Nonlinear complexity of binary sequences and connections with lempel-ziv compression

Authors:
Konstantinos Limniotis;Nicholas Kolokotronis;Nicholas Kalouptsidis
Affiliations:
Department of Informatics and Telecommunications, National and Kapodistrian University of Athens, Athens, Greece;Department of Informatics and Telecommunications, National and Kapodistrian University of Athens, Athens, Greece;Department of Informatics and Telecommunications, National and Kapodistrian University of Athens, Athens, Greece
Venue:
SETA'06 Proceedings of the 4th international conference on Sequences and Their Applications
Year:
2006

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Abstract

The nonlinear complexity of binary sequences is studied in this paper. A new recursive algorithm is presented, which produces the minimal nonlinear feedback shift register of a given sequence. Further, a connection between the nonlinear complexity and the compression capability of a sequence is established. A lower bound for the Lempel-Ziv compression ratio that a given sequence can achieve is proved, which depends on its nonlinear complexity.