8,689 research outputs found
Generalized pairwise z-complementary codes
An approach to generate generalized pairwise Z-complementary (GPZ) codes, which works in pairs in order to offer a zero correlation zone (ZCZ) in the vicinity of zero phase shift and fit extremely well in power efficient quadrature carrier modems, is introduced in this letter. Each GPZ code has MK sequences, each of length 4NK, whereMis the number of Z-complementary mates,
K is a factor to perform Walsh–Hadamard expansions, and N is the sequence length of the Z-complementary code. The proposed GPZ codes include the generalized pairwise complementary (GPC)codes as special cases
Autocorrelations of Binary Sequences and Run Structure
We analyze the connection between the autocorrelation of a binary sequence
and its run structure given by the run length encoding. We show that both the
periodic and the aperiodic autocorrelation of a binary sequence can be
formulated in terms of the run structure. The run structure is given by the
consecutive runs of the sequence. Let C=(C(0), C(1),...,C(n)) denote the
autocorrelation vector of a binary sequence. We prove that the kth component of
the second order difference operator of C can be directly calculated by using
the consecutive runs of total length k. In particular this shows that the kth
autocorrelation is already determined by all consecutive runs of total length
L<k. In the aperiodic case we show how the run vector R can be efficiently
calculated and give a characterization of skew-symmetric sequences in terms of
their run length encoding.Comment: [v3]: minor revisions, accepted for publication in IEEE Trans. Inf.
Theory, 17 page
Perfect domination in regular grid graphs
We show there is an uncountable number of parallel total perfect codes in the
integer lattice graph of . In contrast, there is just one
1-perfect code in and one total perfect code in
restricting to total perfect codes of rectangular grid graphs (yielding an
asymmetric, Penrose, tiling of the plane). We characterize all cycle products
with parallel total perfect codes, and the -perfect and
total perfect code partitions of and , the former
having as quotient graph the undirected Cayley graphs of with
generator set . For , generalization for 1-perfect codes is
provided in the integer lattice of and in the products of cycles,
with partition quotient graph taken as the undirected Cayley graph
of with generator set .Comment: 16 pages; 11 figures; accepted for publication in Austral. J. Combi
Convolutional compressed sensing using deterministic sequences
This is the author's accepted manuscript (with working title "Semi-universal convolutional compressed sensing using (nearly) perfect sequences"). The final published article is available from the link below. Copyright @ 2012 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other users, including reprinting/ republishing this material for advertising or promotional purposes, creating new collective works for resale or redistribution to servers or lists, or reuse of any copyrighted components of this work in other works.In this paper, a new class of orthogonal circulant matrices built from deterministic sequences is proposed for convolution-based compressed sensing (CS). In contrast to random convolution, the coefficients of the underlying filter are given by the discrete Fourier transform of a deterministic sequence with good autocorrelation. Both uniform recovery and non-uniform recovery of sparse signals are investigated, based on the coherence parameter of the proposed sensing matrices. Many examples of the sequences are investigated, particularly the Frank-Zadoff-Chu (FZC) sequence, the m-sequence and the Golay sequence. A salient feature of the proposed sensing matrices is that they can not only handle sparse signals in the time domain, but also those in the frequency and/or or discrete-cosine transform (DCT) domain
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