Golomb Coding Research Articles

Hardware optimization for effective switching power reduction during data compression in GOLOMB rice coding.

Loss-less data compression becomes the need of the hour for effective data compression and computation in VLSI test vector generation and testing in addition to hardware AI/ML computations. Golomb code is one of the effective technique for lossless data compression and it becomes valid only when the divisor can be expressed as power of two. This work aims to increase compression ratio by further encoding the unary part of the Golomb Rice (GR) code so as to decrease the amount of bits used, it mainly focuses on optimizing the hardware for encoding side. The algorithm was developed and coded in Verilog and simulated using Modelsim. This code was then synthesised in Cadence Encounter RTL Synthesiser. The modifications carried out show around 6% to 19% reduction in bits used for a linearly distributed data set. Worst-case delays have been reduced by 3% to 8%. Area reduction varies from 22% to 36% for different methods. Simulation for Power consumption shows nearly 7% reduction in switching power. This ideally suggest the usage of Golomb Rice coding technique for test vector compression and data computation for multiple data types, which should ideally have a geometrical distribution.

Lossless Image Coding Using Non-MMSE Algorithms to Calculate Linear Prediction Coefficients.

This paper presents a lossless image compression method with a fast decoding time and flexible adjustment of coder parameters affecting its implementation complexity. A comparison of several approaches for computing non-MMSE prediction coefficients with different levels of complexity was made. The data modeling stage of the proposed codec was based on linear (calculated by the non-MMSE method) and non-linear (complemented by a context-dependent constant component removal block) predictions. Prediction error coding uses a two-stage compression: an adaptive Golomb code and a binary arithmetic code. The proposed solution results in 30% shorter decoding times and a lower bit average than competing solutions (by 7.9% relative to the popular JPEG-LS codec).

Lossless chain code compression with an improved Binary Adaptive Sequential Coding of zero-runs

A new method for encoding a sequence of integers, named Binary Adaptive Sequential Coding with Return to Bias, is proposed in this paper. It extends the compressing pipeline for chain codes’ compression consisting of Burrows Wheeler Transform, Move-To-Front Transform, and Adaptive Arithmetic Coding. We also explain when to include the Zero-Run Transform into the above-mentioned pipeline. The Zero-Run Transform generates a sequence of integers corresponding to the number of zero-runs. This sequence is encoded by Golomb coding, Binary Adaptive Sequential Coding, and the new Binary Adaptive Sequential Coding with Return to Bias. Finally, a comparison is performed with the two state-of-the-art methods. The proposed method achieved similar compression efficiency for the Freeman chain code in eight directions. However, for the chain codes with shorter alphabets (Freeman chain code in four directions, Vertex Chain Code, and Three-OrThogonal chain code), the introduced method outperforms the referenced ones.

Variants of Golomb Coding and the n-ary Versions

Golomb coding is a type of entropy encoding scheme for geometric distributions. It consists of two parts, and both parts are coded with variable-length coding, which requires a higher computational effort than fixed-length coding schemes. To solve this issue, the first part of this article presents a variant of Golomb coding that uses fixed-length coding to code the first part. The simulations show that the proposed coding scheme has a higher throughput than Golomb coding, due to the reduction of arithmetic complexity. In the second part, we discuss the $n$ -ary versions of Golomb coding and the proposed coding scheme.

Design and Implementation of Hybrid Compression Algorithm for Personal Health Care Big Data Applications

Advanced telemedicine requires the gathering of big data through wireless body area network or internet of things based applications. These networks perform several tasks that consume maximum energy while transmitting the big data, which in turn discharges the battery and would require a battery replacement frequently. Also, the big data to be transferred and stored would require a significant amount of storage space. The above problem is rectified by compressing the big data acquired from the sensors before transmission that would reduce the consumption of power as well as use the storage space efficiently. In this paper, a hybrid compression algorithm (HCA) based on Rice Golomb Coding is proposed. The efficiency of the proposed compression algorithm is tested on ECG data from the physionet ATM database and real-time data acquired from the ECG sensor. The proposed HCA comprises of both lossy and lossless compression. The real-time implementation of the proposed compression algorithm is carried out using NI myRIO hardware and LabVIEW graphical tool. The compressed data then stored in the Google cloud, and the analysis of storage space using the HCA shows a reduction of 70% storage space for 10 minutes of ECG data.

Lightweight Lossless Compression for $N$ -Dimensional Data in Multi-Sensor Systems

During the last years, multi-sensor acquisition systems have experienced a great diffusion. One of the main limiting factors is related to the huge amount of data generated within these systems and that must be carefully addressed to guarantee a certain efficiency. A solution consists in compressing data before transmission or storage. Furthermore, a lossless compression is required in monitoring applications, such as biomedical applications, where even very small signal variations can convey important information about the physical process under analysis. In this paper, we propose the lossless compression algorithm for multi-sensor systems characterized by low computational capabilities. The proposed method is based on a modified Golomb code that takes an advantage of the definition of union sets to reduce the redundancy associated to the prefix of codewords. The experimental results show that a compression gain up to 50%–60% can be achieved in different contexts.

Implementation of Direct Indexing and 2-V Golomb Coding of Lattice Vectors for Image Compression

Indexing of code vectors is a most difficult task in lattice vector quantization. In this work we focus on the problem of efficient indexing and coding of indexes. Index assignment to the quantized lattice vectors is computed by direct indexing method, through which a vector can be represented by a scalar quantity which represents the index of that vector. This eliminates the need of calculating the prefix i.e. index of the radius ( R) or norm and suffix i.e. the index of the position of vector on the shell of radius R, also eliminates index assignment to the suffix based on lattice point enumeration or leader’s indexing . Two value golomb coding is used to enumerate indices of quantized lattice vectors. We use analytical means to emphasize the dominance of two value golomb code over one value golomb code. This method is applied to achieve image compression. Indexes of particular subband of test images like barbara, peppers and boat are coded using 2-value golomb coding (2-V GC) and compression ratio is calculated. We demonstrate the effectiveness of the 2-V GC while the input is scanned columnwise as compare to rowwise. Experimentally we also show that good compression ratio is achieved when only higher order bits of the indexes are encoded instead of complete bits.

Chain code compression with modified interpolative coding

A lossless chain code compression algorithm consisting of Burrows-Wheeler Transform, Move-To-Front Transform, and a modified interpolative coding is presented in this paper. The interpolative coding divides a strictly increasing array of integers and encodes the middle element recursively, where the required number of bits is obtained from the difference of the array’s border values. In this paper, it is shown that, for some intervals, Golomb coding is more efficient than the interpolative coding. This fact was used to construct a hybrid approach that yields slightly better compression results than the state-of-the-art while compressing Three OrThogonal chain code, Freeman chain code in four and eight directions, and Vertex Chain Code.

CRUSH: A New Lossless Compression Algorithm

Multimedia is highly competitive world, one of the properties that is reflected is speed of download and upload of multimedia elements: text, sound, pictures, animation. This paper presents CRUSH algorithm which is a lossless compression algorithm. CRUSH algorithm can be used to compress files. CRUSH method is fast and simple with time complexity O(n) where n is the number of elements being compressed.Furthermore, compressed file is independent from algorithm and unnecessary data structures. As the paper will show comparison with other compression algorithms like Shannon–Fano code, Huffman coding, Run Length Encoding, Arithmetic Coding, Lempel-Ziv-Welch (LZW), Run Length Encoding (RLE), Burrows-Wheeler Transform.Move-to-Front (MTF) Transform, Haar, wavelet tree, Delta Encoding, Rice &Golomb Coding, Tunstall coding, DEFLATE algorithm, Run-Length Golomb-Rice (RLGR).

CRUSH: A New Lossless Compression Algorithm

Multimedia is highly competitive world, one of the properties that is reflected is speed of download and upload of multimedia elements: text, sound, pictures, animation. This paper presents CRUSH algorithm which is a lossless compression algorithm. CRUSH algorithm can be used to compress files. CRUSH method is fast and simple with time complexity O(n) where n is the number of elements being compressed.Furthermore, compressed file is independent from algorithm and unnecessary data structures. As the paper will show comparison with other compression algorithms like Shannon–Fano code, Huffman coding, Run Length Encoding, Arithmetic Coding, Lempel-Ziv-Welch (LZW), Run Length Encoding (RLE), Burrows-Wheeler Transform.Move-to-Front (MTF) Transform, Haar, wavelet tree, Delta Encoding, Rice &Golomb Coding, Tunstall coding, DEFLATE algorithm, Run-Length Golomb-Rice (RLGR).

Low complexity image compression algorithm based on hybrid DPCM for wireless capsule endoscopy

Abstract A lossless image compression algorithm with low computational complexity and to provide high image quality in limited bandwidth transmission is proposed in the paper. New algorithm is based on a new YEN colour transform for WCE images, improved and modified DPCM technique known as hybrid DPCM and new signed Golomb code with less bits skip code. The proposed compression algorithm provides better and efficient computational simplicity and improves compression ratio by 2.3% as compared to traditionally used DPCM based compression algorithms.

Real-Time Lossless Compression Algorithm for Ultrasound Data Using BL Universal Code.

Software-based ultrasound imaging systems provide high flexibility that allows easy and fast adoption of newly developed algorithms. However, the extremely high data rate required for data transfer from sensors (e.g., transducers) to the ultrasound imaging systems is a major bottleneck in the software-based architecture, especially in the context of real-time imaging. To overcome this limitation, in this paper, we present a Binary cLuster (BL) code, which yields an improved compression ratio compared to the exponential Golomb code. Owing to the real-time encoding/decoding features without overheads, the universal code is a good solution to reduce the data transfer rate for software-based ultrasound imaging. The performance of the proposed method was evaluated using in vitro and in vivo data sets. It was demonstrated that the BL-beta code has a good stable lossless compression performance of 20%~30% while requiring no auxiliary memory or storage.

High performance decoding aware FPGA bit-stream compression using RG codes

FPGA design for complex applications need high capacity of configuration memory. To fullfil the large memory requirement, higher end FPGAs are required and it leads to higher cost. In order to reduce the cost constraint, bit-stream compression is prominently involved to reduce the bit-stream size and the memory requirement of FPGA configuration. In this paper new code compression techniques are proposed with minimum cost. The proposed code compression techniques RG-1 and RG-2 codes are designed based on the combination of run length and Golomb coding. The proposed RG codes overcome the limitation of both run length and Golomb coding techniques. The main contribution of this work is to analyze the proposed work in terms of number of 1’s, number of transitions and size of compressed bits. The comparison result shows that the RG code is more robust when compared to other traditional code compression techniques. The results shows that CR improvement of 9 and 5% compare with RLE for the RG-1 and RG-2 respectively and CR improvement of 7 and 2% compare with golomb for the RG-1 and RG-2 respectively.

Design and performance analysis of modified two dimensional Golomb code for optical code division multiple access networks

In this work, a two dimensional (2D) wavelength/time code is developed. The 64 bit 2D code is constructed by a technique based on folding of Golomb rulers referred in this work as modified Golomb code (2D MGC) and the proposed 2D code is generated using Java 8.1 software. The performance of the proposed 2D MGC is evaluated in terms of bit error rate (BER), received signal power, and time domain analysis of multiple users. In this experiment, it is found that the BER increases with multiple numbers of simultaneous users due to multiple access interference. The proposed 2D code yields better network performance in terms of BER compared to that of different existing 2D OCDMA codes. In this work, mathematical analysis is also carried out to prove that the proposed 64 bit code is optimal satisfying auto and cross correlation properties. Furthermore, the complexity analysis of the proposed 64 bit optical code division multiple access (OCDMA) code is analysed. The OCDMA model is validated using the optisystem software.

10Gbps 2D MGC OCDMA Code over FSO Communication System

Currently, wide bandwidth signal dissemination along with low latency is a leading requisite in various applications. Free space optical wireless communication has introduced as a realistic technology for bridging the gap in present high data transmission fiber connectivity and as a provisional backbone for rapidly deployable wireless communication infrastructure. The manuscript highlights on the implementation of 10Gbps SAC-OCDMA FSO communications using modified two dimensional Golomb code (2D MGC) that possesses better auto correlation, minimum cross correlation and high cardinality. A comparison based on pseudo orthogonal (PSO) matrix code and modified two dimensional Golomb code (2D MGC) is developed in the proposed SAC OCDMA-FSO communication module taking different parameters into account. The simulative outcome signifies that the communication radius is bounded by the multiple access interference (MAI). In this work, a comparison is made in terms of bit error rate (BER), and quality factor (Q) based on modified two dimensional Golomb code (2D MGC) and PSO matrix code. It is observed that the 2D MGC yields better results compared to the PSO matrix code. The simulation results are validated using optisystem version 14.

Test Data Compression and Power Reduction Using Similarity Based Reordering Technique for Wireless Systems

System-on-Chip is the major challenge for both design and testing engineers due to its increase in power consumption. The system consumes more power in test mode than the normal mode due to the switching activity that takes place between test data. Similarly, in test mode the volume of test data used is very high when compared to normal mode. This paper presents a novel test data compression approach which simultaneously reduces test volume, test power consumption with less decoder complexity. A test data compression when combined with efficient preprocessing such as filling and reordering of test patterns leads to efficient compression and power reduction. These are some preprocessing steps prior to the compression coding, affects the power. In this paper, the preprocessing steps proposed are column wise bit filling; Similarity based test vector reordering, difference vector techniques. This approach with Modified Golomb coding is proposed to improve the compression as well as to reduce the scan in peak power and average power. This approach efficiently decreases the switching activity and also very simple method to combine with run length based coding. The Power reduction is very efficient by this proposed method compared to other preprocessing methods. A careful analysis of bit filling is proposed that leads to significant reduction in peak and average power. Similarity based test vector reordering technique is also proposed to reorder the test data for reducing the switching activity that takes place in test data and reduces the power consumption. The difference vector is applied which leads to increase in the run length of 0s.The modified Golomb algorithm proposed next can efficiently compress the test set that composed of both 0s and 1s.The decompression architecture is also presented in the paper. Experimental results on ISCAS'89 benchmark circuits show that the proposed approach efficiently reduces the volume of test data and the peak, average power consumption.

A New Variable-Length Integer Code for Integer Representation and Its Application to Text Compression

Data Compression plays an important role in reducing data storage space in computer memory and in achieving minimum data transmission time in communication networks. There are two types of data compression: lossless and lossy. In lossless data compression, decompression reproduces data that is exactly match the original data and in lossy data compression, the decompression reproduces data which is an approximation of the original data. Variable length integer codes such as Elias Gamma Code, Elias Delta Code, Golomb Code, have been used for data compression (i.e. integer compression, text compression, etc). In this paper, a new variable length integer code is proposed based on radix conversion and it is used with Burrows Wheeler Transform for text data compression. The performance of the proposed code is compared with Elias Gamma Code, Elias Delta Code and Golomb Code. For evaluation, Calgary corpus is used in the experiments, which contains both text file and binary files. Experimental results show that the Fibonacci code gives better compression rate on an average than all other coders and Elias Gamma code gives better compression rate for text files. The other coders perform well for binary files compared to Elias gamma code.

Extended Rice Code and Its application to R-Tree Compression

ABSTRACTCompression techniques are essential for those applications which require more disk accesses. Since the uncompressed data need more disk accesses than the compressed data, compression is used for reducing the costs of disk access to enable the retrieval of data to be faster. Various variable length codes, such as Elias codes, Rice code, and fast extended Golomb code have been used in many applications to compress the data. Particularly, these codes have been used in information retrieval-based applications to compress integers. In these applications, integers are the basis of indexes that are used to resolve queries. This paper has proposed a new method to represent non-negative integers based on the idea used in Rice code and fast extended Golomb code. The variable length codes produced by the proposed method can be suitable for representing small, middle, and large range of integers, where Rice code suits well for representing small or middle or large range of integers. This method also gives better representation for most of the integers from small-to-large range than fast extended Golomb code. In this paper, the proposed method has been applied to compress the coordinates (integers) used in the R-tree structure, which is used for indexing the spatial data. In the experiments, TIGER data collections and synthetic data collections have been used to evaluate the compression performance. The experimental results show that our code achieves better bit-rate than other existing codes for those spatial data files, which contain significant distribution of small, middle, and large integers.

Reversible Data Hiding and Reversible Authentication Watermarking for Binary Images DOI: 10.14209/jcis.2008.4

Data hiding is a technique used to embed a sequence of bits in a host image with small visual deterioration and the means to extract it afterwards. Reversible data hiding allows, in addition, recovering the original cover-image exactly. Several reversible data hiding techniques have been developed but very few of them are appropriate for binary images. This paper proposes a reversible data hiding technique for binary images. This technique uses the Golomb code to compress prediction errors of low-visibility pixels, using its neighborhood as side information, to obtain the space to store the hidden data. The proposed technique is then used to reversibly authenticate binary images, including texts, drawings and halftones. All binary images we tested could be authenticated using the proposed technique, except unrealistically small or random images.

Symbol coding of Laplacian distributed prediction residuals

Predictive coding schemes, proposed in the literature, essentially model the residuals with discrete distributions. However, real-valued residuals can arise in predictive coding, for example, from the usage of an r order linear predictor specified by r real-valued coefficients. In this paper, we propose a symbol-by-symbol coding scheme for the Laplace distribution, which closely models the distribution of real-valued residuals in practice. To efficiently exploit the real-valued predictions at a given precision, the proposed scheme essentially combines the process of residual computation and coding, in contrast to conventional schemes that separate these two processes. In the context of adaptive predictive coding framework, where the source statistics must be learnt from the data, the proposed scheme has the advantage of lower ‘model cost’ as it involves learning only one parameter. In this paper, we also analyze the proposed parametric coding scheme to establish the relationship between the optimal value of the coding parameter and the scale parameter of the Laplace distribution. Our experimental results demonstrated the compression efficiency and computational simplicity of the proposed scheme in adaptive coding of residuals against the widely used arithmetic coding, Rice–Golomb coding, and the Merhav–Seroussi–Weinberger scheme adopted in JPEG-LS.