Lattice-reduction-aided preequalization over algebraic signal constellations

Stern, Sebastian; Fischer, Robert F. H.

doi:10.1109/icspcs.2015.7391724

Cited by 9 publications

(27 citation statements)

References 21 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…We use q = 13 and q = 37 as the field size since for both, there are Gaussian and Eisenstein primes whose constellations are isomorphic to F 13 and F 37 respectively, cf. [8].…”

Section: B Numerical Resultsmentioning

confidence: 99%

“…The resulting signal constellation has a hexagonal boundary region and is more densely packed than a signal constellation of the same cardinality over the Gaussian integers or quadrature amplitude modulation, cf. [8].…”

Section: B Eisenstein Integersmentioning

confidence: 99%

“…However, it performs better (in terms of max i f i 2 ) for Eisenstein integers, cf. [8]. 7 For Eisenstein integers, the LLL algorithm has to be adapted, cf.…”

Section: A Channel Transformation Using Lra Techniquesmentioning

confidence: 99%

See 2 more Smart Citations

Space-time codes based on rank-metric codes and their decoding

Puchinger

Stern

Bossert

et al. 2016

2016 International Symposium on Wireless Communication Systems (ISWCS)

Self Cite

View full text Add to dashboard Cite

Abstract-In this paper, a new class of space-time block codes is proposed. The new construction is based on finite-field rank-metric codes in combination with a rank-metric-preserving mapping to the set of Eisenstein integers. It is shown that these codes achieve maximum diversity order and improve upon existing constructions. Moreover, a new decoding algorithm for these codes is presented, utilizing the algebraic structure of the underlying finite-field rank-metric codes and employing latticereduction-aided equalization. This decoder does not achieve the same performance as the classical maximum-likelihood decoding methods, but has polynomial complexity in the matrix dimension, making it usable for large field sizes and numbers of antennas.

show abstract

“…We use q = 13 and q = 37 as the field size since for both, there are Gaussian and Eisenstein primes whose constellations are isomorphic to F 13 and F 37 respectively, cf. [8].…”

Section: B Numerical Resultsmentioning

confidence: 99%

Section: B Eisenstein Integersmentioning

confidence: 99%

See 1 more Smart Citation

Space-time codes based on rank-metric codes and their decoding

Puchinger

Stern

Bossert

et al. 2016

2016 International Symposium on Wireless Communication Systems (ISWCS)

Self Cite

View full text Add to dashboard Cite

show abstract

“…Denote the number of positive and negative tests in Step 9 as K + and K − , respectively. Based on (18), the potential function of the basis decreases in a log 1/δ scale for each negative tests. Let the ratio between the potential functions of the input basis and the minimum possible basis be g(n), then similarly to [12] we can upper bound the total number of loops as K − + K + ≤ 2K − + n − 1 ≤ 2 log 1/δ g(n) + n − 1.…”

Section: B Implementation and Complexitymentioning

confidence: 99%

“…Quite recently, Kim and Lee [16] presents reduction algorithms for arbitrary Euclidean domains. Regarding the second scenario whose basis vectors are in C, the LLL algorithm has also been generalized to Z[i]-lattices [17] and Z[ω]-lattices [18], and these generalizations are used in the context of MIMO detection/precoding whose signal constellations are algebraic.…”

Section: Introductionmentioning

confidence: 99%

Performance Limits of Lattice Reduction over Imaginary Quadratic Fields with Applications to Compute-and-Forward

Lyu

Porter

Ling

2018

2018 IEEE Information Theory Workshop (ITW)

View full text Add to dashboard Cite

Complex bases, along with direct-sums defined by rings of imaginary quadratic integers, induce algebraic lattices.In this work, we study such lattices and their reduction algorithms. First, when the lattice is spanned over a two dimensional basis, we show that the algebraic variant of Gauss's algorithm returns a basis that corresponds to the successive minima of the lattice in polynomial time if the chosen ring is Euclidean. Second, we extend the celebrated Lenstra-Lenstra-Lovász (LLL) reduction from over real bases to over complex bases. Properties and implementations of the algorithm are examined. In particular, satisfying Lovász's condition requires the ring to be Euclidean. Lastly, as an application, we use the algebraic algorithms to find the network coding matrices in compute-and-forward.Such lattice reduction-based approaches have low complexity which is not dictated by the signal-to-noise (SNR) ratio. Moreover, such approaches can not only preserve the degree-of-freedom of computation rates, but ensure the independence in the code space as well. Index Termslattice reduction, Gauss's algorithm, LLL, compute-and-forward. Initially coding lattices from ConstructionA over rational integers Z or Gaussian integers Z[i] are the main enabler in showing the achievable information rate in C&F. Recently, however, the Construction A lattices have been extended to over the ring of Eisenstein integers Z[ω] [4], [5] and other rings of imaginary quadratic integers [6], This work was presented in part at the IEEE Information Theory Workshop 2018, Guangzhou, China, and submitted in part to the IEEE Information Theory Workshop 2019, Visby, Gotland, Sweden. S. Lyu is with the College

show abstract

Quantum-safe cryptography: crossroads of coding theory and cryptography

Wang

Liu

Lyu

et al. 2021

Sci. China Inf. Sci.

View full text Add to dashboard Cite

We present an overview of quantum-safe cryptography (QSC) with a focus on post-quantum cryptography (PQC) and information-theoretic security. From a cryptographic point of view, lattice and code-based schemes are among the most promising PQC solutions. Both approaches are based on the hardness of decoding problems of linear codes with different metrics. From an information-theoretic point of view, lattices and linear codes can be constructed to achieve certain secrecy quantities for wiretap channels as is intrinsically classical- and quantum-safe. Historically, coding theory and cryptography are intimately connected since Shannon’s pioneering studies but have somehow diverged later. QSC offers an opportunity to rebuild the synergy of the two areas, hopefully leading to further development beyond the NIST PQC standardization process. In this paper, we provide a survey of lattice and code designs that are believed to be quantum-safe in the area of cryptography or coding theory. The interplay and similarities between the two areas are discussed. We also conclude our understandings and prospects of future research after NIST PQC standardisation.

show abstract

Lattice-reduction-aided preequalization over algebraic signal constellations

Cited by 9 publications

References 21 publications

Space-time codes based on rank-metric codes and their decoding

Space-time codes based on rank-metric codes and their decoding

Performance Limits of Lattice Reduction over Imaginary Quadratic Fields with Applications to Compute-and-Forward

Quantum-safe cryptography: crossroads of coding theory and cryptography

Contact Info

Product

Resources

About