Entropy of a bit-shift channel. (English) Zbl 1137.94005

Baggen, Stan; Balakirsky, Vladimir; Denteneer, Dee; Egner, Sebastian; Hollmann, Henk; Tolhuizen, Ludo; Verbitskiy, Evgeny

Denteneer, Dee (ed.) et al., Dynamics and stochastics. Festschrift in honor of M. S. Keane. Selected papers based on the presentations at the conference ‘Dynamical systems, probability theory, and statistical mechanics’, Eindhoven, The Netherlands, January 3–7, 2005, on the occasion of the 65th birthday of Mike S. Keane. Beachwood, OH: IMS, Institute of Mathematical Statistics (ISBN 0-940600-64-1/pbk). Institute of Mathematical Statistics Lecture Notes - Monograph Series 48, 274-285 (2006).

In this paper a simplified model for errors is considered, occuring in the readout of digital information stored on an optical recording medium like CD or DVD, cf. K. A. S. Immink (ISBN 90-74249-27-2, 2nd ed. 2004) or B. H. Marcus, R. M. Roth and P. H. Siegel (An Introduction to Coding of Constrained Systems, http://www.math.ubc.ca/\(\sim\)marcus/Handbook/index.html (Lecture Notes of UBC)).
The authors consider a simple transformation (coding) of an i.i.d. source called a bit-shift-channel. This simple tranformation occurs naturally in magnetic or optical data storage. The resulting process is not Markov of any order. Methods of computing the entropy of the transformed process are discussed, some of its properties are studied.
The references contain 20 bibliographical hints.
For the entire collection see [Zbl 1113.60008].

Reviewer: Ludwig Paditz (Dresden)

MSC:

94A17	Measures of information, entropy
28D20	Entropy and other invariants
94A40	Channel models (including quantum) in information and communication theory
94B05	Linear codes (general theory)

Keywords:

hidden Markov process; channel capacity; Gibbs vs. non-Gibbs; RLL-sequences; bit-shift channel; \(g\)-measures