Canonical Huffman Coding Research Articles

Ring Co-XOR encryption based reversible data hiding for 3D mesh model

Reversible data hiding in encrypted domain (RDH-ED) is widely used for ensuring the security of content, protecting privacy, and facilitating the management of digital media stored in the cloud. However, research on the application of RDH-ED technology in 3D mesh model carriers is still in its infancy. This paper proposes a reversible data hiding scheme based on Ring Co-XOR encryption (RCXOR) to address the challenges with the existing RDH-ED algorithms for 3D mesh models. Specifically, the proposed scheme eliminates the need to transmit auxiliary information to a third party and increases the embedding capacity. First, the original 3D mesh model is divided into m non-overlapping rings, where different rings do not share vertices. Next, m sets of random bitstreams are generated based on the encryption key. Within each ring, the vertices are encrypted using bitwise XOR with the same random bitstream. This preserves redundancy between adjacent vertices within the same ring in the encrypted data. Finally, a multi-MSB prediction method based on the ring vertex is proposed using the RCXOR encryption technique. To this end, the ring center vertex (RCV) serves as the reference vertex for predicting the multi-MSB of the ring edge vertex (REV), creating space for data hiding. The Canonical Huffman Coding method is used to compress the label and obtain the optimal embedding capacity for data hiding. The experimental results demonstrate that the proposed algorithm surpasses the current vacating room after encryption (VRAE)-based methods in terms of embedding ability, achieving an average embedding rate of 25.63bits per voxel (bpv) on the dataset, compared to 6bpv for the state-of-the-art approach.

An Improved Image Compression Algorithm Using 2D DWT and PCA with Canonical Huffman Encoding.

Of late, image compression has become crucial due to the rising need for faster encoding and decoding. To achieve this objective, the present study proposes the use of canonical Huffman coding (CHC) as an entropy coder, which entails a lower decoding time compared to binary Huffman codes. For image compression, discrete wavelet transform (DWT) and CHC with principal component analysis (PCA) were combined. The lossy method was introduced by using PCA, followed by DWT and CHC to enhance compression efficiency. By using DWT and CHC instead of PCA alone, the reconstructed images have a better peak signal-to-noise ratio (PSNR). In this study, we also developed a hybrid compression model combining the advantages of DWT, CHC and PCA. With the increasing use of image data, better image compression techniques are necessary for the efficient use of storage space. The proposed technique achieved up to 60% compression while maintaining high visual quality. This method also outperformed the currently available techniques in terms of both PSNR (in dB) and bit-per-pixel (bpp) scores. This approach was tested on various color images, including Peppers 512 × 512 × 3 and Couple 256 × 256 × 3, showing improvements by 17 dB and 22 dB, respectively, while reducing the bpp by 0.56 and 0.10, respectively. For grayscale images as well, i.e., Lena 512 × 512 and Boat 256 × 256, the proposed method showed improvements by 5 dB and 8 dB, respectively, with a decrease of 0.02 bpp in both cases.

Image lossless compression algorithm optimization and FPGA implementation

In this thesis, a minimum redundant prefix coding with higher compression ratio and lower time complexity is proposed for lossless compression of HD images. The compression algorithm is based on Canonical Huffman coding, preprocesses the data source to be compressed according to the image data features, and then compresses the data in batches using the locally uneven features in the data, which improves the compression ratio by 1.678 times compared with the traditional canonical Huffman coding. During the implementation of the algorithm, the counting sorting method with lower time complexity and the code-length table construction method without relying on binary trees are used to reduce the complexity of the algorithm and achieve the purpose of real-time data processing by the system. Finally, the proposed compression algorithm is deployed in FPGA to improve the encoding rate by parallel hardware circuit and pipeline design.

Energy-efficient canonical Huffman decoders on many-core processor arrays and FPGAs

Data compression is essential to reduce high storage and communication costs for a wide range of systems and applications. Canonical Huffman coding plays a pivotal role for several compression standards. This paper presents bit-parallel static and dynamic canonical Huffman decoder implementations using an optimized lookup table approach on a fine-grain many-core processor array and an Intel FPGA. The decoder implementation results are compared with an Intel i7-4850HQ and a massively parallel Nvidia GT 750M GPU executing the corpus benchmarks: Calgary, Canterbury, Artificial, and Large. The many-core implementations achieve a scaled throughput per chip area that is 891× and 7× greater on average than the i7 and GT 750M respectively. Moreover, the many-core implementations result in a scaled energy efficiency (compressed bits decoded per energy) that is 149.5×, 3.9×, and 2.5× greater on average than the i7, GT 750M, and Intel FPGA respectively. In addition, the optimized lookup-table-based static canonical Huffman decoder on the Intel FPGA yields performance and energy efficiency improvements of 2.1× and 3.68× respectively on average compared to a dynamic canonical Huffman decoder at a 17% cost in compression ratio.

Space-efficient Huffman codes revisited

A canonical Huffman code is an optimal prefix-free compression code whose codewords enumerated in the lexicographical order form a list of binary words in non-decreasing lengths. Gagie et al. (2015) gave a representation of this coding capable of encoding and decoding a symbol in constant worst-case time. It uses σlg⁡ℓmax+o(σ)+O(ℓmax2) bits of space, where σ and ℓmax are the alphabet size and maximum codeword length, respectively. We refine their representation to reduce the space complexity to σlg⁡ℓmax(1+o(1)) bits while preserving the constant encode and decode times. Our algorithmic idea can be applied to any canonical code.

Canonical Huffman Coding Based Image Compression using Wavelet

The explosive growth of digital imaging, especially in the fields of medicine, education, and e-commerce, has made data maintenance and transmission over networks a daunting task. Therefore, the development and use of image compression techniques have become vital for overcoming the problems of storage and transmission of digital image data. Two methods that are extensively used for data compression are Discrete Cosine Transformation and Discrete Wavelet Transform (DWT). In our present study, we have shown the benefits of a DWT-based approach by utilizing the canonical Huffman coding as an entropy encoder. DWT decomposes the image into different sub-bands. These sub bands are known as approximate image and detail images. The approximate image is normalized in the range (0, 1) for obtaining the Canonical Huffman coding bit stream. In a similar way, details coefficients are also normalized in the range (0, 1) for obtaining the canonical Huffman coding bit stream of detail images. Hard thresholding is often used to discard insignificant coefficients of detail images. Our proposed method takes less computing time and has a smaller codebook size than that of conventional Huffman coding. Moreover, the results show an improvement over Wavelet Scalar Quantization often used for image compression of fingerprints. We have applied our method to various popular images and obtained promising PSNR, CR, and BPP that highlight the advantages of our approach and the efficiency of our algorithms.

Fractal Image Compression Using Canonical Huffman Coding

Image Compression techniques have become a very important subject with the rapid growth of multimedia application. The main motivations behind the image compression are for the efficient and lossless transmission as well as for storage of digital data. Image Compression techniques are of two types; Lossless and Lossy compression techniques. Lossy compression techniques are applied for the natural images as minor loss of the data are acceptable. Entropy encoding is the lossless compression scheme that is independent with particular features of the media as it has its own unique codes and symbols. Huffman coding is an entropy coding approach for efficient transmission of data. This paper highlights the fractal image compression method based on the fractal features and searching and finding the best replacement blocks for the original image. Canonical Huffman coding which provides good fractal compression than arithmetic coding is used in this paper. The result obtained depicts that Canonical Huffman coding based fractal compression technique increases the speed of the compression and has better PNSR as well as better compression ratio than standard Huffman coding.

An Efficient Lossless Compression Algorithm for Trajectories of Atom Positions and Volumetric Data.

We present our newly developed and highly efficient lossless compression algorithm for trajectories of atom positions and volumetric data. The algorithm is designed as a two-step approach. In the first step, efficient polynomial extrapolation schemes reduce the information entropy of the data by exploiting both spatial and temporal continuity. The second step processes the data by a series of transformations (Burrows-Wheeler, move-to-front, run length encoding) and finally compresses the stream with multitable canonical Huffman coding. Our approach reaches a compression ratio of around 15:1 for typical position trajectories in the XYZ format. For volumetric data trajectories in Gaussian Cube format (such as electron density), even a compression ratio of around 35:1 is yielded, which is by far the smallest size of all formats compared here. At the same time, compression and decompression are still reasonably fast for everyday use. The precision of the data can be selected by the user. For storage of the compressed data, we introduce the BQB file format, which is very robust, flexible, and efficient. In contrast to most archiving formats, it allows fast random access to individual trajectory frames. Our method is implemented in C++ and provided as free software under the GNU LGPL license. It has been included in the TRAVIS program package but is also available as stand-alone tool and as a library ("libbqb") for use in other projects.

Performance analysis for canonical Huffman coding with fixed window size

The compression efficiency of canonical Huffman coding is drastically affected by the size of the compression window, the choice of which is typically done heuristically analytic bounds for the worst-case compression efficiency of canonical Huffman coding are introduced, as a function of the size of the compression window. The derived bounds offer fine-grained control over the compression latency-efficiency trade-off.

A new vector data compression approach for WebGIS

High compression ratio, high decoding performance, and progressive data transmission are the most important requirements of vector data compression algorithms for WebGIS. To meet these requirements, we present a new compression approach. This paper begins with the generation of multiscale data by converting float coordinates to integer coordinates. It is proved that the distance between the converted point and the original point on screen is within 2 pixels, and therefore, our approach is suitable for the visualization of vector data on the client side. Integer coordinates are passed to an Integer Wavelet Transformer, and the high-frequency coefficients produced by the transformer are encoded by Canonical Huffman codes. The experimental results on river data and road data demonstrate the effectiveness of the proposed approach: compression ratio can reach 10% for river data and 20% for road data, respectively. We conclude that more attention needs be paid to correlation between curves that contain a few points.

Canonical Huffman code based full-text index

Full-text indices are data structures that can be used to find any substring of a given string. Many full-text indices require space larger than the original string. In this paper, we introduce the canonical Huffman code to the wavelet tree of a string T [1… n]. Compared with Huffman code based wavelet tree, the memory space used to represent the shape of wavelet tree is not needed. In case of large alphabet, this part of memory is not negligible. The operations of wavelet tree are also simpler and more efficient due to the canonical Huffman code. Based on the resulting structure, the multi-key rank and select functions can be performed using at most nH 0 + ∣ Σ∣(lg lg n + lg n − lg ∣ Σ∣)+ O( nH 0) bits and in O( H 0) time for average cases, where H 0 is the zeroth order empirical entropy of T . In the end, we present an efficient construction algorithm for this index, which is on-line and linear.

Skeleton Trees for the Efficient Decoding of Huffman Encoded Texts

A new data structure is investigated, which allows fast decoding of texts encoded by canonical Huffman codes. The storage requirements are much lower than for conventional Huffman trees, O(log^2 n) for trees of depth O(log n), and decoding is faster, because a part of the bit-comparisons necessary for the decoding may be saved. Empirical results on large real-life distributions show a reduction of up to 50% and more in the number of bit operations. The basic idea is then generalized, yielding further savings.

Adding compression to a full‐text retrieval system

AbstractWe describe the implementation of a data compression scheme as an integral and transparent layer within a full‐text retrieval system. Using a semi‐static word‐based compression model, the space needed to store the text is under 30 per cent of the original requirement. The model is used in conjunction with canonical Huffman coding and together these two paradigms provide fast decompression. Experiments with 500 Mb of newspaper articles show that in full‐text retrieval environments compression not only saves space, it can also yield faster query processing ‐ a win‐win situation.