector exchange. The no direct impact on subsequent search efficiency, while exchange directly impacts efficien...