Decoding by Embedding: Correct Decoding Radius and DMT Optimality

@article{Luzzi2013DecodingBE,
  title={Decoding by Embedding: Correct Decoding Radius and DMT Optimality},
  author={Laura Luzzi and Damien Stehl{\'e} and Cong Ling},
  journal={IEEE Transactions on Information Theory},
  year={2013},
  volume={59},
  pages={2960-2973}
}
The closest vector problem (CVP) and shortest (nonzero) vector problem (SVP) are the core algorithmic problems on Euclidean lattices. They are central to the applications of lattices in many problems of communications and cryptography. Kannan's embedding technique is a powerful technique for solving the approximate CVP; yet, its remarkable practical performance is not well understood. In this paper, the embedding technique is analyzed from a bounded distance decoding (BDD) viewpoint. We present… 
Decoding by Sampling — Part II: Derandomization and Soft-Output Decoding
TLDR
It is demonstrated that the derandomized sampling algorithm is capable of achieving near-maximum a posteriori (MAP) performance, and Simulation results show that near-optimum performance can be achieved by a moderate size K in both lattice decoding and soft-output decoding.
On the Proximity Factors of Lattice Reduction-Aided Decoding
  • Cong Ling
  • Mathematics, Computer Science
    IEEE Transactions on Signal Processing
  • 2011
TLDR
A quantitative error-rate analysis of LRAD is presented and upper bounds on the proximity factors are derived, which are functions of the dimension n of the lattice alone, found that the bounds for dual basis reduction may be smaller.
Deterministic Sampling Decoding: Where Sphere Decoding Meets Lattice Gaussian Distribution
TLDR
The regularized SD (RSD) algorithm based on Klein's sampling probability is proposed, which achieves a better decoding trade-off than the equivalent SD by fully utilizing the regularization terms.
Lattice Gaussian Sampling by Markov Chain Monte Carlo: Bounded Distance Decoding and Trapdoor Sampling
TLDR
The Markov chain Monte Carlo (MCMC)-based sampling technique is advanced in several fronts, revealing a flexible trade-off between the decoding radius and complexity and the independent multiple-try Metropolis-Klein algorithm is proposed to enhance the convergence rate.
On Solving the Shortest Basis Problem Based on Sequential Reduction
TLDR
This work proposes to employ successive interference cancellation (SIC) as a subroutine inside SR, and the whole algorithm is referred to as SR-SIC, and it is proved that the upper bound on the basis length of SR- SIC is better than those of major Lenstra, Lenstra- and Lovász (LLL) based variants when the dimension of the lattice basis is no larger than 4.
Lattice Decoding Attacks on Binary LWE
TLDR
The main result is an improved lattice decoding algorithm for binary-LWE, by translating to the inhomogeneous short integer solution (ISIS) problem, and then re-scaling the lattice.
MIMO Detection by Lagrangian Dual Maximum-Likelihood Relaxation: Reinterpreting Regularized Lattice Decoding
TLDR
Simulation results show that the proposed LDR approach can outperform the conventional MMSE-based lattice decoding approach and it is proved that the LDR problem yields a duality gap no worse than that of the well-known semidefinite relaxation method.
Parallel Implementation of BDD enumeration for LWE
TLDR
This work provides the first parallel implementation of an enumeration-based BDD algorithm that employs the Lindner-Peikert and Linear Length pruning strategies and concludes that lattice-based attacks perform better than recent advanced BKW-type algorithms even for small noise, while requiring way less samples.
Gaussian Sampling in Lattice-Based Cryptography
TLDR
The goal of this thesis is to fill the gap between the theory and practice of Gaussian sampling and to instantiate a signature scheme and an identity-based encryption scheme that yields signatures that are the most compact currently obtained in lattice-based cryptography.
Sliced Lattice Gaussian Sampling: Convergence Improvement and Decoding Optimization
TLDR
It is demonstrated that the Markov chain arising from it is uniformly ergodic, namely, it converges exponentially fast to the stationary distribution.
...
1
2
...

References

SHOWING 1-10 OF 75 REFERENCES
Decoding by Sampling: A Randomized Lattice Algorithm for Bounded Distance Decoding
Despite its reduced complexity, lattice reduction-aided decoding exhibits a widening gap to maximum-likelihood (ML) performance as the dimension increases. To improve its performance, this paper
On Bounded Distance Decoding, Unique Shortest Vectors, and the Minimum Distance Problem
TLDR
This work proves the equivalence, up to a small polynomial approximation factor, of the lattice problems uSVP, BDD and GapSVP and the Ajtai-Dwork and the Regev cryptosystems, which were previously only known to be based on the hardness of USVP.
On lattices, learning with errors, random linear codes, and cryptography
  • O. Regev
  • Mathematics, Computer Science
    STOC '05
  • 2005
TLDR
A public-key cryptosystem whose hardness is based on the worst-case quantum hardness of SVP and SIVP, and an efficient solution to the learning problem implies a <i>quantum</i>, which can be made classical.
On maximum-likelihood detection and the search for the closest lattice point
TLDR
A novel algorithm is developed that is inspired by the Pohst enumeration strategy and is shown to offer a significant reduction in complexity compared to the Viterbo-Boutros sphere decoder and is supported by intuitive arguments and simulation results in many relevant scenarios.
Generalized minimum-distance decoding of Euclidean-space codes and lattices
TLDR
It appears to be practically feasible to implement algebraic multistage GMD decoders for high-dimensional sphere packings, and thus achieve high effective coding gains.
MMSE-GDFE lattice decoding for solving under-determined linear systems with integer unknowns
TLDR
Minimum mean square error generalized decision-feedback equalizer lattice decoding is shown to be an efficient decoding strategy for under-determined linear channels and flexibility in the termination strategy of the lattice search stage allows for trading performance for a reduction in the complexity.
On the Proximity Factors of Lattice Reduction-Aided Decoding
  • Cong Ling
  • Mathematics, Computer Science
    IEEE Transactions on Signal Processing
  • 2011
TLDR
A quantitative error-rate analysis of LRAD is presented and upper bounds on the proximity factors are derived, which are functions of the dimension n of the lattice alone, found that the bounds for dual basis reduction may be smaller.
DMT Optimality of LR-Aided Linear Decoders for a General Class of Channels, Lattice Designs, and System Models
  • J. Jaldén, P. Elia
  • Mathematics, Computer Science
    IEEE Transactions on Information Theory
  • 2010
This paper identifies the first general, explicit, and nonrandom MIMO encoder-decoder structures that guarantee optimality with respect to the diversity-multiplexing tradeoff (DMT), without employing
Analyzing Blockwise Lattice Algorithms Using Dynamical Systems
TLDR
This work shows that BKZ can be terminated long before its completion, while still providing bases of excellent quality and develops a completely new elementary technique based on discrete-time affine dynamical systems, which could lead to the design of improved lattice reduction algorithms.
On the complexity of sphere decoding in digital communications
TLDR
It is found that sphere decoding can be efficient for some SNR and problems of moderate size, even though the number of operations required by the algorithm strictly speaking always grows as an exponential function of the problem size.
...
1
2
3
4
5
...