On Conflict-Avoiding Codes of Length $n=4m$ for Three Active Users

Jimbo, Masakazu; Mishima, Miwako; Janiszewski, Susan; Teymorian, A.Y.; Tonchev, Vladimir D.

doi:10.1109/tit.2007.901233

Cited by 41 publications

(35 citation statements)

References 6 publications

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“…It is also shown in [4] that this upper bound is tight for n ≡ 8 mod 16. Constructions of conflict-avoiding codes achieving the upper bound in [4] are given subsequently in [3,7]. Known results for M (n, 3) for odd n is very few so far.…”

Section: Introductionmentioning

confidence: 83%

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On conflict-avoiding codes of weight three and odd length

Shum

2011

Proceedings of the Fifth International Workshop on Signal Design and Its Applications in Communications

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Explicit constructions of optimal conflictavoiding codes of weight three and even length are recently obtained. For odd length, the construction of optimal conflict-avoiding codes of weight three in general remains open. Previous results by Levenshtein consider the special case of conflict-avoiding codes consisting of equidifference codewords only. In this paper, we take the non-equi-difference codewords into account, and reduce the problem to hypergraph matching problem. Some new optimal conflict-avoiding codes are presented.

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Section: Introductionmentioning

confidence: 83%

“…For n which is a multiple of 4, Jimbo et al obtain a better upper bound on the number of codewords [4]. It is also shown in [4] that this upper bound is tight for n ≡ 8 mod 16.…”

Section: Introductionmentioning

confidence: 99%

On conflict-avoiding codes of weight three and odd length

Shum

2011

Proceedings of the Fifth International Workshop on Signal Design and Its Applications in Communications

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“…Levenshtein and Tonchev [5,6] show that Mðn; 3Þ nþ1 4 and Mðn; 3Þ ¼ M e ðn; 3Þ ¼ nÀ2 4 if n 2 ðmod 4Þ. When n is a multiple of 4, Jimbo et al [4] give a better upper bound on Mðn; 3Þ. They also prove this upper bound is sharp if n 8 ðmod 16Þ.…”

Section: Introductionmentioning

confidence: 99%

“…Mðn; 3Þ and U e ð2n; 3Þ ! M e ðn; 3Þ:It is worth to note the SCAC e ð2n; wÞ constructed from CACðn; wÞ is not definitely optimal.Example 24 The case n ¼ 48; w ¼ 3, according to[4, Theorem 2.13], there exists an optimal CAC e ð24; 3Þ with 4 codewords, however we can construct an SCAC e ð48; 3Þ with the following 5 codewords:…”

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confidence: 99%

Strongly Conflict-Avoiding Codes with Weight Three

Wang

2015

Wireless Pers Commun

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Strongly conflict-avoiding codes are used in the asynchronous multiple-access collision channel without feedback. The number of codewords in a strongly conflictavoiding code is the number of potential users that can be supported in the system. In this paper, an improved upper bound on the size of strongly conflict-avoiding codes of length n and weight three is obtained. This bound is further shown to be tight for some cases by direct constructions.

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“…At last of this section, we present some applications of δ-supp (n, k) μ -CDFs. The study of the concept of δ-supp (n, k) μ -CDFs is motivated by optical orthogonal codes [2,6,[8][9][10]20,26] and conflictavoiding codes [13,18,19], which come from applications for multiple-access communications. For general background, we refer to [14][15][16][17]23,24].…”

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confidence: 99%

On cyclic 2(k−1)-support (n,k)

Momihara

2009

Finite Fields and Their Applications

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A cyclic δ-support (n, k) μ difference family (briefly δ-supp (n, k) μ -CDF) is a family F of k-subsets of Z n such that (i) every nonzero element x of Z n appears in the list B of differences of exactly one member B of F ; (ii) the number of times that x appears in B is at most μ; and (iii) the number of distinct elements appearing in B is exactly δ for every B ∈ F . The study of this concept is motivated by applications for multiple-access communication systems.In this paper, we treat the case when (δ, μ) = (2(k − 1), k − 1) and discuss about the existence of 2(k − 1)-supp (p, k) k−1 -CDFs with p primes in relation to the problem of perfect packings. Furthermore, we prove that the set of primes p for which there exist 2(k − 1)-supp (p, k) k−1 -CDFs is infinite for the cases k = 4 and 5 by investigating the Kronecker density.

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On Conflict-Avoiding Codes of Length $n=4m$ for Three Active Users

Cited by 41 publications

References 6 publications

On conflict-avoiding codes of weight three and odd length

On conflict-avoiding codes of weight three and odd length

Strongly Conflict-Avoiding Codes with Weight Three

On cyclic 2(k−1)-support (n,k)

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