We consider the design of asymmetric multiple description lattice quantizers that cover the entire spectrum of the distortion profile, ranging from symmetric or balanced to successively refinable. We present a solution to a labeling problem, which is an important part of the construction, along with a general design procedure. This procedure is illustrated using the Z2 lattice. The asymptotic p...

We present results for the coupling of the light vector mesons to the tensor current, relative to the standard vector meson decay constants. From an O(a)-improved lattice study, performed at three values of the lattice spacing in the quenched approximation, our final values (in the continuum limit), in the MS scheme at μ = 2 GeV, are: fT ρ /fρ = 0.72(2)( +2 −0), f T K∗/fK∗ = 0.74(2), f T φ /fφ ...

Two methods to overcome the problems with large vector quantization (VQ) codebooks are lattice VQ (LVQ) and product codes. The approach described in this paper takes advantage of both methods by applying residual VQ with LVQ at all stages. Using LVQ in conjunction with entropy coding is strongly motivated by the fact that entropy constrained but structurally unconstrained VQ design leads to mor...

We give a simpliied proof of a theorem of Lagarias, Lenstra and Schnorr 17] that the problem of approximating the length of the shortest lattice vector within a factor of Cn, for an appropriate constant C, cannot be NP-hard, unless NP = coNP. We also prove that the problem of ndng a n 1=4-unique shortest lattice vector is not NP-hard under polynomial time many-one reductions, unless the polynom...

Lattice vector quantization (LVQ) reduces computational load and design complexity due to its regular structure. In this letter, we introduce and analyze the performance of two hybrid combinations of two lattices i.e. the AnAn and AnDn. Experiment results show that multistage LVQ with lattice AnA combination in four dimensional vector offers the least quantization errors with p = 0.0098 as comp...

In this paper we make a first feasibility analysis for implementing lattice reduction algorithms on GPU using CUDA, a programming framework for NVIDIA graphics cards. The enumeration phase of the BKZ lattice reduction algorithm is chosen as a good candidate for massive parallelization on GPU. Given the nature of the problem we gain large speedups compared to previous CPU implementations. Our im...

From the above definition, we have the following geometrical interpretation of the dual lattice. For any vector x, the set of all points whose inner product with x is integer forms a set of hyperplanes perpendicular to x and separated by distance 1/‖x‖. Hence, any vector x in a lattice Λ imposes the constraint that all points in Λ∗ lie in one of the hyperplanes defined by x. See the next figure...

We prove that given a point ~z outside a given lattice L then there is a dual vector which gives a fairly good estimate for how far from the lattice the vector is. To be more precise, there is a set of translated hyperplanes Hi such that L S iHi and d(~z; S iHi) 1 6n+1 d(~z; L). Warning: Essentially this paper has been published in Combinatorica and is hence subject to copyright restrictions. I...