Improved methods for calculating vectors of short length in a lattice, including a complexity analysis

Fincke, Ulrich; Pohst, Michael

doi:10.1090/s0025-5718-1985-0777278-8

Cited by 1,154 publications

(409 citation statements)

References 3 publications

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“…10 shows the synthesis results of hard-output SD with ordered ∞ -norm enumeration and pipeline interleaving with different number of pipeline stages. 5 The proposed architectures have been implemented with support for multiple modulation schemes (BPSK, QPSK, 16-QAM, and 64-QAM) and for up to four spatial streams (configurable at runtime). Fig.…”

Section: Implementation Results For Hard-output Sdmentioning

confidence: 99%

See 1 more Smart Citation

VLSI Implementation of Hard- and Soft-Output Sphere Decoding for Wide-Band MIMO Systems

Studer

Wenk

Burg

2012

VLSI-SoC: Forward-Looking Trends in IC and Systems Design

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Abstract. Multiple-input multiple-output (MIMO) technology in combination with orthogonal frequency-division multiplexing (OFDM) is the key to meet the demands for data rate and link reliability of modern wideband wireless communication systems, such as IEEE 802.11n or 3GPP-LTE. The full potential of such systems can, however, only be achieved by high-performance data-detection algorithms, which typically exhibit prohibitive computational complexity. Hard-output sphere decoding (SD) and soft-output single tree-search (STS) SD are promising means for realizing high-performance MIMO detection and have been demonstrated to enable efficient implementations in practical systems. In this chapter, we consider the design and optimization of register transfer-level implementations of hard-output SD and soft-output STS-SD with minimum area-delay product, which are well-suited for wide-band MIMO systems. We explain in detail the design, implementation, and optimization of VLSI architectures and present corresponding implementation results for 130 nm CMOS technology. The reported implementations significantly outperform the area-delay product of previously reported hard-output SD and soft-output STS-SD implementations.

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Section: Implementation Results For Hard-output Sdmentioning

confidence: 99%

“…Sphere-Decoding Algorithm The SD algorithm [5][6][7][8][9] starts with the QR decomposition (QRD) of the channel matrix H = QR, where the M R × M T matrix Q satisfies Q H Q = I MT , and the M T ×M T matrix R is upper-triangular. The QRD enables us to rewrite the ML-detection problem (2) as follows:…”

Section: Detection Using the Sphere-decoding Algorithmmentioning

confidence: 99%

VLSI Implementation of Hard- and Soft-Output Sphere Decoding for Wide-Band MIMO Systems

Studer

Wenk

Burg

2012

VLSI-SoC: Forward-Looking Trends in IC and Systems Design

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“…We can then combine a variant of the Fincke-Pohst algorithm [2] with the sieving ideas of [4] to determine all elements in T j,p (H i , R i , R i+1 ).…”

Section: P Infinite Just As Before We Deduce Thatmentioning

confidence: 99%

“…Wildanger makes use of the Fincke-Pohst algorithm [2]. We try to avoid the use of this algorithm for as long as possible.…”

mentioning

confidence: 99%

Determining the small solutions to 𝑆-unit equations

Smart

1999

Math. Comp.

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Abstract. In this paper we generalize the method of Wildanger for finding small solutions to unit equations to the case of S-unit equations. The method uses a minor generalization of the LLL based techniques used to reduce the bounds derived from transcendence theory, followed by an enumeration strategy based on the Fincke-Pohst algorithm. The method used reduces the computing time needed from MIPS years down to minutes.

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“…The first deterministic algorithm to find the shortest vector in a given lattice was proposed by Fincke, Pohst [5,6] and Kannan [11], by enumerating all lattice vectors shorter than a prescribed bound. If the input is an LLL-reduced basis, the running time is 2 O(n 2 ) polynomial-time operations.…”

Section: Introductionmentioning

confidence: 99%

A Three-Level Sieve Algorithm for the Shortest Vector Problem

Zhang

Pan

2014

Lecture Notes in Computer Science

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Abstract. In AsiaCCS 2011, Wang et al. proposed a two-level heuristic sieve algorithm for the shortest vector problem in lattices, which improves the Nguyen-Vidick sieve algorithm. Inspired by their idea, we present a three-level sieve algorithm in this paper, which is shown to have better time complexity. More precisely, the time complexity of our algorithm is 2 0.3778n+o(n) polynomial-time operations and the corresponding space complexity is 2 0.2833n+o(n) polynomially many bits.

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Improved methods for calculating vectors of short length in a lattice, including a complexity analysis

Cited by 1,154 publications

References 3 publications

VLSI Implementation of Hard- and Soft-Output Sphere Decoding for Wide-Band MIMO Systems

VLSI Implementation of Hard- and Soft-Output Sphere Decoding for Wide-Band MIMO Systems

Determining the small solutions to 𝑆-unit equations

A Three-Level Sieve Algorithm for the Shortest Vector Problem

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