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1.
Gray code is a natural way of ordering binary vectors in dyadic space, hence it appears frequently in connetion with Walsh functions. In Paley's definition of Walsh functions their sequencies are arranged in Gray code. Gray code also appears in a new Walsh function generation algorithm which obtains a function by locating all its sign changes. There are certain computational advantages in using Gray code rather than sequency ordering. Examples in fast Walsh transform, dyadic convolution and digital filtering are given. Methods of Gray code to binary conversion are discussed.  相似文献   

2.
This letter describes a simplification in a previously described a.d. convertor using a digital discriminator, which results in a Gray code output. Practical details are given of a 4-bit encoder using this technique, which confirms that the principle is valid.  相似文献   

3.
Phase unwrapping is used to establish the mapping relationship between camera and projector, which is one of the key technologies in fringe projection profilometry(FPP) based three-dimensional(3D) measurement. Although complementary Gray code assisted phase unwrapping technology can get a good result on the periodic boundary, it needs more coded images to obtain a high frequency fringe. Aiming at this problem, a complementary binary code assisted phase unwrapping method is proposed in this paper...  相似文献   

4.
多脉冲位置调制(multi-pulse position modulation,MPPM)与脉冲位置调制相比具有能量信息效率高和带宽低的优点,是水下激光通信中一种有效的通信方式.为了研究时钟抖动对激光水下多脉冲位置调制通信的误码影响,在分析MPPM时钟抖动时的性能的基础上,通过理论计算提出了MPPM最小误比特率的映射列表的方法,分析并仿真了MPPM使用二进制码和格雷码两种编码方式的误比特率.结果表明,在相同的传输带宽和传输速率下,使用格雷码编码的MPPM误码性能优于二进制编码,且MPPM的性能优于脉冲位置调制,误比特率降低约2.4dB.该研究结果对提高水下激光通信性能具有一定的理论参考价值.  相似文献   

5.
卡诺图是组合逻辑电路设计和分析常用和有效的数学工具,既可以化简逻辑函数,也可以分析组合逻辑电路的竞争冒险。对于多输入变量的逻辑函数,要排列其卡诺图则不是易事。格雷码的相邻码之间只有1位不同,这与卡诺图的循环邻接有相同之处,因而可以利用格雷码快速排列多变量卡诺图。首先介绍二进制码转化为格雷码的方法并用C语言编程实现其码制转换,接着叙述用格雷码规律快速排列多变量卡诺图的方法,最后举例说明卡诺图在组合逻辑电路竞争冒险中的应用。  相似文献   

6.
格雷码以及应用   总被引:3,自引:0,他引:3  
杨凌波 《电子质量》2004,(3):J007-J007,J012
文章基于浮子式水位计监测系统,介绍了格雷码的概念、优点,并介绍了格雷码和二进制码之间的转换方法  相似文献   

7.
该文定义了环R=F2+uF2+u2F2+u3F2到F42的一个新的Gray映射,其中u4=0。证明了R上长为n的(1+u+u2+u3)-循环码的Gray象是F2上长为4n的距离不变的线性循环码。进一步确定了R上奇长度的该常循环码的Gray象的生成多项式,并得到了一些最优的二元线性循环码。  相似文献   

8.
Contrary to what has been believed, it is found that weights can be associated with different bit positions of the standard binary reflected Gray code. Therefore, two algorithms are devised for direct Gray-to-decimal and decimal-to-Gray conversions. These algorithms are much simpler than old algorithms which involve conversions to and from binary code and exclusive-OR operations.  相似文献   

9.
DSP指令生成与优化和二进制翻译是现代编译工具值得关注的热点问题。针对DSP指令的特点提出一种通用的DSP指令生成(支持VLIW指令)与二进制翻译技术,并应用于GNU汇编器(GAS)。包含该技术的汇编器PCA(Post Compilation Assembler)先将输入的汇编指令转化成类似LISP的中间语言。PCA通过对此中间语言分析以及窥孔优化,最终生成高质量的目标平台DSP代码。  相似文献   

10.
The discrete-binary conversion stage, which plays the role of converting quantized hash vectors into binary hash strings by encoding, is one of the most important parts of authentication-oriented image hashing. However, very few works have been done on the discrete-binary conversion stage. In this paper, based on Gray code, we propose a key-dependent code called random Gray (RGray) code for image hashing, which, according to our theoretical analysis and experimental results, is likely to increase the security of image hashing to some extent and meanwhile maintains the performance of Gray code in terms of the tradeoff between robustness and fragility. We also apply a measure called distance distortion, which was proposed by Rothlauf (2002) [1] for evolutionary search, to investigate the influence of the discrete-binary conversion stage on the performance of image hashing. Based on distance distortion, we present a theoretical comparison of the encodings applied in the discrete-binary conversion stage of image hashing, including RGray encoding. And our experimental results validate the practical applicability of distance distortion on the performance evaluation of the discrete-binary conversion stage.  相似文献   

11.
On the optimality of the binary reflected Gray code   总被引:2,自引:0,他引:2  
This paper concerns the problem of selecting a binary labeling for the signal constellation in M-PSK, M-PAM, and M-QAM communication systems. Gray labelings are discussed and the original work by Frank Gray is analyzed. As is noted, the number of distinct Gray labelings that result in different bit-error probability grows rapidly with increasing constellation size. By introducing a recursive Gray labeling construction method called expansion, the paper answers the natural question of what labeling, among all possible constellation labelings, will give the lowest possible average probability of bit errors for the considered constellations. Under certain assumptions on the channel, the answer is that the labeling proposed by Gray, the binary reflected Gray code, is the optimal labeling for all three constellations, which has, surprisingly, never been proved before.  相似文献   

12.
As an alternative to trellis coding, a binary convolutional code is considered for use with such nonbinary modulation schemes as quadrature amplitude modulation (QAM). A Gray code is used to map the encoder output to the M-ary QAM constellation. The focus is on the design of 16-ary coded QAM with a rate 3/4 punctured convolutional code of a constraint length 7. A quantized binary metric generation method is proposed and shown to be suboptimum as compared to the direct use of a M-ary unquantized metric. Impressive coding gains and bandwidth efficiency are shown in comparison with uncoded systems  相似文献   

13.
王浩  谢剑斌 《通信学报》2007,28(9):34-39
提出了一种基于混沌动力系统的按格雷码表顺序分块对视频图像进行数据置乱的完全加密方法。首先采用Chebyshev映射和Logistic映射相互迭代的方法产生混沌二值密钥,有效的克服了一维混沌动力系统中的平凡密钥和拟平凡密钥现象,并用此密钥对主要视频图像信息进行一次一密完全加密,然后利用格雷码序列的良好的空间遍历性和易生成性来对主要数据进行置乱,另外加密时保留了原数据的主体格式和大小。实验结果表明,算法安全性高,可有效抵抗已知明文攻击,速度快,加密后可播放,且可移植性良好。  相似文献   

14.
绝对式编码器编码码制通常采用自然二进制码、格雷码、格雷余码等。本文介绍了这三种编码码制的特点及其对应位置如何读数。  相似文献   

15.
This paper is devoted to the study of con- stacyclic codes over a non-chain ring R. The generator polynomials of all constacyclic codes over R are characterized and their dual codes are also determined. We also introduce a Gray map. It is proved that the image of a vconstacyclic code of length n over R under the Gray map is a cyclic code of length 2n over a field with p elements, where p is odd prime. Moreover, we obtain a substantial number of optimal p-ary linear (cyclic) codes, in terms of their parameters, via the Gray map.  相似文献   

16.
基于格雷码-相移的双目三维测量方法研究   总被引:2,自引:0,他引:2  
本文采用格雷码-相移组合的结构光,结合双目立体视觉技术,研究了三维表面测量方法.三维测量精度主要取决于格雷码-相移的解码精度,由于物体表面反射率不一致,不同区域又会相互反射,一般的阈值分割无法得到准确的二值化条纹图.因此在投射格雷码条纹图案基础上,再投射一组格雷码反码条纹图案.针对格雷码-相移解码过程中的周期错位问题,提出一种新的校正方法.将文中三维测量方法应用在人眼石膏模型的表面测量实验中,重建结果验证该方法的准确性和可靠性.  相似文献   

17.

In this paper, an all-optical miniaturized binary to gray code converter is designed and analyzed. The all-optical domain is now an alternative for electronic devices, where performance and speed are the key issues. Code converters are significantly used in digital data transmission in the areas of error detection and correction. Gray code is one of the cyclic codes, where the cyclic shift of each codeword is also a code word. An all-optical XOR gate, realized using a Y-shaped power combiner is used in this design to generate the desired gray code from the given binary code. The insertion loss and extinction ratio parameters are found to be 0.347 dB and 22.26 dB, respectively. The entire simulation is carried out using finite-difference time-domain method. The obtained practical results are verified mathematically using MATLAB.

  相似文献   

18.
Previously, (linear) codes over Z4 and quasi-cyclic (QC) codes (over fields) have been shown to yield useful results in coding theory. Combining these two ideas we study Z 4-QC codes and obtain new binary codes using the usual Gray map. Among the new codes, the lift of the famous Golay code to Z4 produces a new binary code, a (92, 224, 28)-code, which is the best among all binary codes (linear or nonlinear). Moreover, we characterize cyclic codes corresponding to free modules in terms of their generator polynomials  相似文献   

19.
Certain nonlinear binary codes contain more codewords than any comparable linear code presently known. These include the Kerdock (1972) and Preparata (1968) codes that can be very simply constructed as binary images, under the Gray map, of linear codes over Z4 that are defined by means of parity checks involving Galois rings. This paper describes how Fourier transforms on Galois rings and elementary symmetric functions can be used to derive lower bounds on the minimum distance of such codes. These methods and techniques from algebraic geometry are applied to find the exact minimum distance of a family of Z 4. Linear codes with length 2m (m, odd) and size 2(2m+1-5m-2). The Gray image of the code of length 32 is the best (64, 237) code that is presently known. This paper also determines the exact minimum Lee distance of the linear codes over Z4 that are obtained from the extended binary two- and three-error-correcting BCH codes by Hensel lifting. The Gray image of the Hensel lift of the three-error-correcting BCH code of length 32 is the best (64, 232) code that is presently known. This code also determines an extremal 32-dimensional even unimodular lattice  相似文献   

20.
The problem of Gray image of constacyclic code over finite chain ring is studied. A Gray map between codes over a finite chain ring and a finite field is defined. The Gray image of a linear constacyclic code over the finite chain ring is proved to be a distance invariant quasi-cyclic code over the finite field. It is shown that every code over the finite field, which is the Gray image of a cyclic code over the finite chain ring, is equivalent to a quasi-cyclic code.  相似文献   

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