Gray Code Generation for MPSK Signals

Ludman, Jacques E.

doi:10.1109/tcom.1981.1094886

Cited by 40 publications

(24 citation statements)

References 3 publications

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“…Combining gcd(n, 30) = 1 and n ≡ 4 (mod 9), we get that n ≡ 13,31,49,67 (mod 90) is sufficient to prove the claim. We note that the conditions described in Lemma 18 are not the only cases in which gcd(n, N ′ (n)/3) = 1, but are just the ones easy to derive.…”

Section: Lemma 18mentioning

confidence: 78%

Constant-Weight Gray Codes for Local Rank Modulation

Gad

Langberg

Schwartz

et al. 2011

IEEE Trans. Inform. Theory

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Abstract-We consider the local rank-modulation scheme in which a sliding window going over a sequence of real-valued variables induces a sequence of permutations. Local rankmodulation is a generalization of the rank-modulation scheme, which has been recently suggested as a way of storing information in flash memory.We study constant-weight Gray codes for the local rankmodulation scheme in order to simulate conventional multi-level flash cells while retaining the benefits of rank modulation. We provide necessary conditions for the existence of cyclic and cyclic optimal Gray codes. We then specifically study codes of weight 2 and upper bound their efficiency, thus proving that there are no such asymptotically-optimal cyclic codes. In contrast, we study codes of weight 3 and efficiently construct codes which are asymptotically-optimal. We conclude with a construction of codes with asymptotically-optimal rate and weight asymptotically half the length, thus having an asymptotically-optimal charge difference between adjacent cells.

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Section: Lemma 18mentioning

confidence: 78%

Constant-Weight Gray Codes for Local Rank Modulation

Gad

Langberg

Schwartz

et al. 2011

IEEE Trans. Inform. Theory

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“…The base case is the list s(0) = 0, s(1) = 1 for m = 1. BRGC was first designed to speed up telegraphy by Frank Gray [17], but now has numerous applications including databases, experimental design, and puzzle solving [15,16,22,23,26]. The term Gray code more generally refers to an exhaustive listing of combinatorial objects.…”

Section: Loopless Generation Of 2-way Binary-reflected Gray Codesmentioning

confidence: 99%

Amortized efficiency of generating planar paths in convex position

Chang

Pai

et al. 2011

Theoretical Computer Science

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a b s t r a c tLet S be a set of n ⩾ 3 points arranged in convex position in the plane and suppose that all points of S are labeled from 1 to n in clockwise direction. A planar path P on S is a path whose edges connect all points of S with straight line segments such that no two edges of P cross. Flipping an edge on P means that a new path P ′ is obtained from P by a single edge replacement. In this paper, we provide efficient algorithms to generate all planar paths. With the help of a loopless algorithm to produce a set of 2-way binary-reflected Gray codes, the proposed algorithms generate the next planar path by means of a flip and such that the number of position changes for points in the path has a constant amortized upper bound.

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“…Some of them are mentioned here as follows. However, more can be learned through the references pro vided as in the references (Sundberg, 1975;Ludman, 1981;Er, 1984, andProskurowski andRuskey, 1985; _____________________________________ *Corresponding author's e-mail: afaq@squ.edu.om Lee, 1986;Conway, et al 1989;Skiena, 1990;Press, et al 1992;Etzion and Peterson, 1992;Hiltgen, et al 1996;Savage, 1997;Ruskey, 1997;Guan andDah-Jyu, 1998, Moshe andTuvi, 1999;Black Paul 2004;Alan and Alessandro Mei, 2004;Jywe-Fei and Lai, 2005;Bitner, et al 2005).…”

Section: Introductionmentioning

confidence: 99%

“…Since the Gray code has enormous applications as mentioned above has many facet researches as is evident in surveying the literature (Gray, 1953;Sundberg, 1975;Ludman, 1981;Lee, 1986;Conway, et al 1989;Skiena, 1990;Press, et al 1992;Etzion Peterson, 1992;Hiltgen, et al 1996;Savage, 1997;Ruskey, 1997;Guan Dah-Jyu, 1998, Moshe andTuvi, 1999;Black Paul 2004;Alan and Alessandro Mei, 2004;Jywe-Fei and Lai, 2005;Bitner, et al 1976;Er, 1984;Proskurowski and Ruskey, 1985;Ruskey, 1993;Dominique, 2000;Lassing, et al 2003, Goddyn and Gvozdjak 2003and Vajnovszki and Walsh 2006. It is clear through the literature survey that there had been much discovered and written about the Gray code; it is associated with many elegant circuits and algorithms.…”

Section: Introductionmentioning

confidence: 99%

A Less Complex Algorithmic Procedure for Computing Gray Codes

Ahmad

Suwailam

2009

Jou. Eng. Res.

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Abstract:The purpose of this paper is to present a new and faster algorithmic procedure for generating the nbit Gray codes. Thereby, through this paper we have presented the derivation, design and implementation of a newly developed algorithm for the generation of an n-bit binary reflected Gray code sequences. The developed algorithm is stemmed from the fact of generating and properly placing the min-terms from the universal set of all the possible min-terms [m 0 m 1 m 2 …. m N ] of Boolean function of n variables, where, 0 < N < 2 n -1. The resulting algorithm is in concise form and trivial to implement. Furthermore, the developed algorithm is equipped with added attributes of optimizing of time and space while executed.

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Gray Code Generation for MPSK Signals

Cited by 40 publications

References 3 publications

Constant-Weight Gray Codes for Local Rank Modulation

Constant-Weight Gray Codes for Local Rank Modulation

Amortized efficiency of generating planar paths in convex position

A Less Complex Algorithmic Procedure for Computing Gray Codes

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