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On MaximumLikelihood Detection and the Search for the Closest Lattice Point
 IEEE TRANS. INFORM. THEORY
, 2003
"... Maximumlikelihood (ML) decoding algorithms for Gaussian multipleinput multipleoutput (MIMO) linear channels are considered. Linearity over the field of real numbers facilitates the design of ML decoders using numbertheoretic tools for searching the closest lattice point. These decoders are colle ..."
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Cited by 273 (9 self)
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Maximumlikelihood (ML) decoding algorithms for Gaussian multipleinput multipleoutput (MIMO) linear channels are considered. Linearity over the field of real numbers facilitates the design of ML decoders using numbertheoretic tools for searching the closest lattice point. These decoders
An Algorithmic Theory of Lattice Points in Polyhedra
, 1999
"... We discuss topics related to lattice points in rational polyhedra, including efficient enumeration of lattice points, “short” generating functions for lattice points in rational polyhedra, relations to classical and higherdimensional Dedekind sums, complexity of the Presburger arithmetic, efficien ..."
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Cited by 128 (7 self)
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We discuss topics related to lattice points in rational polyhedra, including efficient enumeration of lattice points, “short” generating functions for lattice points in rational polyhedra, relations to classical and higherdimensional Dedekind sums, complexity of the Presburger arithmetic
Lattice point simplices
 DISCRETE MATHEMATICS
, 1986
"... We consider simplices in [w ” with lattice point vertices, no other boundary lattice points and n interior lattice points, with an emphasis on the barycentric coordinates of the interior points. We completely classify such triangles under unimodular equivalence and enumerate. For example, in a latti ..."
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Cited by 15 (3 self)
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We consider simplices in [w ” with lattice point vertices, no other boundary lattice points and n interior lattice points, with an emphasis on the barycentric coordinates of the interior points. We completely classify such triangles under unimodular equivalence and enumerate. For example, in a
Sampling lattice points
 IN PROCEEDINGS OF THE TWENTYNINTH ANNUAL ACM SYMPOSIUM ON THEORY OF COMPUTING
, 1997
"... When is the volume of a convex polytope in R^n close to the number of lattice points in the polytope? We show that if the polytope contains a ball of radius nplog m, where m is the number of facets, then the volume approximates the number of lattice points to within a constant factor. This general c ..."
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Cited by 12 (2 self)
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When is the volume of a convex polytope in R^n close to the number of lattice points in the polytope? We show that if the polytope contains a ball of radius nplog m, where m is the number of facets, then the volume approximates the number of lattice points to within a constant factor. This general
Covering lattice points by subspaces
 PERIOD. MATH. HUNGAR
, 2001
"... We find tight estimates for the minimum number of proper subspaces needed to cover all lattice points in an ndimensional convex body C, symmetric about the origin 0. This enables us to prove the following statement, which settles a problem of G. Halász. The maximum number of nwise linearly indepe ..."
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Cited by 5 (0 self)
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We find tight estimates for the minimum number of proper subspaces needed to cover all lattice points in an ndimensional convex body C, symmetric about the origin 0. This enables us to prove the following statement, which settles a problem of G. Halász. The maximum number of nwise linearly
Lattice points in the sphere
 In Number theory in progress
, 1999
"... Our goal in this paper is to give a new estimate for the number of integer lattice points lying in a sphere of radius R centred at the origin. Thus we define S(R) = #{x ∈ ZZ3: x  ≤ R}, ..."
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Cited by 5 (0 self)
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Our goal in this paper is to give a new estimate for the number of integer lattice points lying in a sphere of radius R centred at the origin. Thus we define S(R) = #{x ∈ ZZ3: x  ≤ R},
Lattice Points and Exponential Sums
, 1996
"... Suppose you have a closed curve. How do you find the area inside? While I was writing my first paper on exponential sums and lattice points, my seven year old daughter came home from school and said. "I know how you find the area of a curve. You count the squares". In other words, copy the ..."
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Cited by 49 (0 self)
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Suppose you have a closed curve. How do you find the area inside? While I was writing my first paper on exponential sums and lattice points, my seven year old daughter came home from school and said. "I know how you find the area of a curve. You count the squares". In other words, copy
Lattice points in Minkowski sums
"... Fakhruddin has proved that for two lattice polygons P and Q any lattice point in their Minkowski sum can be written as a sum of a lattice point in P and one in Q, provided P is smooth and the normal fan of P is a subdivision of the normal fan of Q. We give a shorter combinatorial proof of this fact ..."
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Cited by 2 (1 self)
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Fakhruddin has proved that for two lattice polygons P and Q any lattice point in their Minkowski sum can be written as a sum of a lattice point in P and one in Q, provided P is smooth and the normal fan of P is a subdivision of the normal fan of Q. We give a shorter combinatorial proof of this fact
Lattice Points in Lattice Polytopes
, 2000
"... We show that, for any lattice polytope P R d , the set int(P ) \ lZ d (provided it is nonempty) contains a point whose coecient of asymmetry with respect to P is at most 8d (8l +7) 2 2d+1 . If, moreover, P is a simplex, then this bound can be improved to 8 (8l + 7) 2 d+1 . As an appl ..."
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Cited by 19 (0 self)
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We show that, for any lattice polytope P R d , the set int(P ) \ lZ d (provided it is nonempty) contains a point whose coecient of asymmetry with respect to P is at most 8d (8l +7) 2 2d+1 . If, moreover, P is a simplex, then this bound can be improved to 8 (8l + 7) 2 d+1
Counting lattice points
, 2006
"... Abstract. For a locally compact second countable group G and a lattice subgroup Γ, we give an explicit quantitative solution of the lattice point counting problem in general domains in G, provided that i) G has finite upper local dimension, and the domains satisfy a basic regularity condition, ii) t ..."
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Cited by 16 (6 self)
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Abstract. For a locally compact second countable group G and a lattice subgroup Γ, we give an explicit quantitative solution of the lattice point counting problem in general domains in G, provided that i) G has finite upper local dimension, and the domains satisfy a basic regularity condition, ii
Results 1  10
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6,417