Information rates and power spectra of digital codes

Jørn Justesen

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    Abstract

    The encoding of independent data symbols as a sequence of discrete amplitude, real variables with given power spectrum is considered. The maximum rate of such an encoding is determined by the achievable entropy of the discrete sequence with the given constraints. An upper bound to this entropy is expressed in terms of the rate distortion function for a memoryless finite alphabet source and mean-square error distortion measure. A class of simple dc-free power spectra is considered in detail, and a method for constructing Markov sources with such spectra is derived. It is found that these sequences have greater entropies than most codes with similar spectra that have been suggested earlier, and that they often come close to the upper bound. When the constraint on the power spectrum is replaced by a constraint On the variance of the sum of the encoded symbols, a stronger upper bound to the rate of dc-free codes is obtained. Finally, the optimality of the binary biphase code and of the ternary bipolar code is decided.
    Original languageEnglish
    JournalI E E E Transactions on Information Theory
    Volume28
    Issue number3
    Pages (from-to)457-472
    ISSN0018-9448
    DOIs
    Publication statusPublished - 1982

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