Generating De Bruijn sequences: an efficient implementation

Annexstein, Fred S.

doi:10.1109/12.565596

Cited by 55 publications

(42 citation statements)

References 2 publications

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“…This proves (1). We already know that L(M i ) ⊂ m i so let c ∈ m i and, by part (1), let a 0 ∈ S be an element such that L(a 0 ) = 1.…”

Section: 4b the Trace And The Normmentioning

confidence: 88%

“…(3) Let n = df . By (1), an element a k has order d if and only if gcd(n, k) = n/d = f . This holds precisely when k = gf with g relatively prime to n/f = d and 0 < k < n. That is, 0 < g < d.…”

Section: 1b Subgroupsmentioning

confidence: 99%

“…One of the most fascinating aspects of this theory concerns the design of shift registers that produce maximal length sequences, or m-sequences, and the remarkable statistical and correlation properties of these sequences, which we describe in Chapter 13: besides having maximal length, each m-sequence a of rank k is also a (punctured) de Bruijn sequence 1 and its autocorrelation function is optimal. It is an amazing fact that the design problem can be completely solved using the Galois theory of finite fields.…”

Section: Chapter 1 Introductionmentioning

confidence: 99%

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Algebraic Shift Register Sequences

Goresky

Klapper

2012

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Pseudo-random sequences are essential ingredients of every modern digital communication system including cellular telephones, GPS, secure internet transactions and satellite imagery. Each application requires pseudo-random sequences with specific statistical properties. This book describes the design, mathematical analysis and implementation of pseudo-random sequences, particularly those generated by shift registers and related architectures such as feedback-with-carry shift registers. The earlier chapters may be used as a textbook in an advanced undergraduate mathematics course or a graduate electrical engineering course; the more advanced chapters provide a reference work for researchers in the field. Background material from algebra, beginning with elementary group theory, is provided in an appendix.

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“…This proves (1). We already know that L(M i ) ⊂ m i so let c ∈ m i and, by part (1), let a 0 ∈ S be an element such that L(a 0 ) = 1.…”

Section: 4b the Trace And The Normmentioning

confidence: 88%

Section: 1b Subgroupsmentioning

confidence: 99%

Section: Chapter 1 Introductionmentioning

confidence: 99%

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Algebraic Shift Register Sequences

Goresky

Klapper

2012

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“…A recursive algorithm for generating de Bruijn sequences based on Lempels Dhomomorphism was presented by Annexstein [1]. A more efficient, non-recursive algorithm based on Lempels D-homomorphism was given by Chang et al in [4].…”

Section: Previous Workmentioning

confidence: 99%

A Scalable Method for Constructing Galois NLFSRs With Period $2^n-1$ Using Cross-Join Pairs

Dubrova

2013

IEEE Trans. Inform. Theory

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Abstract. This paper presents a method for constructing n-stage Galois NLFSRs with period 2 n − 1 from n-stage maximum length LFSRs. We introduce nonlinearity into state cycles by adding a nonlinear Boolean function to the feedback polynomial of the LFSR. Each assignment of variables for which this function evaluates to 1 acts as a crossing point for the LFSR state cycle. By adding a copy of the same function to a later stage of the register, we cancel the effect of nonlinearity and join the state cycles back. The presented method requires no extra time steps and it has a smaller area overhead compared to the previous approaches based on cross-join pairs. It is feasible for large n. However, it has a number of limitations. One is that the resulting NLFSRs can have at most ⌊n/2⌋-1 stages with a nonlinear update. Another is that feedback functions depend only on state variables which are updated linearly. The latter implies that sequences generated by the presented method can also be generated using a nonlinear filter generator.

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“…The color stripe pattern used in that system is based on pseudorandom De Brujin sequences [7]. The decoding algorithm works per scanline and is based on dynamic programming.…”

Section: Single-shot Structured Lightmentioning

confidence: 99%

Belief Propagation for Improved Color Assessment in Structured Light

Schmalz

Angelopoulou

2010

Lecture Notes in Computer Science

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Abstract. Single-Shot Structured Light is a well-known method for acquiring 3D surface data of moving scenes with simple and compact hardware setups. Some of the biggest challenges in these systems is their sensitivity to textured scenes, subsurface scattering and low-contrast illumination. Recently, a graphbased method has been proposed that largely eliminates these shortcomings. A key step in the graph-based pattern decoding algorithm is the estimation of color of local image regions which correspond to the vertex colors of the graph. In this work we propose a new method for estimating the color of a vertex based on belief propagation (BP). The BP framework allows the explicit inclusion of cues from neigboring vertices in the color estimation. This is especially beneficial for low-contrast input images. The augmented method is evaluated using typical lowquality real-world test sequences of the interior of a pig stomach. We demonstrate a significant improvement in robustness. The number of 3D data points generated increases by 30 to 50 percent over the plain decoding.

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Generating De Bruijn sequences: an efficient implementation

Cited by 55 publications

References 2 publications

Algebraic Shift Register Sequences

Algebraic Shift Register Sequences

A Scalable Method for Constructing Galois NLFSRs With Period $2^n-1$ Using Cross-Join Pairs

Belief Propagation for Improved Color Assessment in Structured Light

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