Boosted KZ and LLL Algorithms

Lyu, Shanxiang; Ling, Cong

doi:10.1109/tsp.2017.2708020

Cited by 37 publications

(55 citation statements)

References 40 publications

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“…A shortest vector v = n i=1 c i b i with at least one coefficient c k = ±1 must be contained in the SR-CVP reduced basis. 2) Comparison with KZ and its variants [16], [35]. Recall that a basis B is called KZ reduced if it satisfies the size reduction conditions, and π ⊥ [35].…”

Section: B Discussionmentioning

confidence: 99%

“…The modulation is set as 16 QAM, and the results are obtained from 1 × 10 4 Monte Carlo runs. We denote the zero-forcing detector by "ZF", the successive interference cancellation detector by "SIC", and lattice-reduction-aided detectors with prefixes: "LLL-SIC/ZF" [32], "bLLL-SIC/ZF" [16], "SR-Pair-SIC/ZF" (this paper), "SR-Hash-SIC/ZF" (this paper), and "Seysen-SIC/ZF" [26]. Here comparisons are made for major lattice-reduction-aided methods in large-scale MIMO systems, because they represent pre-processing based methods that may attain the diversity order of ML detection [6], [44].…”

Section: B Sr-hash Vs Sr-pair and Lll Variantsmentioning

confidence: 99%

See 1 more Smart Citation

On Low-Complexity Lattice Reduction Algorithms for Large-Scale MIMO Detection: The Blessing of Sequential Reduction

Lyu¹,

Wen²,

Weng³

et al. 2020

IEEE Trans. Signal Process.

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Lattice reduction is a popular preprocessing strategy in multiple-input multiple-output (MIMO) detection. In a quest for developing a low-complexity reduction algorithm for largescale problems, this paper investigates a new framework called sequential reduction (SR), which aims to reduce the lengths of all basis vectors. The performance upper bounds of the strongest reduction in SR are given when the lattice dimension is no larger than 4. The proposed new framework enables the implementation of a hash-based low-complexity lattice reduction algorithm, which becomes especially tempting when applied to large-scale MIMO detection. Simulation results show that, compared to other reduction algorithms, the hash-based SR algorithm exhibits the lowest complexity while maintaining comparable error performance.

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Section: B Discussionmentioning

confidence: 99%

Section: B Sr-hash Vs Sr-pair and Lll Variantsmentioning

confidence: 99%

On Low-Complexity Lattice Reduction Algorithms for Large-Scale MIMO Detection: The Blessing of Sequential Reduction

Lyu¹,

Wen²,

Weng³

et al. 2020

IEEE Trans. Signal Process.

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“…In the following theorem we provide a new upper bound on α n for n ≥ 109, which is sharper than that in (12) for n ≥ 111. The new bound on α n is based on the new upper bound on the Hermite constant γ n (4), which is sharper than that in (3) for n ≥ 109. , for n ≥ 109.…”

Section: A Sharper Bound On the Kz Constantmentioning

confidence: 92%

Improved Upper Bounds on the Hermite and KZ Constants

Wen

Chang

Weng

2019

2019 IEEE International Symposium on Information Theory (ISIT)

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The Korkine-Zolotareff (KZ) reduction is a widely used lattice reduction strategy in communications and cryptography. The Hermite constant, which is a vital constant of lattice, has many applications, such as bounding the length of the shortest nonzero lattice vector and orthogonality defect of lattices. The KZ constant can be used in quantifying some useful properties of KZ reduced matrices. In this paper, we first develop a linear upper bound on the Hermite constant and then use the bound to develop an upper bound on the KZ constant. These upper bounds are sharper than those obtained recently by the first two authors. Some examples on the applications of the improved upper bounds are also presented.

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“…They also investigated algorithms based on Hermite-Korkine-Zolotareff (HKZ) and Minkowski lattice basis reduction algorithms, see [8] for more detail discussion. Other efficient algorithms can be found in [26]- [28].…”

Section: B Decoding Complexitymentioning

confidence: 99%

Steepest Gradient-Based Orthogonal Precoder for Integer-Forcing MIMO

Hasan

Kurkoski

Sakzad

et al. 2020

IEEE Trans. Wireless Commun.

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In this paper, we develop an orthogonal precoding scheme for integer-forcing (IF) linear receivers using the steepest gradient algorithm. Although this scheme can be viewed as a special case of the unitary precoded integer-forcing (UPIF), it has two major advantages. First, the orthogonal precoding outperforms its unitary counterpart in terms of achievable rate, outage probability, and error rate. We verify this advantage via theoretical and numerical analyses. Second, it exhibits lower complexity as the dimension of orthogonal matrices is half that of unitary matrices in the real-valued domain. For finding "good" orthogonal precoder matrices, we propose an efficient algorithm based on the steepest gradient algorithm that exploits the geometrical properties of orthogonal matrices as a Lie group. The proposed algorithm has low complexity and can be easily applied to an arbitrary MIMO configuration.We also confirm numerically that the proposed orthogonal precoding outperforms UPIF type II in some scenarios and the X-precoder in high-order QAM schemes, e.g., 64and 256-QAM.

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Boosted KZ and LLL Algorithms

Cited by 37 publications

References 40 publications

On Low-Complexity Lattice Reduction Algorithms for Large-Scale MIMO Detection: The Blessing of Sequential Reduction

On Low-Complexity Lattice Reduction Algorithms for Large-Scale MIMO Detection: The Blessing of Sequential Reduction

Improved Upper Bounds on the Hermite and KZ Constants

Steepest Gradient-Based Orthogonal Precoder for Integer-Forcing MIMO

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