An efficient implementation algorithm for generating de Bruijn sequences

Zhang, Weiguo; Liu, Shuanggen; Huang, Huawei

doi:10.1016/j.csi.2008.12.001

Cited by 4 publications

(2 citation statements)

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“…This paper employs a fourth common construction technique: a cycle joining (a.k.a. cross-join) construction [3,4,7,10,20,25,27,29,39,46]. Roughly speaking, in this technique, the n-length words are divided into the equivalence classes of the 'rotation of' equivalence relation.…”

Section: Introductionmentioning

confidence: 99%

A Cycle Joining Construction of the Prefer-Max De Bruijn Sequence

Amram,

Rubin,

Weiss

2021

Preprint

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We propose a novel construction for the well-known prefer-max De Bruijn sequence, based on the cycle joining technique. We further show that the construction implies known results from the literature in a straightforward manner. First, it implies the correctness of the onion theorem, stating that, effectively, the reverse of prefer-max is in fact an infinite De Bruijn sequence. Second, it implies the correctness of recently discovered shift rules for prefer-max, prefer-min, and their reversals. Lastly, it forms an alternative proof for the seminal FKM-theorem.

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Section: Introductionmentioning

confidence: 99%

A Cycle Joining Construction of the Prefer-Max De Bruijn Sequence

Amram,

Rubin,

Weiss

2021

Preprint

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“…A useful overview of possible alternative approaches suggested in the literature may be found in [17]. However, the main limitation of such solutions is related to the reduced number of sequences they allow to obtain by a single generation step.…”

Section: Evaluation Of Binary De Bruijn Sequences In Ds-cdma Systemsmentioning

confidence: 99%

Binary De Bruijn sequences for DS-CDMA systems: analysis and results

Spinsante

Andrenacci

Gambi

2011

J Wireless Com Network

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Code division multiple access (CDMA) using direct sequence (DS) spread spectrum modulation provides multiple access capability essentially thanks to the adoption of proper sequences as spreading codes. The ability of a DS-CDMA receiver to detect the desired signal relies to a great extent on the auto-correlation properties of the spreading code associated to each user; on the other hand, multi-user interference rejection depends on the crosscorrelation properties of all the spreading codes in the considered set. As a consequence, the analysis of new families of spreading codes to be adopted in DS-CDMA is of great interest. This article provides results about the evaluation of specific full-length binary sequences, the De Bruijn ones, when applied as spreading codes in DS-CDMA schemes, and compares their performance to other families of spreading codes commonly used, such as msequences, Gold, OVSF, and Kasami sequences. While the latter sets of sequences have been specifically designed for application in multi-user communication contexts, De Bruijn sequences come from combinatorial mathematics, and have been applied in completely different scenarios. Considering the similarity of De Bruijn sequences to random sequences, we investigate the performance resulting by applying them as spreading codes. The results herein presented suggest that binary De Bruijn sequences, when properly selected, may compete with more consolidated options, and encourage further investigation activities, specifically focused on the generation of longer sequences, and the definition of correlation-based selection criteria.

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