47,511 research outputs found

    Recursion Polynomials of Unfolded Sequences

    Get PDF
    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

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

    Full text link
    In this paper we study pseudorandomness of a family of sequences in terms of two measures, the family complexity (ff-complexity) and the cross-correlation measure of order \ell. We consider sequences not only on binary alphabet but also on kk-symbols (kk-ary) alphabet. We first generalize some known methods on construction of the family of binary pseudorandom sequences. We prove a bound on the ff-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 ff-complexity and low cross-correlation measure. Then we extend the results to the family of sequences on kk-symbols alphabet.Comment: 13 pages. Comments are welcome

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

    Full text link
    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

    New Constructions of Zero-Correlation Zone Sequences

    Full text link
    In this paper, we propose three classes of systematic approaches for constructing zero correlation zone (ZCZ) sequence families. In most cases, these approaches are capable of generating sequence families that achieve the upper bounds on the family size (KK) and the ZCZ width (TT) for a given sequence period (NN). Our approaches can produce various binary and polyphase ZCZ families with desired parameters (N,K,T)(N,K,T) and alphabet size. They also provide additional tradeoffs amongst the above four system parameters and are less constrained by the alphabet size. Furthermore, the constructed families have nested-like property that can be either decomposed or combined to constitute smaller or larger ZCZ sequence sets. We make detailed comparisons with related works and present some extended properties. For each approach, we provide examples to numerically illustrate the proposed construction procedure.Comment: 37 pages, submitted to IEEE Transactions on Information Theor
    corecore