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Entropy and Power Spectrum of Asymmetrically Dc-Constrained Binary Sequences

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Abstract

The eigenstructure of bidiagonal Hessenberg-Toeplitz matrices is determined. These matrices occur as skeleton matrices of finite-state machines generating certain asymmetrically DC-constrained binary sequences that can be used for simulating pilot tracking tones in digital magnetic recording. The eigenstructure is used to calculate the Shannon upper bound to the entropy of the finite state machine as well as the power spectrum of the maxentropic process generated by it.

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... The classes of runlengthlimited constraints and spectral-null constraints have already been introduced. In addition, there are constraints that generate spectral lines at specified frequencies, called pilot tracking tones, which can be used for servo tracking systems in videotape recorders [118], [115]. Certain channels require a combination of time and frequency constraints [128], [157], [160]; specifically DC-balanced RLL sequences have found widespread usage in recording practice. ...
... The classes of runlengthlimited constraints and spectral-null constraints have already been introduced. In addition, there are constraints that generate spectral lines at specified frequencies, called pilot tracking tones, which can be used for servo tracking systems in videotape recorders [118], [115]. Certain channels require a combination of time and frequency constraints [128], [157], [160]; specifically DC-balanced RLL sequences have found widespread usage in recording practice. ...
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Spectral analysis of low frequencies, where for an encoded sequence a = aOal * * . aL, functions of Markov chains with applications
  • G Bilardi
  • R Padovani
  • G Pierobon
G. Bilardi, R. Padovani, and G. Pierobon, "Spectral analysis of low frequencies, where for an encoded sequence a = aOal * *. aL, functions of Markov chains with applications," IEEE Trans. Com-RDS, of a is defined by mun., vol. COM-31, pp. 853-861, July 1983.