232,396 research outputs found

    Construction and Applications of CRT Sequences

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    Protocol sequences are used for channel access in the collision channel without feedback. Each user accesses the channel according to a deterministic zero-one pattern, called the protocol sequence. In order to minimize fluctuation of throughput due to delay offsets, we want to construct protocol sequences whose pairwise Hamming cross-correlation is as close to a constant as possible. In this paper, we present a construction of protocol sequences which is based on the bijective mapping between one-dimensional sequence and two-dimensional array by the Chinese Remainder Theorem (CRT). In the application to the collision channel without feedback, a worst-case lower bound on system throughput is derived.Comment: 16 pages, 5 figures. Some typos in Section V are correcte

    Symplectic reduction and the problem of time in nonrelativistic mechanics

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    The deep connection between the interpretation of theories invariant under local symmetry transformations (i.e. gauge theories) and the philosophy of space and time can be illustrated nonrelativistically via the investigation of reparameterisation invariant reformulations of Newtonian mechanics, such as Jacobi's theory. Like general relativity, the canonical formulation of such theories feature Hamiltonian constraints; and like general relativity, the interpretation of these constraints along conventional Dirac lines is highly problematic in that it leads to a nonrelativistic variant of the infamous problem of time. I argue that, nonrelativistically at least, the source of the problem can be found precisely within the symplectic reduction that goes along with strict adherence to the Dirac view. Avoiding reduction, two viable alternative strategies for dealing with Hamiltonian constraints are available. Each is found to lead us to a novel and interesting re-conception of time and change within nonrelativistic mechanics. Both these strategies and the failure of reduction have important implications for the debate concerning the relational or absolute status of time within physical theory

    A Systematic Framework for the Construction of Optimal Complete Complementary Codes

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    The complete complementary code (CCC) is a sequence family with ideal correlation sums which was proposed by Suehiro and Hatori. Numerous literatures show its applications to direct-spread code-division multiple access (DS-CDMA) systems for inter-channel interference (ICI)-free communication with improved spectral efficiency. In this paper, we propose a systematic framework for the construction of CCCs based on NN-shift cross-orthogonal sequence families (NN-CO-SFs). We show theoretical bounds on the size of NN-CO-SFs and CCCs, and give a set of four algorithms for their generation and extension. The algorithms are optimal in the sense that the size of resulted sequence families achieves theoretical bounds and, with the algorithms, we can construct an optimal CCC consisting of sequences whose lengths are not only almost arbitrary but even variable between sequence families. We also discuss the family size, alphabet size, and lengths of constructible CCCs based on the proposed algorithms

    A Family of Binary Sequences with Optimal Correlation Property and Large Linear Span

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    A family of binary sequences is presented and proved to have optimal correlation property and large linear span. It includes the small set of Kasami sequences, No sequence set and TN sequence set as special cases. An explicit lower bound expression on the linear span of sequences in the family is given. With suitable choices of parameters, it is proved that the family has exponentially larger linear spans than both No sequences and TN sequences. A class of ideal autocorrelation sequences is also constructed and proved to have large linear span.Comment: 21 page
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