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24
Unitary SpaceTime Modulation for MultipleAntenna Communications in Rayleigh Flat Fading
 IEEE Trans. Inform. Theory
, 1998
"... Motivated by informationtheoretic considerations, we propose a signalling scheme, unitary spacetime modulation, for multipleantenna communication links. This modulation is ideally suited for Rayleigh fastfading environments, since it does not require the receiver to know or learn the propagation ..."
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Cited by 307 (19 self)
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Motivated by informationtheoretic considerations, we propose a signalling scheme, unitary spacetime modulation, for multipleantenna communication links. This modulation is ideally suited for Rayleigh fastfading environments, since it does not require the receiver to know or learn the propagation coefficients. Unitary spacetime modulation uses constellations of T \cross M spacetime signals {\Phi_l, l= 1,...L},where T represents the coherence interval during which the fading is approximately constant, and M > M . We design some multipleantenna signal constellations and simulate their effectiveness as measured by bit error probability with maximum likelihood decoding. We demonstrate that two antennas have a 6dB diversity gain over one antenna at 15db SNR.
Constructions of Mutually Unbiased Bases
 in Proc. 7th Int. Conf. on finite fields and applications, Lecture
"... Abstract. Two orthonormal bases B and B ′ of a ddimensional complex innerproduct space are called mutually unbiased if and only if 〈bb ′ 〉  2 = 1/d holds for all b ∈ B and b ′ ∈ B ′. The size of any set containing pairwise mutually unbiased bases of C d cannot exceed d + 1. If d is a power of ..."
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Cited by 32 (1 self)
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Abstract. Two orthonormal bases B and B ′ of a ddimensional complex innerproduct space are called mutually unbiased if and only if 〈bb ′ 〉  2 = 1/d holds for all b ∈ B and b ′ ∈ B ′. The size of any set containing pairwise mutually unbiased bases of C d cannot exceed d + 1. If d is a power of a prime, then extremal sets containing d+1 mutually unbiased bases are known to exist. We give a simplified proof of this fact based on the estimation of exponential sums. We discuss conjectures and open problems concerning the maximal number of mutually unbiased bases for arbitrary dimensions.
New construction of mutually unbiased bases in square dimensions
"... We show that k = w + 2 mutually unbiased bases can be constructed in any square dimension d = s 2 provided that there are w mutually orthogonal Latin squares of order s. The construction combines the designtheoretic objects (k, s)nets (which can be constructed from w mutually orthogonal Latin squa ..."
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Cited by 26 (2 self)
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We show that k = w + 2 mutually unbiased bases can be constructed in any square dimension d = s 2 provided that there are w mutually orthogonal Latin squares of order s. The construction combines the designtheoretic objects (k, s)nets (which can be constructed from w mutually orthogonal Latin squares of order s and vice versa) and generalized Hadamard matrices of size s. Using known lower bounds on the asymptotic growth of the number of mutually orthogonal Latin squares (based on number theoretic sieving techniques), we obtain that the number of mutually unbiased bases in dimensions d = s 2 is greater than s 1/14.8 for all s but finitely many exceptions. Furthermore, our construction gives more mutually orthogonal bases in many nonprimepower dimensions than the construction that reduces the problem to prime power dimensions. 1
Solving the Shortest Lattice Vector Problem in Time 2 2.465n
"... Abstract. The Shortest lattice Vector Problem is central in latticebased cryptography, as well as in many areas of computational mathematics and computer science, such as computational number theory and combinatorial optimisation. We present an algorithm for solving it in time 2 2.465n+o(n) and spa ..."
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Cited by 20 (3 self)
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Abstract. The Shortest lattice Vector Problem is central in latticebased cryptography, as well as in many areas of computational mathematics and computer science, such as computational number theory and combinatorial optimisation. We present an algorithm for solving it in time 2 2.465n+o(n) and space 2 1.233n+o(n) , where n is the lattice dimension. This improves the best previously known algorithm, by Micciancio and Voulgaris [SODA 2010], which runs in time 2 3.199n+o(n) and space 2 1.325n+o(n).
New lattice packings of spheres
 Canad. J. Math
, 1983
"... for lattice packings of spheres in real wdimensional space R w and complex space C n. These lead to denser lattice packings than any previously known in R 36, R 64, R 80,..., R 128,.... A sequence of lattices is constructed in R n for n = 24m ^ 98328 (where m is an integer) for which the density A ..."
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Cited by 13 (4 self)
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for lattice packings of spheres in real wdimensional space R w and complex space C n. These lead to denser lattice packings than any previously known in R 36, R 64, R 80,..., R 128,.... A sequence of lattices is constructed in R n for n = 24m ^ 98328 (where m is an integer) for which the density A
A generalized Pauli problem and an infinite family of MUBtriplets in dimension 6
 J. Physics A
"... Abstract. We exhibit an infinite family of triplets of mutually unbiased bases (MUBs) in dimension 6. These triplets involve the Fourier family of Hadamard matrices, F (a, b). However, in the main result of the paper we also prove that for any values of the parameters (a, b), the standard basis and ..."
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Cited by 12 (5 self)
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Abstract. We exhibit an infinite family of triplets of mutually unbiased bases (MUBs) in dimension 6. These triplets involve the Fourier family of Hadamard matrices, F (a, b). However, in the main result of the paper we also prove that for any values of the parameters (a, b), the standard basis and F (a, b) cannot be extended to a MUBquartet. The main novelty lies in the method of proof which may successfully be applied in the future to prove that the maximal number of MUBs in dimension 6 is three.
A lower bound on the average error of vector quantizers
 IEEE Trans. Inform. Theory
, 1985
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Capacity and Coding for the BlockIndependent Noncoherent AWGN Channel
 IEEE TRANSACTIONS ON INFORMATION THEORY
, 2005
"... Communication over the noncoherent additive white Gaussian noise channel is considered, where the transmitted signal undergoes a phase rotation, unknown to the transmitter and the receiver. The effects of phase dynamics are explicitly taken into account by considering a blockindependent model fo ..."
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Cited by 10 (0 self)
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Communication over the noncoherent additive white Gaussian noise channel is considered, where the transmitted signal undergoes a phase rotation, unknown to the transmitter and the receiver. The effects of phase dynamics are explicitly taken into account by considering a blockindependent model for the phase process: the unknown phase is constant for a block of N complex symbols and independent from block to block. In the first
A new upper bound for the minimum of an integral lattice of determinant 1
 Bull. Amer. Math. Soc. (N.S
, 1990
"... ABSTRACT. Let A be an «dimensional integral lattice of determinant 1. We show that, for all sufficiently large n, the minimal nonzero squared length in A does not exceed [(n + 6)/10]. This bound is a consequence of some new conditions on the theta series of these lattices; these conditions also ena ..."
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Cited by 9 (5 self)
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ABSTRACT. Let A be an «dimensional integral lattice of determinant 1. We show that, for all sufficiently large n, the minimal nonzero squared length in A does not exceed [(n + 6)/10]. This bound is a consequence of some new conditions on the theta series of these lattices; these conditions also enable us to find the greatest possible minimal squared length in all dimensions n < 33. In particular, we settle the "noroots" problem: There is a determinant 1 lattice containing no vectors of squared length 1 or 2 precisely when w>23,«^25. There are also analogues of all these results for codes. 1.
Average Time Fast SVP and CVP Algorithms for Low Density Lattices and the Factorization of Integers
, 2010
"... Abstract. We propose and analyze novel algorithms for finding shortest and closest lattice vectors. The algorithm New Enum performs the stages of exhaustive enumeration of short / close lattice vectors in order of decreasing success rate. We analyze New Enum under GSA which in practice holds on the ..."
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Cited by 6 (1 self)
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Abstract. We propose and analyze novel algorithms for finding shortest and closest lattice vectors. The algorithm New Enum performs the stages of exhaustive enumeration of short / close lattice vectors in order of decreasing success rate. We analyze New Enum under GSA which in practice holds on the average for well reduced bases. New Enum solves SVP in n n 8 +o(n) time for bases of dimension n that satisfy GSA. Under the volume heuristics a shortest lattice vector is found in polynomial time if the density of the lattice is moderately small. This might affect the RSA scheme. Integers N can be factored by solving (ln N) O(1) CVP’s for the prime number lattice. Under combined standard and new heuristics these CVP’s are solvable in polynomial time.