Determining deep holes is an important open problem in decoding Reed-Solomon codes. It is well known that the received word is trivially a deep hole if the degree of its Lagrange interpolation polynomial equals the di...Determining deep holes is an important open problem in decoding Reed-Solomon codes. It is well known that the received word is trivially a deep hole if the degree of its Lagrange interpolation polynomial equals the dimension of the Reed-Solomon code. For the standard Reed-Solomon codes [p-1, k]p with p a prime, Cheng and Murray conjectured in 2007 that there is no other deep holes except the trivial ones. In this paper, we show that this conjecture is not true. In fact, we find a new class of deep holes for standard Reed-Solomon codes [q-1, k]q with q a power of the prime p. Let q≥4 and 2≤k≤q-2. We show that the received word u is a deep hole if its Lagrange interpolation polynomial is the sum of monomial of degree q-2 and a polynomial of degree at most k-1. So there are at least 2(q-1)qk deep holes if k q-3.展开更多
OFDM(Orthogonal Frequency Division Multiplexing,正交频分复用)是第四代移动通信技术的核心技术。首先简要介绍了OFDM的基本原理,分析了两种OFDM信号生成方法,建立了系统仿真模型,对两种信号实现方法进行了分析比较。并基于所建模型...OFDM(Orthogonal Frequency Division Multiplexing,正交频分复用)是第四代移动通信技术的核心技术。首先简要介绍了OFDM的基本原理,分析了两种OFDM信号生成方法,建立了系统仿真模型,对两种信号实现方法进行了分析比较。并基于所建模型,给出了OFDM信号频谱及解码星座图。仿真结果表明,所建模型很好地完成OFDM的实现与解调。展开更多
A numerical simulation method based on inverse discrete Fourier transform(IDFT)is presented for generating Gaussian rough surface with a desired autocorrelation function(ACF). The probability density function of the h...A numerical simulation method based on inverse discrete Fourier transform(IDFT)is presented for generating Gaussian rough surface with a desired autocorrelation function(ACF). The probability density function of the height distribution of the generated Gaussian surface and the root-mean-square height of the rough surface are also considered. It is found that the height distribution of the generated surface follows the Gaussian distribution, the deviation of the root-mean-square height of the modeled rough surface from the desired value is smaller than that of Patir's method, and the autocorrelation function of the modeled surface is also in good agreement with the desired autocorrelation function. Compared with Patir's method, the modeled surface generated by the IDFT method is in better agreement with the desired autocorrelation function, especially when the correlation length is relatively large.展开更多
In this paper a novel technique, Authentication and Secret Message Transmission using Discrete Fourier Transformation (ASMTDFT) has been proposed to authenticate an image and also some secret message or image can be t...In this paper a novel technique, Authentication and Secret Message Transmission using Discrete Fourier Transformation (ASMTDFT) has been proposed to authenticate an image and also some secret message or image can be transmitted over the network. Instead of direct embedding a message or image within the source image, choosing a window of size 2 x 2 of the source image in sliding window manner and then con-vert it from spatial domain to frequency domain using Discrete Fourier Transform (DFT). The bits of the authenticating message or image are then embedded at LSB within the real part of the transformed image. Inverse DFT is performed for the transformation from frequency domain to spatial domain as final step of encoding. Decoding is done through the reverse procedure. The experimental results have been discussed and compared with the existing steganography algorithm S-Tools. Histogram analysis and Chi-Square test of source image with embedded image shows the better results in comparison with the S-Tools.展开更多
基金supported by National Natural Science Foundation of China (Grant No.10971145)by the Ph.D. Programs Foundation of Ministry of Education of China (Grant No. 20100181110073)
文摘Determining deep holes is an important open problem in decoding Reed-Solomon codes. It is well known that the received word is trivially a deep hole if the degree of its Lagrange interpolation polynomial equals the dimension of the Reed-Solomon code. For the standard Reed-Solomon codes [p-1, k]p with p a prime, Cheng and Murray conjectured in 2007 that there is no other deep holes except the trivial ones. In this paper, we show that this conjecture is not true. In fact, we find a new class of deep holes for standard Reed-Solomon codes [q-1, k]q with q a power of the prime p. Let q≥4 and 2≤k≤q-2. We show that the received word u is a deep hole if its Lagrange interpolation polynomial is the sum of monomial of degree q-2 and a polynomial of degree at most k-1. So there are at least 2(q-1)qk deep holes if k q-3.
文摘OFDM(Orthogonal Frequency Division Multiplexing,正交频分复用)是第四代移动通信技术的核心技术。首先简要介绍了OFDM的基本原理,分析了两种OFDM信号生成方法,建立了系统仿真模型,对两种信号实现方法进行了分析比较。并基于所建模型,给出了OFDM信号频谱及解码星座图。仿真结果表明,所建模型很好地完成OFDM的实现与解调。
基金Supported by the National Basic Research Program of China("973"Program,No.2013CB632305)
文摘A numerical simulation method based on inverse discrete Fourier transform(IDFT)is presented for generating Gaussian rough surface with a desired autocorrelation function(ACF). The probability density function of the height distribution of the generated Gaussian surface and the root-mean-square height of the rough surface are also considered. It is found that the height distribution of the generated surface follows the Gaussian distribution, the deviation of the root-mean-square height of the modeled rough surface from the desired value is smaller than that of Patir's method, and the autocorrelation function of the modeled surface is also in good agreement with the desired autocorrelation function. Compared with Patir's method, the modeled surface generated by the IDFT method is in better agreement with the desired autocorrelation function, especially when the correlation length is relatively large.
文摘In this paper a novel technique, Authentication and Secret Message Transmission using Discrete Fourier Transformation (ASMTDFT) has been proposed to authenticate an image and also some secret message or image can be transmitted over the network. Instead of direct embedding a message or image within the source image, choosing a window of size 2 x 2 of the source image in sliding window manner and then con-vert it from spatial domain to frequency domain using Discrete Fourier Transform (DFT). The bits of the authenticating message or image are then embedded at LSB within the real part of the transformed image. Inverse DFT is performed for the transformation from frequency domain to spatial domain as final step of encoding. Decoding is done through the reverse procedure. The experimental results have been discussed and compared with the existing steganography algorithm S-Tools. Histogram analysis and Chi-Square test of source image with embedded image shows the better results in comparison with the S-Tools.
