Golomb Coding Research Articles

Study on Nearly Lossless Compression with Progressive Decoding

A progressive transmission and decoding nearly lossless compression algorithm is proposed. The image data are grouped according to different frequencies based on DCT transform, then it uses the JPEG-LS core algorithmtexture prediction and Golomb coding on each group of data, in order to achieve progressive image transmission and decoding. Experimentation on the standard test images with this algorithm and comparing with JPEG-LS shows that the compression ratio of this algorithm is very similar to the compression ratio of JPEG-LS, and this algorithm loses a little image information but it has the ability of the progressive transmission and decoding.

High-resolution long-reach distributed Brillouin sensing based on combined time-domain and correlation-domain analysis

A new scheme for distributed Brillouin sensing of strain and temperature in optical fibers is proposed, analyzed and demonstrated experimentally. The technique combines between time-domain and correlation-domain analysis. Both Brillouin pump and signal waves are repeatedly co-modulated by a relatively short, high-rate phase sequence, which introduces Brillouin interactions in a large number of discrete correlation peaks. In addition, the pump wave is also modulated by a single amplitude pulse, which leads to a temporal separation between the generation of different peaks. The Brillouin amplification of the signal wave at individual peak locations is resolved in the time domain. The technique provides the high spatial resolution and long range of unambiguous measurement offered by correlation-domain Brillouin analysis, together with reduced acquisition time through the simultaneous interrogation of a large number of resolution points. In addition, perfect Golomb codes are used in the phase modulation of the two waves instead of random sequences, in order to reduce noise due to residual, off-peak Brillouin interactions. The principle of the method is supported by extensive numerical simulations. Using the proposed scheme, the Brillouin gain spectrum is mapped experimentally along a 400 m-long fiber under test with a spatial resolution of 2 cm, or 20,000 resolution points, with only 127 scans per choice of frequency offset between pump and signal. Compared with corresponding phase-coded, Brillouin correlation domain analysis schemes with equal range and resolution, the acquisition time is reduced by a factor of over 150. A 5 cm-long hot spot, located towards the output end of the pump wave, is properly identified in the measurements. The method represents a significant advance towards practical high-resolution and long range Brillouin sensing systems.

Experimental demonstration of localized Brillouin gratings with low off-peak reflectivity established by perfect Golomb codes

Dynamic Brillouin gratings (DBGs), inscribed by comodulating two writing pump waves with a perfect Golomb code, are demonstrated and characterized experimentally. Compared with pseudo-random bit sequence (PRBS) modulation of the pump waves, the Golomb code provides lower off-peak reflectivity due to the unique properties of its cyclic autocorrelation function. Golomb-coded DBGs allow the long variable delay of one-time probe waveforms with higher signal-to-noise ratios, and without averaging. As an example, the variable delay of return-to-zero, on-off keyed data at a 1 Gbit/s rate, by as much as 10 ns, is demonstrated successfully. The eye diagram of the reflected waveform remains open, whereas PRBS modulation of the pump waves results in a closed eye. The variable delay of data at 2.5 Gbit/s is reported as well, with a marginally open eye diagram. The experimental results are in good agreement with simulations.

Adaptive Golomb Code for Joint Geometrically Distributed Data and Its Application in Image Coding

This paper proposes joint-probability-based adaptive Golomb coding (JPBAGC) to improve the performances of the Golomb family of codes, including Golomb coding (GC), Golomb–Rice coding (GRC), exp-Golomb coding (EGC), and hybrid Golomb coding (HGC), for image compression. The Golomb family of codes is ideally suited to the processing of data with geometric distribution. Since it does not require a coding table, it has higher coding efficiency than Huffman coding. In this paper, we find that there are many situations in which the probability distribution of data is not only geometric, but also depends on the probability distribution of the other data. Accordingly, we used the joint probability of generalizing the Golomb family of codes and exploiting the dependence between neighboring image data. The proposed JPBAGC improves the efficiency of many image and video compression standards, such as the joint photographic experts group (JPEG) compression scheme and the H.264-intra JPEG-based image coding system. Simulation results demonstrate the superior coding efficiency of the proposed scheme over those of Huffman coding, GC, GRC, EGC, and HGC.

Re-Ordered FEGC and Block Based FEGC for Inverted File Compression

Data compression has been widely used in many Information Retrieval based applications like web search engines, digital libraries, etc. to enable the retrieval of data to be faster. In these applications, universal codes (Elias codes (EC), Fibonacci code (FC), Rice code (RC), Extended Golomb code (EGC), Fast Extended Golomb code (FEGC) etc.) have been preferably used than statistical codes (Huffman codes, Arithmetic codes etc). Universal codes are easy to be constructed and decoded than statistical codes. In this paper, the authors have proposed two methods to construct universal codes based on the ideas used in Rice code and Fast Extended Golomb Code. One of the authors’ methods, Re-ordered FEGC, can be suitable to represent small, middle and large range integers where Rice code works well for small and middle range integers. It is also competing with FC, EGC and FEGC in representing small, middle and large range integers. But it could be faster in decoding than FC, EGC and FEGC. The authors’ another coder, Block based RFEGC, uses local divisor rather than global divisor to improve the performance (both compression and decompression) of RFEGC. To evaluate the performance of the authors’ coders, the authors have applied their methods to compress the integer values of the inverted files constructed from TREC, Wikipedia and FIRE collections. Experimental results show that their coders achieve better performance (both compression and decompression) for those files which contain significant distribution of middle and large range integers.

Low-noise delays from dynamic Brillouin gratings based on perfect Golomb coding of pump waves

A method for long variable all-optical delay is proposed and simulated, based on reflections from localized and stationary dynamic Brillouin gratings (DBGs). Inspired by radar methods, the DBGs are inscribed by two pumps that are comodulated by perfect Golomb codes, which reduce the off-peak reflectivity. Compared with random bit sequence coding, Golomb codes improve the optical signal-to-noise ratio (OSNR) of delayed waveforms by an order of magnitude. Simulations suggest a delay of 5 Gb/s data by 9ns, or 45bit durations, with an OSNR of 13dB.

Comparative Analysis of Lossless Text Compression Techniques

Data compression is an effective means for saving storage space and channel bandwidth. There are two main types of compression lossy and lossless. This paper will deal with lossless compression techniques named Huffman, Arithmetic, LZ-78 and Golomb coding. The paper attempts to do comparative analysis in terms of their compression efficiency and speed. The test files used for this include English text files, Log files, Sorted word list and geometrically distributed data text file. The implementation results of these compression algorithms suggest the efficient algorithm to be used for a certain type of file to be compressed taking into consideration both the compression ratio and speed of operation. In terms of compression ratios, Golomb is best suited for very low frequency Text files, arithmetic for moderate and high frequency. Implementation is done using MATLAB software. General Terms Text Compression.

Test Data Compression Based on GOLOMB Coding and Two-Value GOLOMB Coding

In this paper, we discuss test data compression and decompression method based on variable length Golomb codes and 2-V Golomb Codes for test data. The method is targeted to minimize the amount of test data, which reduces the size of memory required in ATE for test data and also time required to transfer test data to specific device on SOC. We completed MATLAB coding for both methods and applied test vectors of some standard ISCAS benchmark circuits and compared results for same. Experimental results on ISCAS benchmark circuits show that the compressed data produced by 2-V Golomb coding is better than Golomb Coding method.

Inverted File Compression using EGC and FEGC

Inverted files are most commonly used technique for efficient query processing and fast text searching in Information Retrieval System (IRS). But the size of the inverted files is extremely large due to rapid growth in the size of the data in the information retrieval system. So as to reduce the index size and increase the accessing speed, compression techniques are used. In this paper, we propose a new integer compression technique called Fast Extended Golomb code (FEGC) based on Extended Golomb Code (EGC), to reduce the size as well as increasing the decoding speed of the inverted index. The decoding speed is very important to increase the speed of query processing in IRS applications. We have implemented and tested the performance of FEGC and EGC with other existing techniques. Experimental results show that the EGC compression techniques perform well and give better compression than other existing techniques. EGC is also relatively better than FEGC. But the number of CPU cycles required by EGC is more than that of FEGC for encoding and decoding an integer. Hence FEGC could be faster encoder than EGC while it gives comparable results with respect to EGC in compressing doc–ids for IRS applications.

A High-Capacity Lossless Data Hiding Scheme for Binary Images

Many previous binary image lossless data hiding schemes often cause serious perceptible distortion and have poor visual quality of stego-images. To obtain better invisibility and higher hiding capacity, a novel reversible data hiding scheme for binary images is proposed by combining pattern substitution and human visual perception. Firstly, an improved binary image boundary detection method is presented by avoiding successive boundary pixel flipping. Secondly, secret messages are embedded into binary image boundaries by employing interlaced block partition. Finally, to achieve lossless recovery of original binary image, the side-information is lossless compressed by using the Golomb Code and the occurrence frequency of each pattern. Extensive experiments show that the proposed scheme is effective, and obtain at least 3.6 dB higher PSNR values of stego-image and 92.5% higher embedding capacity compared with Ho et al’s method.

Comparison of variable-length codes: Elias and Fibonacci codes as applied to problems of data compression

The analysis of the recorded geophysical information shows that there is a large spread in probability of instrument readings at the moment of seismic activity. In order to lower demands for computer data resources and decrease the power consumption when applying autonomous computer-based systems, the coding algorithms with minimal requirements for the involvement of the computer central processor and, as a consequence, its power consumption are used. These include the Huffman static algorithm and algorithms using Elias, Rice, Golomb, and Fibonacci codes. The application of Fibonacci codes for coding this information leads to a gain in compression ratio of 10–30% relative to other coding methods.

Test Compression for Robust Testable Path Delay Fault Testing Using Interleaving and Statistical Coding

This paper proposes a method providing efficient test compression. The proposed method is for robust testable path delay fault testing with scan design facilitating two-pattern testing. In the proposed method, test data are interleaved before test compression using statistical coding. This paper also presents test architecture for two-pattern testing using the proposed method. The proposed method is experimentally evaluated from several viewpoints such as compression rates, test application time and area overhead. For robust testable path delay fault testing on 11 out of 20 ISCAS89 benchmark circuits, the proposed method provides better compression rates than the existing methods such as Huffman coding, run-length coding, Golomb coding, frequency-directed run-length (FDR) coding and variable-length input Huffman coding (VIHC).

Context-based entropy coding in AVS video coding standard

In this paper, two context-based entropy coding schemes for AVS Part-2 video coding standard are presented. One is Context-based 2D Variable Length Coding (C2DVLC) as a low complexity entropy coding scheme for AVS Part-2 Jizhun profile. C2DVLC uses multiple 2D-VLC tables to exploit the statistical features of DCT coefficients for higher coding efficiency. Exponential–Golomb codes are applied in C2DVLC to code the pairs of the run-length of zero coefficients and the non-zero coefficients for lower storage requirement. The other is Context-based Binary Arithmetic Coding (CBAC) as an enhanced entropy coding scheme for AVS Part-2 Jiaqiang profile. CBAC utilizes all previously coded coefficient magnitudes in a DCT block for context modeling. This enables adaptive arithmetic coding to exploit the redundancy of the high-order Markov process in DCT domain with a few contexts. In addition, a context weighting technique is used to further improve CBAC's coding efficiency. Moreover, CBAC is designed to be compatible to C2DVLC in coding elements which simplifies the implementations. The experimental results demonstrate that both C2DVLC and CBAC can achieve comparable or even slightly higher coding performance when compared to Context-Adaptive Variable Length Coding (CAVLC) in H.264/AVC baseline profile and Context-Based Adaptive Binary Arithmetic Coding (CABAC) in H.264/AVC main profile respectively.

Reversible Data Hiding and Reversible Authentication Watermarking for Binary Images

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.

A New Multistage Lattice Vector Quantization with Adaptive Subband Thresholding for Image Compression

Lattice vector quantization (LVQ) reduces coding complexity and computation due to its regular structure. A new multistage LVQ (MLVQ) using an adaptive subband thresholding technique is presented and applied to image compression. The technique concentrates on reducing the quantization error of the quantized vectors by "blowing out" the residual quantization errors with an LVQ scale factor. The significant coefficients of each subband are identified using an optimum adaptive thresholding scheme for each subband. A variable length coding procedure using Golomb codes is used to compress the codebook index which produces a very efficient and fast technique for entropy coding. Experimental results using the MLVQ are shown to be significantly better than JPEG 2000 and the recent VQ techniques for various test images.

Extended Golomb Code for Integer Representation

In this paper, we have proposed two methods to represent nonnegative integers based on the principle used in Golomb code (GC). In both methods, the given integer is successively divided with a divisor, the quotient and the remainders are then used to represent the integer. One of our methods is best suited for representing short integers and gives bit length comparable to that of Elias radic code which is best for representing short-range integers. Another of our methods is best suited for representing both short and long integers and gives a bit length comparable to that of Fibonacci code which is best for representing long integers. Application of our methods as a final stage encoder of the Burrows-Wheeler transform compressor shows that our codes give a better compression rate than the Elias, Fibonacci, punctured, and GC codes

Efficient Integer Coding for Arbitrary Probability Distributions

Performance bounds on the average codeword length of Golomb codes for arbitrary probability distributions are derived in terms of the mean. Then based on Golomb codes, a class of extended gamma codes which are the generalizations of Elias gamma code is constructed and proved to be universal. Optimal decision rules for choosing parameters of Golomb codes and extended gamma codes for arbitrary probability distributions are also derived. Finally, the concept of maximum entropy codes is introduced and the existence of such codes is investigated for source classes with linear constraints. Golomb codes with optimal parameters turn out to be maximum entropy codes for sources with a fixed mean

ECG compression based on wavelet transform and Golomb coding

A new wavelet-based ECG compression method is presented. Wavelet transform coefficients are quantised with a uniform scalar dead zone quantiser. The Exp-Golomb coding is used to code the lengths of runs of the zero coefficients. The Golomb-Rice coding is used to code the nonzero coefficients. Experiments on several records from the MIT-BIH arrhythmia database show that the proposed coding algorithm outperforms other recently developed ECG compression algorithms.

Application of Arithmetic Coding to Compression of VLSI Test Data

This paper proposes arithmetic coding for application to data compression for VLSI testing. The use of arithmetic codes results in a codeword whose length is close to the optimal value (as predicted by entropy in information theory), thus achieving a higher compression. Previous techniques (such as those based on Huffman or Golomb coding) result in optimal codes for data sets in which the probability model of the symbols satisfies specific requirements. This paper shows empirically and analytically that Huffman and Golomb codes can result in a large difference between the bound established by the entropy and the attained compression; therefore, the worst-case difference is studied using information theory. Compression results for arithmetic coding are presented using ISCAS benchmark circuits; a practical integer implementation of arithmetic coding/decoding and an analysis of its deviation from the entropy bound are pursued. A software implementation is proposed using embedded DSP cores. In the experimental evaluation, fully specified test vectors and test cubes from two different ATPG programs are utilized. The implications of arithmetic coding on manufacturing test using an ATE are also investigated.

Group testing for image compression

This paper presents Group Testing for Wavelets (GTW), a novel embedded-wavelet-based image compression algorithm based on the concept of group testing. We explain how group testing is a generalization of the zerotree coding technique for wavelet-transformed images. We also show that Golomb coding is equivalent to Hwang's group testing algorithm. GTW is similar to SPIHT but replaces SPIHT's significance pass with a new group testing based method. Although no arithmetic coding is implemented, GTW performs competitively with SPIHT's arithmetic coding variant in terms of rate-distortion performance.