### 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 language | English |
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Journal | I E E E Transactions on Information Theory |

Volume | 28 |

Issue number | 3 |

Pages (from-to) | 457-472 |

ISSN | 0018-9448 |

DOIs | |

Publication status | Published - 1982 |

### Bibliographical note

Copyright 1982 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE.## Cite this

Justesen, J. (1982). Information rates and power spectra of digital codes.

*I E E E Transactions on Information Theory*,*28*(3), 457-472. https://doi.org/10.1109/TIT.1982.1056516