On codes that avoid specified differences

Author

Moision, Bruce E. ; Orlitsky, Alon ; Siegel, Paul H.

Author_Institution

Math. Sci. Res. Center, Lucent Technol., Murray Hill, NJ, USA

Volume

47

Issue

1

fYear

2001

fDate

1/1/2001 12:00:00 AM

Firstpage

433

Lastpage

442

Abstract

Certain magnetic recording applications call for a large number of sequences whose differences do not include certain disallowed binary patterns. We show that the number of such sequences increases exponentially with their length and that the growth rate, or capacity, is the logarithm of the joint spectral radius of an appropriately defined set of matrices. We derive a new algorithm for determining the joint spectral radius of sets of nonnegative matrices and combine it with existing algorithms to determine the capacity of several sets of disallowed differences that arise in practice

Keywords

binary codes; binary sequences; combinatorial mathematics; digital magnetic recording; matrix algebra; partial response channels; capacity; codes; disallowed binary patterns; joint spectral radius; magnetic recording applications; nonnegative matrices; sequences; Binary codes; Bit error rate; Communication channels; Error probability; Magnetic materials; Magnetic recording; Maximum likelihood estimation; System performance; Viterbi algorithm; Yield estimation;

fLanguage

English

Journal_Title

Information Theory, IEEE Transactions on

Publisher

ieee

ISSN

0018-9448

Type

jour

DOI

10.1109/18.904557

Filename

904557