Skip to content
University of Maryland LibrariesDigital Repository at the University of Maryland
    • Login
    View Item 
    •   DRUM
    • Theses and Dissertations from UMD
    • UMD Theses and Dissertations
    • View Item
    •   DRUM
    • Theses and Dissertations from UMD
    • UMD Theses and Dissertations
    • View Item
    JavaScript is disabled for your browser. Some features of this site may not work without it.

    Combinatorial Methods in Coding Theory

    Thumbnail
    View/Open
    Mazumdar_umd_0117E_12137.pdf (743.2Kb)
    No. of downloads: 17280

    Date
    2011
    Author
    Mazumdar, Arya
    Advisor
    Barg, Alexander
    Metadata
    Show full item record
    Abstract
    This thesis is devoted to a range of questions in applied mathematics and signal processing motivated by applications in error correction, compressed sensing, and writing on non-volatile memories. The underlying thread of our results is the use of diverse combinatorial methods originating in coding theory and computer science. The thesis addresses three groups of problems. The first of them is aimed at the construction and analysis of codes for error correction. Here we examine properties of codes that are constructed using random and structured graphs and hypergraphs, with the main purpose of devising new decoding algorithms as well as estimating the distribution of Hamming weights in the resulting codes. Some of the results obtained give the best known estimates of the number of correctable errors for codes whose decoding relies on local operations on the graph. In the second part we address the question of constructing sampling operators for the compressed sensing problem. This topic has been the subject of a large body of works in the literature. We propose general constructions of sampling matrices based on ideas from coding theory that act as near-isometric maps on almost all sparse signal. This matrices can be used for dimensionality reduction and compressed sensing. In the third part we study the problem of reliable storage of information in non-volatile memories such as flash drives. This problem gives rise to a writing scheme that relies on relative magnitudes of neighboring cells, known as rank modulation. We establish the exact asymptotic behavior of the size of codes for rank modulation and suggest a number of new general constructions of such codes based on properties of finite fields as well as combinatorial considerations.
    URI
    http://hdl.handle.net/1903/11547
    Collections
    • Electrical & Computer Engineering Theses and Dissertations
    • UMD Theses and Dissertations

    DRUM is brought to you by the University of Maryland Libraries
    University of Maryland, College Park, MD 20742-7011 (301)314-1328.
    Please send us your comments.
    Web Accessibility
     

     

    Browse

    All of DRUMCommunities & CollectionsBy Issue DateAuthorsTitlesSubjectsThis CollectionBy Issue DateAuthorsTitlesSubjects

    My Account

    LoginRegister
    Pages
    About DRUMAbout Download Statistics

    DRUM is brought to you by the University of Maryland Libraries
    University of Maryland, College Park, MD 20742-7011 (301)314-1328.
    Please send us your comments.
    Web Accessibility