Optimal Dual Frames for Communication Coding With Probabilistic Erasures

    Authors

    J. S. Leng; D. G. Han;T. Z. Huang

    Comments

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    Abbreviated Journal Title

    IEEE Trans. Signal Process.

    Keywords

    Codes; erasures; frames; optimal dual frames; OVERSAMPLED FILTER BANKS; THEORETIC ANALYSIS; REPRESENTATIONS; TRANSMISSION; QUANTIZATION; EXPANSIONS; SYSTEMS; Engineering, Electrical & Electronic

    Abstract

    Assume that a frame is preselected for encoding in a communication system. We investigate the optimal dual frames for signal reconstruction (decoding) which minimize the maximal error when the probabilistic erasures occur in the transmission process from the perspective of mathematical theory of frames. We set up a probability model under which we define the probability optimal (PO) dual frames for a given frame when the frame-based coding involves probabilistic erasures. We obtain a sufficient and necessary condition under which the canonical dual frame is the unique PO dual frame. Additionally, we derive some general sufficient conditions for which the canonical dual frame is either not optimal or it is optimal but not the unique optimal one. We present two simulation examples to compare the reconstruction effects when both the PO dual frames and the general optimal (GO) dual frames are used for reconstruction.

    Journal Title

    Ieee Transactions on Signal Processing

    Volume

    59

    Issue/Number

    11

    Publication Date

    1-1-2011

    Document Type

    Article

    Language

    English

    First Page

    5380

    Last Page

    5389

    WOS Identifier

    WOS:000297113500023

    ISSN

    1053-587X

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