Abstract
The encoding of data in a number of recording and transmission devices can be modelized by a Markov process. Several performance statistics of the encoded signal (e.g. : frequency spectrum, run-length distribution, error propagation, etc) can be derived from a probability state vector, which is an Eigenvector for the encoder transition matrix.
We develop a very simple integer algorithm, applicable in this case. The integer nature of the result, not only facilitates subsequent calculations (e.g. : autocorrelation function), but also saves the code structure, which might help in analyzing many other properties.
This algorithm is part of a fully integrated program for frequency spectrum calculation, running on a microcomputer.
This is a preview of subscription content, log in via an institution to check access.
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
Significant references
ADLER, COPPERSMITH & HASSNER “Algorithms for sliding Block Codes” IEEE — Vol IT 29 — N 1 — Jan 1983 — pp 5–22
CARRIDLARD & Al. “Spectral Analysis of Variable Lenght Coded Digital Signals” IEEE — Vol IT 28 — N 3 — May 1982 — pp 473–481
CHIEN “Upper Bound on Efficiency of DC-Constrained Codes” BSTJ — Vol 49 — N 9 — Nov 1970 — pp 2267–2287
DAVIS “Monte-Carlo Analysis of Recording Codes” INTERMAG Conference — HAMBURG — April 1984
EGGENBERGER & HODGES “Sequential Encoding & Decoding of Variable Length Codes.” US Patent 4115768 — 19 Sep 78
FRANASZEK “A Sequence-State Coding for Digital Transmission” BSTJ — Vol 47 — N 1 — JAN 1968 — pp 143–157
FRANASZEK “Run-Length Limited Variable Length Coding with error propagation limitation.” US Patent 3689889 — 5 Sep 72
FROEBENIUS “Ueber Matrizen aus Nicht-Negativen Elementen” BERLIN — 1912
IMAI & SAITO “State-Function Decoding Methods for (d,k) Run-Length Limited Codes” 7th Symposium on Information Theory and its Applications of Japan. KINUGAWA — Nov 1984
JUSTESEN “Information Rate and Power Spectra of digital Codes” IEEE — Vol IT 28 — N 3 — May 1982 — pp 457–472
LEWIN “LOGICAL DESIGN OF SWITCHING CIRCUITS” ... In French: “SYSTEMES LOGIQUES” Editions SPES S.A. — LAUSANNE — 1972
LINHOLM “Power Spectra of Channel Codes for digital Magnetic Recording” IEEE — Vol MAG14 — N 5 — Sep 1978 — pp 321–323
TANG & BAHL “Block Codes for a Class of Constrained Noisless Channels” INFO & CONTROL — Vol 17 — Dec 1970 — pp 436–461
VARGA “MATRIX ITERATIVE ANALYSIS” — Prentice Hall — 1962
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1986 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Oisel, A. (1986). Integer programming applied to eigenvector computation in a class of Markov processes. In: Calmet, J. (eds) Algebraic Algorithms and Error-Correcting Codes. AAECC 1985. Lecture Notes in Computer Science, vol 229. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-16776-5_706
Download citation
DOI: https://doi.org/10.1007/3-540-16776-5_706
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-16776-1
Online ISBN: 978-3-540-39855-4
eBook Packages: Springer Book Archive