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New Sequences with Low Correlation and Large Family Size
Fanxin ZENG
Publication
IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences
Vol.E91A
No.9
pp.26152625 Publication Date: 2008/09/01 Online ISSN: 17451337
DOI: 10.1093/ietfec/e91a.9.2615 Print ISSN: 09168508 Type of Manuscript: PAPER Category: Information Theory Keyword: sequence, low correlation, family size, optimal, decimation, DSCDMA/UWB,
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Summary:
In directsequence codedivision multipleaccess (DSCDMA) communication systems and directsequence ultra wideband (DSUWB) radios, sequences with low correlation and large family size are important for reducing multiple access interference (MAI) and accepting more active users, respectively. In this paper, a new collection of families of sequences of length p^{n}1, which includes three constructions, is proposed. The maximum number of cyclically distinct families without GMW sequences in each construction is , where p is a prime number, n is an even number, and n=2m, and these sequences can be binary or polyphase depending upon choice of the parameter p. In Construction I, there are p^{n} distinct sequences within each family and the new sequences have at most d+2 nontrivial periodic correlation {p^{m}1,1,p^{m}1,2p^{m}1,,dp^{m}1}. In Construction II, the new sequences have large family size p^{2n} and possibly take the nontrivial correlation values in {p^{m}1,1,p^{m}1,2p^{m}1,,(3d4)p^{m}1}. In Construction III, the new sequences possess the largest family size p^{(d1)n} and have at most 2d correlation levels {p^{m}1,1,p^{m}1,2p^{m}1,,(2d2)p^{m}1}. Three constructions are nearoptimal with respect to the Welch bound because the values of their WelchRatios are moderate, WR d, WR 3d4 and WR 2d2, respectively. Each family in Constructions I, II and III contains a GMW sequence. In addition, Helleseth sequences and Niho sequences are special cases in Constructions I and III, and their restriction conditions to the integers m and n, p^{m}≠ 2(mod 3) and n≡ 0 (mod 4), respectively, are removed in our sequences. Our sequences in Construction III include the sequences with Niho type decimation 32^{m}2, too. Finally, some open questions are pointed out and an example that illustrates the performance of these sequences is given.

