algorithmics and modular computations, Theory of Codes and Cryptography (3).From an analytical 1. RE Blahut. Theory and practice of error control codes. eecs.uottawa.ca/∼yongacog/courses/coding/ (3) R.E. Blahut,Theory and Practice of Error Control Codes, Addison Wesley, 1983. QA 268. Cached. Download as a PDF 457, Theory and Practice of Error Control CodesBlahut 1984 (Show Context). Citation Context..ontinued fractions.

Theory and practice of error control codes

To protect the copyright of digital image, this paper proposed a combined Discrete Wavelet Transform (DWT) and Discrete Cosine Transform (DCT) based watermarking scheme. To embed the watermark, the cover image was decomposed by a 2-level DWT, and the HL2 sub-band coefficient was divided into 4x4 blocks, then the DCT was performed on each of these blocks. The watermark bit was embedded by predefined pattern_0 or pattern_1 on the middle band coefficients of DCT. After watermark insertion, inverse DCT was applied to each of the 4x4 blocks of HL2 sub-band coefficient, and inverse DWT was applied to obtain the watermarked image. For watermark extraction, the watermarked image, which may be attacked by various image attacks, was decomposed with 2-level DWT and DCT similarly as watermark embedding process, then correlation between middle band coefficients of block DCT and the predefined pattern (pattern_0 and pattern_1) was calculated to decide whether a bit 0 or a bit 1 was embedded. Genetic algorithm was used for embedding and extraction parameters optimization. Optimization is to maximize PSNR of the watermarked image and NCC of the extracted watermark. Experiment results show that the proposed scheme in this paper is robust against many image attacks, and improvement can be observed when compared to other existing schemes.

A Combined DWT and DCT Watermarking Scheme Optimized Using Genetic Algorithm

We propose a robust digital watermarking algorithm for copyright protection. A stable feature is obtained by utilizing QR factorization and discrete cosine transform (DCT) techniques, and a meaningful watermark image is embedded into an image by modifying the stable feature with a quantization index modulation (QIM) method. The combination of QR factorization, DCT, and QIM techniques guarantees the robustness of the algorithm. Furthermore, an embedding location selection method is exploited to select blocks with small modifications as the embedding locations. This can minimize the embedding distortion and greatly improve the imperceptibility of our scheme. Several standard images were tested and the experimental results were compared with those of other published schemes. The results demonstrate that our proposed scheme can achieve not only better imperceptibility, but also stronger robustness against common signal processing operations and lossy compressions, such as filtering, noise addition, scaling, sharpening, rotation, cropping, and JPEG/JPEG2000 compression.

A robust watermarking algorithm based on QR factorization and DCT using quantization index modulation technique

Digital image authentication under varying transmission and acquisition conditions is very challenging and efficient watermarking is an effective approach to solve this problem. In this paper, we propose a transform domain approach in YCbCr color space for enhancing the performance of a watermarking system, employing the unique combination of 2-Level Discrete Wavelet Transform (DWT), Discrete Fourier Transform (DFT) and Singular Value Decomposition (SVD). Individual stages of the system are examined and an attempt is made to improve each stage. YCbCr color space is utilized to make use of its decorrelation property in order to improve correlation between original and watermarked image. DWT stage selectively utilizes the horizontal and vertical detail coefficients of the 2-dimensional DWT of an image. The translation variance problem of the DWT is compensated in the following DFT stage, which also exploits the frequency characteristics of the image. Finally SVD is used to embed the watermark data. The method gives better results in terms of increased PSNR values and is able to withstand a variety of image processing attacks.

Novel digital image watermarking using DWT-DFT-SVD in YCbCr color space

Digital watermarking is a technique for resolving copyright law in E-Commerce. In this article a combined watermarking method based on Discrete Wavelet Transform (DWT) and Discrete Cosine Transform (DCT) is proposed. For embedding watermark, a cover image is decomposed by a 2-level DWT, and the HL2 subband coefficients are divided into 4 × 4 blocks, then the DCT is performed on each of these blocks. The watermark bits are embedded by predefined pattern_0 or pattern_1 on the middle band coefficients of DCT. After inserting watermark, inverse DCT is applied to each 4 × 4 blocks of HL2 subband coefficients, and inverse DWT is applied to obtain the watermarked image. For watermark extraction, the watermarked image, which may be attacked by various image attacks, is decomposed with 2-level DWT and DCT similarly as watermark embedding process, then correlation between middle band coefficients of block DCT and the predefined pattern (pattern_0 and pattern_1) is calculated to decide whether a 0 bit or a 1...

An Improved Image Watermarking Method in Frequency Domain

A watermarking technique based on the frequency domain is presented in this paper. The one of the basic demands for the robustness in the watermarking mechanism should be able to dispute the JPEG attack since the JPEG is a usually file format for transmitting the digital content on the network. Thus, the proposed algorithm can used to resist the JPEG attach and avoid the some weaknesses of JPEG quantification. And, the information of the original host image and watermark are not needed in the extracting process. In addition, two important but conflicting parameters are adopted to trade-off the qualities between the watermarked image and the retrieve watermark. The experimental results have demonstrated that the proposed scheme has satisfied the basic requirements of watermarking such as robustness and imperceptible.

A Watermarking Technique based on the Frequency Domain

A watermarking algorithm based on the concepts of the JPEG quantization and absolute value is introduced in this paper. The JPEG is a usually file format for transmitting the digital content on the...

A watermarking algorithm

The modulation method base on Reed-Solomon code for watermarking technology is proposed here. The DC, low-frequency coefficients, the inter-block correlation and Reed-Solomon code will be combined in order to develop a robustness watermarking. In other words, the inter-block correlation and the DC, low frequency coefficients which are belongs to the important parameter in the image are used to output the message vector of Reed-Solomon code. After adjusting, the redundancy vector will be embedded in the host image. In addition, the result of Reed-Solomon decoder, succeed or fail, will be used to represent the watermark in the further. That is to say, as Reed-Solomon code succeeds in decoding step, the ones that mean the embedding / extracting watermark materials are i¥1i¦. On the contrary, it is i¥0i¦. Moreover, the proposed algorithm is belongs to oblivious watermarking. The experimental results have demonstrated that the proposed scheme has satisfied the basic requirements of watermarking.

The Modulation Method Based on Reed-Solomon Code for Watermarking

In 1988, Eastman showed that the Euclideanized Berlekamp-Massey (BM) algorithm can be used to eliminate the calculation of discrepancies and the divisions of the finite field elements to find the errata locator polynomial in a Reed-Solomon (RS) decoder. However, the separate computations of the errata locator and the errata evaluator polynomials are still needed in Eastman’s decoder. In this paper, a modified decoding algorithm based on the idea of Eastman is presented. It is derived to solve the errata locator and the errata evaluator polynomials simultaneously without performing the operations of polynomial division and field element inversion. Moreover, the weights used to represent the discrepancies at each iteration can be directly extracted from the coefficient. Therefore, the proposed algorithm saves many controlling circuits and provides a modular VLSI architecture with parallel. As a consequence, it is simple and easy to implement. And the decoding complexity of the algorithm proposed by Eastman can be further reduced.

VLSI Architecture of Euclideanized BM Algorithm for Reed-Solomon Code

Digital watermarking is an effective and popular technique to disapprove illegal copying and distribution of copyrighted digital content. One of the important issues of watermarking is the robustness subject to resist the lossy compression of the watermarked image. In addition, in JPEG quantification, there is a question which is that the two similar DCT coefficients will be quantified to the same rank. It will cause the mistake of the extracting watermark from the lossy compression of the watermarked image. In this paper, a robust oblivious watermarking technique is proposed. This presented scheme performed in the middle frequency region of the original host image. The modification of the mid-frequency coefficients is corresponding to the quantization table in JPEG standard. And, the permutation operation is adopted in the block of the host image in order to discourage the effect of the JPEG quantification as discuss above. With this technique, the watermark can survive when the watermarked image is compressed using JPEG. Moreover, the proposed scheme doesn't require the information of the watermark and the original host image in the extracting process.

Yu-Wen Chang

Papers

A Watermarking Technique based on the Frequency Domain

A watermarking algorithm

The Modulation Method Based on Reed-Solomon Code for Watermarking

VLSI Architecture of Euclideanized BM Algorithm for Reed-Solomon Code

A robust oblivious watermarking technique