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In direct-sequence code-division multiple-access (DS-CDMA) communication systems and direct-sequence ultra wideband (DS-UWB) 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 *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}-1,2*p*^{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}-1,2*p*^{m}-1,*d*-4)*p*^{m}-1}. In Construction III, the new sequences possess the largest family size *p*^{(d-1)n} and have at most 2*d* correlation levels {-*p*^{m}-1,-1,*p*^{m}-1,2*p*^{m}-1,*d*-2)*p*^{m}-1}. Three constructions are near-optimal with respect to the Welch bound because the values of their Welch-Ratios are moderate, *WR**d*, *WR**d*-4 and *WR**d*-2, 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 3^{m}-2, too. Finally, some open questions are pointed out and an example that illustrates the performance of these sequences is given.

- Publication
- IEICE TRANSACTIONS on Fundamentals Vol.E91-A No.9 pp.2615-2625

- Publication Date
- 2008/09/01

- Publicized

- Online ISSN
- 1745-1337

- DOI
- 10.1093/ietfec/e91-a.9.2615

- Type of Manuscript
- PAPER

- Category
- Information Theory

The copyright of the original papers published on this site belongs to IEICE. Unauthorized use of the original or translated papers is prohibited. See IEICE Provisions on Copyright for details.

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Fanxin ZENG, "New Sequences with Low Correlation and Large Family Size" in IEICE TRANSACTIONS on Fundamentals,
vol. E91-A, no. 9, pp. 2615-2625, September 2008, doi: 10.1093/ietfec/e91-a.9.2615.

Abstract: In direct-sequence code-division multiple-access (DS-CDMA) communication systems and direct-sequence ultra wideband (DS-UWB) 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 *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}-1,2*p*^{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}-1,2*p*^{m}-1,*d*-4)*p*^{m}-1}. In Construction III, the new sequences possess the largest family size *p*^{(d-1)n} and have at most 2*d* correlation levels {-*p*^{m}-1,-1,*p*^{m}-1,2*p*^{m}-1,*d*-2)*p*^{m}-1}. Three constructions are near-optimal with respect to the Welch bound because the values of their Welch-Ratios are moderate, *WR**d*, *WR**d*-4 and *WR**d*-2, 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 3^{m}-2, too. Finally, some open questions are pointed out and an example that illustrates the performance of these sequences is given.

URL: https://global.ieice.org/en_transactions/fundamentals/10.1093/ietfec/e91-a.9.2615/_p

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@ARTICLE{e91-a_9_2615,

author={Fanxin ZENG, },

journal={IEICE TRANSACTIONS on Fundamentals},

title={New Sequences with Low Correlation and Large Family Size},

year={2008},

volume={E91-A},

number={9},

pages={2615-2625},

abstract={In direct-sequence code-division multiple-access (DS-CDMA) communication systems and direct-sequence ultra wideband (DS-UWB) 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 *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}-1,2*p*^{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}-1,2*p*^{m}-1,*d*-4)*p*^{m}-1}. In Construction III, the new sequences possess the largest family size *p*^{(d-1)n} and have at most 2*d* correlation levels {-*p*^{m}-1,-1,*p*^{m}-1,2*p*^{m}-1,*d*-2)*p*^{m}-1}. Three constructions are near-optimal with respect to the Welch bound because the values of their Welch-Ratios are moderate, *WR**d*, *WR**d*-4 and *WR**d*-2, 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 3^{m}-2, too. Finally, some open questions are pointed out and an example that illustrates the performance of these sequences is given.

keywords={},

doi={10.1093/ietfec/e91-a.9.2615},

ISSN={1745-1337},

month={September},}

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TY - JOUR

TI - New Sequences with Low Correlation and Large Family Size

T2 - IEICE TRANSACTIONS on Fundamentals

SP - 2615

EP - 2625

AU - Fanxin ZENG

PY - 2008

DO - 10.1093/ietfec/e91-a.9.2615

JO - IEICE TRANSACTIONS on Fundamentals

SN - 1745-1337

VL - E91-A

IS - 9

JA - IEICE TRANSACTIONS on Fundamentals

Y1 - September 2008

AB - In direct-sequence code-division multiple-access (DS-CDMA) communication systems and direct-sequence ultra wideband (DS-UWB) 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 *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}-1,2*p*^{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}-1,2*p*^{m}-1,*d*-4)*p*^{m}-1}. In Construction III, the new sequences possess the largest family size *p*^{(d-1)n} and have at most 2*d* correlation levels {-*p*^{m}-1,-1,*p*^{m}-1,2*p*^{m}-1,*d*-2)*p*^{m}-1}. Three constructions are near-optimal with respect to the Welch bound because the values of their Welch-Ratios are moderate, *WR**d*, *WR**d*-4 and *WR**d*-2, 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 3^{m}-2, too. Finally, some open questions are pointed out and an example that illustrates the performance of these sequences is given.

ER -