270 research outputs found
Low Correlation Sequences over the QAM Constellation
This paper presents the first concerted look at low correlation sequence
families over QAM constellations of size M^2=4^m and their potential
applicability as spreading sequences in a CDMA setting.
Five constructions are presented, and it is shown how such sequence families
have the ability to transport a larger amount of data as well as enable
variable-rate signalling on the reverse link.
Canonical family CQ has period N, normalized maximum-correlation parameter
theta_max bounded above by A sqrt(N), where 'A' ranges from 1.8 in the 16-QAM
case to 3.0 for large M. In a CDMA setting, each user is enabled to transfer 2m
bits of data per period of the spreading sequence which can be increased to 3m
bits of data by halving the size of the sequence family. The technique used to
construct CQ is easily extended to produce larger sequence families and an
example is provided.
Selected family SQ has a lower value of theta_max but permits only (m+1)-bit
data modulation. The interleaved 16-QAM sequence family IQ has theta_max <=
sqrt(2) sqrt(N) and supports 3-bit data modulation.
The remaining two families are over a quadrature-PAM (Q-PAM) subset of size
2M of the M^2-QAM constellation. Family P has a lower value of theta_max in
comparison with Family SQ, while still permitting (m+1)-bit data modulation.
Interleaved family IP, over the 8-ary Q-PAM constellation, permits 3-bit data
modulation and interestingly, achieves the Welch lower bound on theta_max.Comment: 21 pages, 3 figures. To appear in IEEE Transactions on Information
Theory in February 200
Cocyclic simplex codes of type alpha over Z4 and Z2s
Over the past decade, cocycles have been used to construct Hadamard and generalized Hadamard matrices. This, in turn, has led to the construction of codes-self-dual and others. Here we explore these ideas further to construct cocyclic complex and Butson-Hadamard matrices, and subsequently we use the matrices to construct simplex codes of type /spl alpha/ over Z(4) and Z(2/sup s/), respectively
A Survey of Finite Algebraic Geometrical Structures Underlying Mutually Unbiased Quantum Measurements
The basic methods of constructing the sets of mutually unbiased bases in the
Hilbert space of an arbitrary finite dimension are discussed and an emerging
link between them is outlined. It is shown that these methods employ a wide
range of important mathematical concepts like, e.g., Fourier transforms, Galois
fields and rings, finite and related projective geometries, and entanglement,
to mention a few. Some applications of the theory to quantum information tasks
are also mentioned.Comment: 20 pages, 1 figure to appear in Foundations of Physics, Nov. 2006 two
more references adde
A generalization of the binary Preparata code
AbstractA classical binary Preparata code P2(m) is a nonlinear (2m+1,22(2m-1-m),6)-code, where m is odd. It has a linear representation over the ring Z4 [Hammons et al., The Z4-linearity of Kerdock, Preparata, Goethals and related codes, IEEE Trans. Inform. Theory 40(2) (1994) 301–319]. Here for any q=2l>2 and any m such that (m,q-1)=1 a nonlinear code Pq(m) over the field F=GF(q) with parameters (q(Δ+1),q2(Δ-m),d⩾3q), where Δ=(qm-1)/(q-1), is constructed. If d=3q this set of parameters generalizes that of P2(m). The equality d=3q is established in the following cases: (1) for a series of initial admissible values q and m such that qm<2100; (2) for m=3,4 and any admissible q, and (3) for admissible q and m such that there exists a number m1 with m1|m and d(Pq(m1))=3q. We apply the approach of [Nechaev and Kuzmin, Linearly presentable codes, Proceedings of the 1996 IEEE International Symposium Information Theory and Application Victoria, BC, Canada 1996, pp. 31–34] the code P is a Reed–Solomon representation of a linear over the Galois ring R=GR(q2,4) code P dual to a linear code K with parameters near to those of generalized linear Kerdock code over R
- …