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Extended golomb code for Integer representation

IEEE TRANSACTIONS ON MULTIMEDIA 2007年第2期9卷 239-246页

作者： Somasundaram, K. Domnic, S. Gandhigram Rural Inst Dept Comp Sci & Appl Gandhigram 624302 India

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 root 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.

关键词： Burrows-Wheeler compression Eilas root code Fibonacci code golomb code Huffman code integer coding Punctured Elias code

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Extended-Domain golomb code and Symmetry of Relative Redundancy

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IEICE TRANSACTIONS ON FUNDAMENTALS OF ELECTRONICS COMMUNICATIONS AND COMPUTER SCIENCES 2021年第8期E104A卷 1033-1042页

作者： Sugiura, Ryosuke Kamamoto, Yutaka Moriya, Takehiro NTT Corp NTT Commun Sci Labs Atsugi Kanagawa 2430198 Japan

This paper presents extended-domain golomb (XDG) code, an extension of golomb code for sparse geometric sources as well as a generalization of extended-domain golomb-Rice (XDGR) code, based on the idea of almost instantaneous fixed-to-variable length (AIFV) codes. Showing that the XDGR encoding can be interpreted as extended usage of the code proposed in the previous works, this paper discusses the following two facts: The proposed XDG code can be constructed as an AIFV code relating to golomb code as XDGR code does to Rice code;XDG and golomb codes are symmetric in the sense of relative redundancy. The proposed XDG code can be efficiently used for losslessly compressing geometric sources too sparse for the conventional golomb and Rice codes. According to the symmetry, its relative redundancy is guaranteed to be as low as golomb code compressing non-sparse geometric sources. Awing to this fact, the parameter of the proposed XDG code, which is more finely tunable than the conventional XDGR code, can be optimized for given inputs using the conventional techniques. Therefore, it is expected to be more useful for many coding applications that deal with geometric sources at low bit rates.

关键词： data compression FVcodes golomb code Rice code golomb-Rice code AIFV codes run-length codes

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

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TELECOMMUNICATION SYSTEMS 2018年第1期69卷 77-94页

作者： Singhdeo, Sutikshna Bhanja, Urmila IISER Dept Math Mohali India IGIT Dept Elect & Telecommun Engn Dhenkanal India

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.

关键词： golomb code OCDMA Multiple access interference Algorithm complexity code optimality Fiber non-linearity

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Co-optimization for test data compression and testing power based on variable-tall code 5

Co-optimization for test data compression and testing power ...

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5th International Conference on ASIC

作者： Han, YH Xu, YJ Li, XW Chinese Acad Sci Inst Comp Technol Beijing 100080 Peoples R China

ISBN: (纸本)078037889X

We present a novel code: Variable-Tail code to compress the test data, which is, proved to be better than the golomb code. An efficient reordering algorithm(ERA) is proposed to optimize the distribution of run-lengths in the test data in order to improve the compression effectiveness. On other hand,since the pourer during testing is always higher than the normal functional mode, the power dissipated in the CUT must be reduced during testing which is omitted previously. The analysis and experiments have demonstrated that our ERA can significantly reduce the total testing power and average power dissipated in the CUT with no hardware penalty.

关键词： golomb code Variable-Tail code total transitions count(ITC) total hamming distance(THD)

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Symbol coding of Laplacian distributed prediction residuals

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DIGITAL SIGNAL PROCESSING 2015年第1期44卷 76-87页

作者： Ali, Mortuza Murshed, Manzur Federat Univ Australia Sch Engn & IT Churchill Vic 3842 Australia

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. (C) 2015 Elsevier Inc. All rights reserved.

关键词： Predictive coding Symbol-by-symbol coding Laplace distribution golomb code Rice mapping

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

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IEEE SENSORS JOURNAL 2019年第19期19卷 8895-8903页

作者： Giorgi, Giada Univ Padua Dept Informat Engn I-35131 Padua Italy

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.

关键词： Lossless compression golomb code wireless body sensor networks (WBSN) wireless sensor networks (WSN) wearable sensors multisensor systems

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Lossless ECG encoding

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COMPUTER METHODS AND PROGRAMS IN BIOMEDICINE 1997年第1期52卷 23-33页

作者： Koski, A University of Turku Department of Computer Science Lemminkäisenkatu 14 A 20520 Turku Finland

We have studied the lossless encoding of ECG signals. With suitable code we aim to reduce the storage space needed by ECG signals. Several methods designed for ECG compression use lossy, i.e. irreversible techniques, in which the original signal is lost, but the restored approximation is almost equal to the original. We aimed, however, to use reversible methods which are able to restore the original signal exactly. We have examined various methods and developed a new approach based on structural recognition and extraction of ECG complexes. Comparative conclusions are drawn from the compression efficiency of lossless and lossy methods. In this study, the effect of sampling frequency, resolution and filtering is also examined.

关键词： compression ECG complex electrocardiograph (EGG) signal encoding filtering gamma code golomb code Huffman code pattern recognition Ziv-Lempel method

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

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CLUSTER COMPUTING-THE JOURNAL OF NETWORKS SOFTWARE TOOLS AND APPLICATIONS 2019年第6-Sup期22卷 15007-15013页

作者： Kumar, J. Satheesh Kumar, G. Saravana Ahilan, A. Hindusthan Coll Engn & Technol Dept Elect & Commun Engn Coimbatore Tamil Nadu India Tamil Nadu Coll Engn Dept Instrumentat & Control Engn Coimbatore Tamil Nadu India GCT Coimbatore Tamil Nadu India

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.

关键词： FPGA (field programmable gate array) Run length code golomb code CR (compression ratio)

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A Combined Approach for Real-Time Data Compression in Wireless Body Sensor Networks

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IEEE SENSORS JOURNAL 2017年第18期17卷 6129-6135页

作者： Giorgi, Giada Univ Padua Dept Informat Engn I-35131 Padua Italy

Wireless body sensor networks (WBSNs) represent an enabling technology for unobtrusive patient monitoring. Unlike wireless sensor networks (WSNs), they are characterized by relatively few and heterogeneous sensors placed in, on, or around the human body. An important issue consists in designing efficient solutions for optimizing network resource usage, such as computational capacity, energy, and bandwidth. Compression algorithms for WBSNs need to satisfy more stringent requirements than solutions for typical WSNs. In particular, to guarantee real-time monitoring of vital signals, the algorithms cannot introduce latency. Furthermore, the maximum reconstruction error is usually very small and it needs to be known in advance. In this scenario, we propose a combined compression algorithm, which satisfied the previous requirements. Results obtained by considering different biomedical signals show that a significant compression ratio can be achieved also when very small values of the maximum error are considered.

关键词： Compression lossy lossless golomb code wireless body sensor networks wireless sensor networks

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Asymptotic average redundancy of Huffman (and other) block codes

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IEEE TRANSACTIONS ON INFORMATION THEORY 2000年第7期46卷 2434-2443页

作者： Szpankowski, W Purdue Univ Dept Comp Sci W Lafayette IN 47907 USA

We study asymptotically the redundancy of Huffman (and other) codes. It has been known from the inception of the Huffman code that in the worst case its redundancy-defined as the excess of the code length over the optimal (ideal) code length-is not more than one. However, to the best of our knowledge edge no precise asymptotic results have been reported in literature thus far. We consider here a memoryless binary source generating a sequence of length n distributed as Binomial(n, p) with p being the probability of emitting 0. Based on recent results of Stubley, we prove that for p < 1/2 the average redundancy <(R)over bar>(H)(n) of the Huffman code becomes as n --> infinity [GRAPHICS] where alpha = log(2)(1 - p)/p and beta = -log(2)(1 - p), p < 1, M, N are integers such that gcd (N, M) = 1, and [x] = x - [x] is the fractional part of x. The appearance of the fractal-like function [Mn] explains the erratic behavior of the Huffman redundancy, and its "resistance" to succumb to a precise analysis. As a side result, we prove that the average redundancy of the Shannon block code is as n --> infinity [GRAPHICS] where p < 1. Finally, we derive the redundancy of the golomb code (for the geometric distribution) which can be viewed as a special case of the Huffman code for infinite alphabets. Unlike the redundancy of Huffman and Shannon codes, golomb's code redundancy has only oscillating behavior (i.e., there is no convergent mode). These findings are obtained by analytic methods such as theory of distribution of sequences modulo 1 and Fourier series.

关键词： average redundancy distribution of sequences modulo 1 Fourier analysis golomb code Huffman code Shannon-Fano code Weyl's criterion

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