Lattice Reduction

Wübben, Dirk; Seethaler, D.; Jaldén, Joakim; Matz, Gerald

doi:10.1109/msp.2010.938758

Cited by 202 publications

(138 citation statements)

References 51 publications

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“…Block-Toeplitz matrices have been considered to evaluate the performance of the different implementations. These type of matrices are usually used in wireless communications [17]. Figure 3 shows the computational times of the MB-LLL algorithm based on the architectures discussed in Section 3. l denotes the size of the processed blocks.…”

Section: Evaluation Resultsmentioning

confidence: 99%

“…The Minkowski or Hermite-Korkine-Zolotareff reductions are the techniques that obtain the best performance in terms of reduction, but also the ones with a higher computational cost. Both techniques require the calculation of the shortest lattice vector, which has been proved to be NP-hard (see [17] and references therein).…”

Section: Introductionmentioning

confidence: 99%

“…This algorithm can be seen as a relaxation of HermiteKorkine-Zolotareff conditions [4] or an extension of Gauss reduction [17] and obtains the reduced basis by applying two different operations over the original basis: size-reduction (linear combination between columns) and column swap. Although further reduction techniques have been proposed afterwards, the LLL algorithm is the most used due to the good trade-off between performance and computational complexity.…”

Section: Introductionmentioning

confidence: 99%

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High performance lattice reduction on heterogeneous computing platform

et al. 2014

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Jozsa, CM.; Domene Oltra, F.; Vidal Maciá, AM.; Piñero Sipán, MG.; González Salvador, A. (2014). High performance lattice reduction on heterogeneous computing platform. Journal of Supercomputing. 70(2):772-785. doi:10.1007/s11227-014-1201-2. Abstract The lattice reduction (LR) technique has become very important in many engineering fields. However, its high complexity makes difficult its use in real-time applications, especially in applications that deal with large matrices. As a solution, the Modified Block LLL (MB-LLL) algorithm was introduced in [10], where several levels of parallelism were exploited: (i.) coarse-grained parallelism was achieved by applying the block-reduction concept presented in [15] and (ii.) fine-grained parallelism was achieved through the Cost Reduced All-Swap LLL (CR-AS-LLL) algorithm introduced in [10].In this paper, we present the Cost Reduced MB-LLL (CR-MB-LLL) algorithm, which allows to significantly reduce the computational complexity of the MB-LLL by allowing the relaxation of the first LLL condition while executing the LR of submatrices, resulting in the delay of the GS coefficients update and by using less costly procedures during the boundary checks. The effects of complexity reduction and implementation details are analyzed and discussed for several architectures. A mapping of the CR-MB-LLL on a heterogenenous platform is proposed and it is compared with implementations running on a dynamic parallelism enabled GPU and a multi-core CPU. The mapping on the architecture proposed allows a dynamic scheduling of kernels where the overhead introduced is hidden by the use of several CUDA streams. Results show that the execution time of the CR-MB-LLL algorithm on the heterogeneous platform outperforms the multi-core CPU and it is more efficient than the CR-AS-LLL algorithm in case of large matrices.

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Section: Evaluation Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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High performance lattice reduction on heterogeneous computing platform

et al. 2014

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“…In addition to the LLL algorithm, these include Korkine-Zolotarev (KZ) [13], and Seysen's [14] lattice reduction algorithms; see [2] and the references therein for applications to MIMO detection. In this chapter we restrict attention to the LLL algorithm, since numerous simulation studies suggest that lattice-reduction-aided detection is well suited to low-complexity MIMO receivers when large constellations are used [15,16].…”

Section: Design and Architectures For Digital Signal Processingmentioning

confidence: 99%

A Digital Signal Processing Architecture for Soft-Output MIMO Lattice Reduction Aided Detection

Murray¹,

Weller²

2013

Design and Architectures for Digital Signal Processing

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“…The transformation is performed on the H channel matrix finding another base with better orthogonality. Different reduction techniques have been proposed [69], however the algorithm proposed by Lenstra, Lenstra and Lovász known as LLL [70] is the most commonly used because although it is a suboptimal method, it offers a good tradeoff between performance and complexity. However, the total number of arithmetic operations required by the LLL algorithm is difficult to predict due to the lack of a bounded worst case complexity.…”

Section: : End Formentioning

confidence: 99%

Effi cient algorithms for iterative detection and decoding in Multiple-Input and Multiple-Output Communication Systems.

Haro¹,

Angeles²

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Lattice Reduction

Cited by 202 publications

References 51 publications

High performance lattice reduction on heterogeneous computing platform

High performance lattice reduction on heterogeneous computing platform

A Digital Signal Processing Architecture for Soft-Output MIMO Lattice Reduction Aided Detection

Effi cient algorithms for iterative detection and decoding in Multiple-Input and Multiple-Output Communication Systems.

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