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Theoretical exploration of pattern attributes for maximum-length shift-register sequences

Published: 21 June 2009 Publication History

Abstract

The maximum-length shift-register sequences (m-sequences) are the often-used pseudo-random sequences for multi-access communications. It is well known that the generation of the m-sequences relies on the initial seed and the cyclic shift. Although we can identify a particular m-sequence using a unique initial seed and the step of the cyclic shift, the categorization or the classification of the m-sequence structures has never been studied to the best of our knowledge. In this paper, we study the m-sequence structures by means of the attributes (common subsequences or patterns). Such patterns are a set of binary sequences with finite length occurring in the full-length m-sequences and they can be used to denote the special attributes (common features) for transceivers. In addition, we design a parallel method to compute all the possible positions of bits "0" and "1" for each underlying pattern using the Berlekamp's algorithm and then we employ the solution to a generalized traveling salesman problem for constructing the shortest binary sequences, each of which contains all underlying patterns. From these shortest binary sequences, we can thus evaluate the number of m-sequences that include the underlying patterns. We also define the attributability, and discriminability for the population analysis of the jointly- or exclusively-attributed m-sequences.

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  1. Theoretical exploration of pattern attributes for maximum-length shift-register sequences

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        cover image ACM Conferences
        IWCMC '09: Proceedings of the 2009 International Conference on Wireless Communications and Mobile Computing: Connecting the World Wirelessly
        June 2009
        1561 pages
        ISBN:9781605585697
        DOI:10.1145/1582379
        Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

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        Published: 21 June 2009

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        Author Tags

        1. m-sequences
        2. berlekamp's algorithm
        3. finite fields
        4. pattern attribute
        5. traveling salesman problem

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