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

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

Families of sequences with good family complexity and cross-correlation measure

In this paper we study pseudorandomness of a family of sequences in terms of two measures, the family complexity ($f$-complexity) and the cross-correlation measure of order $\ell$. We consider sequences not only on binary alphabet but also on $k$-symbols ($k$-ary) alphabet. We first generalize some known methods on construction of the family of binary pseudorandom sequences. We prove a bound on the $f$-complexity of a large family of binary sequences of Legendre-symbols of certain irreducible polynomials. We show that this family as well as its dual family have both a large family complexity and a small cross-correlation measure up to a rather large order. Next, we present another family of binary sequences having high $f$-complexity and low cross-correlation measure. Then we extend the results to the family of sequences on $k$-symbols alphabet.Comment: 13 pages. Comments are welcome

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

Recursion Polynomials of Unfolded Sequences

Watermarking digital media is one of the important chal- lenges for information hiding. Not only the watermark must be resistant to noise and against attempts of modification, legitimate users should not be aware that it is embedded in the media. One of the techniques for watermarking is using an special variant of spread-spectrum tech- nique, called frequency hopping. It requires ensembles of periodic binary sequences with low off-peak autocorrelation and cross-correlation. Un- fortunately, they are quite rare and difficult to find. The small Kasami, Kamaletdinov, and Extended Rational Cycle constructions are versatile, because they can also be converted into Costas-like arrays for frequency hopping. We study the implementation of such ensembles using linear feedback shift registers. This permits an efficient generation of sequences and arrays in real time in FPGAs. Such an implementation requires minimal memory usage and permits dynamic updating of sequences or arrays. The aim of our work was to broaden current knowledge of sets of se- quences with low correlation studying their implementation using linear feedback shift registers. A remarkable feature of these families is their similarities in terms of implementation and it may open new way to characterize sequences with low correlation, making it easier to gener- ate them. It also validates some conjectures made by Moreno and Tirkel about arrays constructed using the method of composition.Supported by Consejería de Universidades e Investigación, Medio Ambiente y Política Social, Gobierno de Cantabria (ref. VP34