Soft decoding techniques for codes and Lattices, including the Golay code and the Leech Lattice
IEEE Transactions on Information Theory
Trellis-coded modulation with multidimensional constellations
IEEE Transactions on Information Theory
Minkowski's convex body theorem and integer programming
Mathematics of Operations Research
Generating hard instances of lattice problems (extended abstract)
STOC '96 Proceedings of the twenty-eighth annual ACM symposium on Theory of computing
A public-key cryptosystem with worst-case/average-case equivalence
STOC '97 Proceedings of the twenty-ninth annual ACM symposium on Theory of computing
The art of computer programming, volume 2 (3rd ed.): seminumerical algorithms
The art of computer programming, volume 2 (3rd ed.): seminumerical algorithms
Expected time bounds for selection
Communications of the ACM
Algorithm 489: the algorithm SELECT—for finding the ith smallest of n elements [M1]
Communications of the ACM
Introduction to Algorithms
An Algorithm to Compute a Nearest Point in the Lattice An*
AAECC-13 Proceedings of the 13th International Symposium on Applied Algebra, Algebraic Algorithms and Error-Correcting Codes
Frequency estimation, phase unwrapping and the nearest lattice point problem
ICASSP '99 Proceedings of the Acoustics, Speech, and Signal Processing, 1999. on 1999 IEEE International Conference - Volume 03
Linear-time block noncoherent detection of PSK
ICASSP '09 Proceedings of the 2009 IEEE International Conference on Acoustics, Speech and Signal Processing
Performance of vector perturbation multiuser MIMO systems with limited feedback
IEEE Transactions on Communications
Identifiability and aliasing in polynomial-phase signals
IEEE Transactions on Signal Processing
Journal of Computer and System Sciences
Frequency estimation by phase unwrapping
IEEE Transactions on Signal Processing
Approximate Maximum-Likelihood Period Estimation From Sparse, Noisy Timing Data
IEEE Transactions on Signal Processing
A universal lattice code decoder for fading channels
IEEE Transactions on Information Theory
The hardness of the closest vector problem with preprocessing
IEEE Transactions on Information Theory
Closest point search in lattices
IEEE Transactions on Information Theory
Lattice decoding for joint detection in direct-sequence CDMA systems
IEEE Transactions on Information Theory
An Algorithm to Compute the Nearest Point in the Lattice
IEEE Transactions on Information Theory
Some new lattice quantization algorithms for video compression coding
IEEE Transactions on Circuits and Systems for Video Technology
Hi-index | 754.84 |
The Coxeter lattices are a family of lattices containing many of the important lattices in lowdimensions. This includes An, E7, E8 and their duals An*, E7*, and E8*. We consider the problem of finding a nearest point in a Coxeter lattice. We describe two new algorithms, one with worst case arithmetic complexity O(n log n) and the other with worst case complexity O(n) where n is the dimension of the lattice. We show that for the particular lattices An and An* the algorithms are equivalent to nearest point algorithms that already exist in the literature.