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

Document Type

Conference Proceeding

Publication Date

1-1-2009

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. Copyright © 2009 ACM.

Publication Source (Journal or Book title)

Proceedings of the 2009 ACM International Wireless Communications and Mobile Computing, Connecting the World Wirelessly, IWCMC 2009

First Page

1116

Last Page

1120

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