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Codecell convexity in optimal entropy-constrained vector quantization

IEEE TRANSACTIONS ON INFORMATION THEORY 2003年第7期49卷 1821-1828页

作者： György, A Linder, T Hungarian Acad Sci Informat Lab Comp & Automat Res Inst H-1518 Budapest Hungary Queens Univ Dept Math & Stat Kingston ON K7L 3N6 Canada

Properties of optimal entropy-constrained vector quantizers (ECVQs) Are studied for the squared-error distortion, measure. It is known that restricting an ECVQ to have convex codecells may preclude its optimality for some sources with discrete distribution. We show that for sources with continuous distribution, any finite-level ECVQ can be replaced by another finite-level ECVQ with convex codecells that has equal or better performance. We generalize this result to infinite-level quantizers, and also consider the problem of existence of optimal ECVQs for continuous source distributions. In particular, we show that given any entropy constraint, there exists an ECVQ With (possibly infinitely many) convex codecells that has minimum distortion among all ECVQs satisfying the constraint. These results extend analogous statements in entropy-constrained scalar quantization. They also generalize results in entropy-constrained vector quantization that were obtained via the, Lagrangian formulation and, therefore, are valid only for certain values of the entropy constraint.

关键词： convex polytopes entropy coding infinite-level quantizers optimal vector quantization squared-error distortion

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PRINCIPLES OF QUANTIZATION

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IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS 1978年第7期25卷 427-436页

作者： GERSHO, A UNIV CALIF LOS ANGELES DEPT SYST SCI LOS ANGELES CA 90024 USA

Quantization is the process of replacing analog samples with approximate values taken from a finite set of allowed values. The approximate values corresponding to a sequence of analog samples can then be specified by a digital signal for transmission, storage, or other digital processing. In this expository paper, the basic ideas of uniform quantization, companding, robustness to input power level, and optimal quantization are reviewed and explained. The performance of various schemes are compared using the ratio of signal power to mean-square quantizing noise as a criterion. entropy coding and the ultimate theoretical bound on block quantizer performance are also compared with the simpler zero-memory quantizer.

关键词： Quantization Bit rate Limiting Noise robustness Noise level Signal to noise ratio entropy coding Signal processing Communication systems

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OPTIMAL QUANTIZATION OF THE RAYLEIGH PROBABILITY DISTRIBUTION

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IEEE TRANSACTIONS ON COMMUNICATIONS 1979年第1期27卷 101-112页

作者： PEARLMAN, WA SENGE, GH Department of Electrical and Computer Engineering University of Wisconsin Madison WI USA Radar Systems Group Hughes Aircraft Company Culver CA USA

We have derived an efficient and general algorithm for optimal quantization and applied it to the important, but neglected Rayleigh random variable. The optimal quantization range and output levels for the distortion criterion of minimum mean squared error have been calculated and tabulated for numbers of output levels from 1 to 64. We also compute and report the corresponding distortions and output entropies. For the sake of comparison, we also calculate and tabulate level spacings, minimum errors, and entropies for the optimal uniform (equal step size) quantization of the Rayleigh density. Distortion-rate curves are presented for uncoded and entropy coded quantizer outputs and compared with the distortion-rate function. We judge that these results will be useful to workers in the fields of optical holography, image processing, and communications.

关键词： Quantization Probability distribution Optical distortion Holographic optical components Holography Image processing entropy coding Random variables Statistical distributions Gaussian processes

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entropy of the Mixture of Sources and entropy Dimension

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IEEE TRANSACTIONS ON INFORMATION THEORY 2012年第5期58卷 2719-2728页

作者： Smieja, Marek Tabor, Jacek Jagiellonian Univ Inst Comp Sci Dept Math & Comp Sci PL-30348 Krakow Poland

Suppose that we are given two sources S-1, S-2 which both send us information from the data space X. We assume that we lossy-code information coming from S-1 and S-2 with the same maximal error but with different alphabets P-1 and P-2, respectively. Consider a new source S which sends a signal produced by source S-1 with probability a(1) and by source S-2 with probability a(2) = 1 - a(1). We provide a simple greedy algorithm which constructs a coding alphabet P which encodes data from S with the same value of maximal error as single sources, such that the entropy h(S;P) satisfies: h(S;P) <= a(1)h(S-1;P-1) + a(2)h(S-2;P-2) + 1. In the proof of the aforementioned formula, the basic role is played by a new equivalent definition of entropy based on measures instead of partitions. As a consequence, we decompose the entropy dimension of the mixture of sources in terms of the convex combination of the entropy dimensions of the single sources. In the case of probability measures in R-N, this allows us to link the upper local dimension at point with the upper entropy dimension of a measure by an improved version of Young estimation.

关键词： entropy coding entropy dimension lossy coding mixture of sources Renyi information dimension Shannon entropy

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CoGI: Towards Compressing Genomes as an Image

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IEEE-ACM TRANSACTIONS ON COMPUTATIONAL BIOLOGY AND BIOINFORMATICS 2015年第6期12卷 1275-1285页

作者： Xie, Xiaojing Zhou, Shuigeng Guan, Jihong Fudan Univ Shanghai Key Lab Intelligent Informat Proc Shanghai 200433 Peoples R China Fudan Univ Sch Comp Sci Shanghai 200433 Peoples R China Tongji Univ Dept Comp Sci & Technol Shanghai 201804 Peoples R China

Genomic science is now facing an explosive increase of data thanks to the fast development of sequencing technology. This situation poses serious challenges to genomic data storage and transferring. It is desirable to compress data to reduce storage and transferring cost, and thus to boost data distribution and utilization efficiency. Up to now, a number of algorithms / tools have been developed for compressing genomic sequences. Unlike the existing algorithms, most of which treat genomes as one-dimensional text strings and compress them based on dictionaries or probability models, this paper proposes a novel approach called CoGI (the abbreviation of Compressing Genomes as an Image) for genome compression, which transforms the genomic sequences to a two-dimensional binary image (or bitmap), then applies a rectangular partition coding algorithm to compress the binary image. CoGI can be used as either a reference-based compressor or a reference-free compressor. For the former, we develop two entropy-based algorithms to select a proper reference genome. Performance evaluation is conducted on various genomes. Experimental results show that the reference-based CoGI significantly outperforms two state-of-the-art reference-based genome compressors GReEn and RLZ-opt in both compression ratio and compression efficiency. It also achieves comparable compression ratio but two orders of magnitude higher compression efficiency in comparison with XM-one state-of-the-art reference-free genome compressor. Furthermore, our approach performs much better than Gzip-a general-purpose and widely-used compressor, in both compression speed and compression ratio. So, CoGI can serve as an effective and practical genome compressor. The source code and other related documents of CoGI are available at: http://***/projects/***.

关键词： Genomics genomes compression reference-based compression sequence matrixization rectangular partition coding entropy coding

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Lightweight Compression of Intermediate Neural Network Features for Collaborative Intelligence

IEEE OPEN JOURNAL OF CIRCUITS AND SYSTEMS

引用

IEEE OPEN JOURNAL OF CIRCUITS AND SYSTEMS 2021年 2卷 350-362页

作者： Cohen, Robert A. Choi, Hyomin Bajic, Ivan, V Simon Fraser Univ Sch Engn Sci Burnaby BC V5A 1S6 Canada

In collaborative intelligence applications, part of a deep neural network (DNN) is deployed on a lightweight device such as a mobile phone or edge device, and the remaining portion of the DNN is processed where more computing resources are available, such as in the cloud. This paper presents a novel lightweight compression technique designed specifically to quantize and compress the features output by the intermediate layer of a split DNN, without requiring any retraining of the network weights. Mathematical models for estimating the clipping and quantization error of leaky-ReLU and ReLU activations at this intermediate layer are used to compute optimal clipping ranges for coarse quantization. A mathematical model for estimating the clipping and quantization error of leaky-ReLU activations at this intermediate layer is developed and used to compute optimal clipping ranges for coarse quantization. We also present a modified entropy-constrained design algorithm for quantizing clipped activations. When applied to popular object-detection and classification DNNs, we were able to compress the 32-bit floating point intermediate activations down to 0.6 to 0.8 bits, while keeping the loss in accuracy to less than 1%. When compared to HEVC, we found that the lightweight codec consistently provided better inference accuracy, by up to 1.3%. The performance and simplicity of this lightweight compression technique makes it an attractive option for coding an intermediate layer of a split neural network for edge/cloud applications.

关键词： Quantization (signal) Tensors Image coding Neural networks Mobile handsets entropy coding Mathematical model Collaborative intelligence deep learning neural network compression feature compression quantization

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A PARALLEL DECODER OF PROGRAMMABLE HUFFMAN CODES

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IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS FOR VIDEO TECHNOLOGY 1995年第2期5卷 175-178页

作者： WEI, BWY MENG, TH STANFORD UNIV COMP SYST LABSTANFORDCA 94305

Huffman coding, a variable-length entropy coding scheme, is an integral component of international standards on image and video compression including high-definition television (HDTV). The high-bandwidth HDTV systems of data rate in excess of 100 Mpixels/s presents a challenge fur designing a fast and economic circuit for intrinsically sequential Huffman decoding operations. This paper presents an algorithm and a circuit implementation for parallel decoding of programmable Huffman codes by using the numerical properties of Huffman codes. The 1.2 mu m CMOS implementation for a single JPEG AC table of 256 codewords of up to 16-b codeword lengths is estimated to run at 40 MHz with a chip area of 11 mm(2), decoding one codeword per cycle, The design can be pipelined to deliver a throughput of 80 MHz for decoding input streams of consecutive Huffman codes, Furthermore, our programmable scheme can be easily integrated into data paths of video processors to support different Huffman tables used in image/video applications.

关键词： CMOS digital integrated circuits Huffman codes entropy codes high definition television image coding parallel processing sequential decoding television standards variable length codes video coding 1.2 μm CMOS 1.2 micron 16 bit 40 MHz 80 MHz HDTV Huffman CMOS digital integrated circuits Video coding 16-bit sequential decoding Huffman codes image coding television standards entropy coding PARALLEL PROCESSING (COMPUTERS) variable length codes

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CONTOUR coding BASED ON THE DECOMPOSITION OF LINE SEGMENTS

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PATTERN RECOGNITION LETTERS 1990年第3期11卷 191-195页

作者： KIM, WS PARK, RH Department of Electronic Engineering Sogang University C.P.O. Box 1142 Seoul 100-611 Korea

This paper proposes an information-preserving contour coding scheme based on the decomposition of the original chain code into the smoothed code and its difference code. High data compression can be achieved by applying entropy coding technique to the proposed algorithm. This proposed algorithm using decomposition is combined with the fixed- or variable-length coding schemes to compare its performance to those of the conventional coding algorithms. Since the proposed algorithm is so simple, it can be adopted to other contour coding algorithms for high data compression.

关键词： Contour coding data compression decomposition entropy coding

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entropy CODED DIFFERENTIAL PULSE-CODE MODULATION SYSTEMS FOR TELEVISION

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IEEE TRANSACTIONS ON COMMUNICATIONS 1975年第6期CO23卷 660-666页

作者： GOYAL, SK ONEAL, JB N CAROLINA STATE UNIV DEPT ELECT ENGNRALEIGHNC 27607

This paper describes experiments with a television (TV) source encoder which consists of a differential PCM encoder followed by entropy coding. This encoder converts analog television signals into a digital bit stream for digital transmission or storage. When optimized, this type of system is known to perform very close to the rate distortion bound. The differential PCM encoder has a 16-level quantizer during low entropy areas of the picture (quiet areas) but switches to a 6-level quantizer in high entropy (busy) areas of the picture which tend to fill up the buffer. This strategy avoids buffer overflow and has the desirable property that it produces low noise in quiet areas of the picture and higher noise in busy areas of the picture.

关键词： Pulse modulation Modulation coding TV Rate-distortion entropy coding Gaussian noise Distortion measurement Power measurement Noise measurement

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Prioritized DCT for compression and progressive transmission of images

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IEEE TRANSACTIONS ON IMAGE PROCESSING 1992年第4期1卷 477-487页

作者： Huang, Yunming Dreizen, Howard M. Galatsanos, Nikolas P. IIT Dept Elect & Comp Engn Chicago IL 60616 USA

In this paper a new approach based on the block discrete cosine transform (DCT) for compression and progressive transmission of images is presented. The novelty of this approach is that the transform coefficients of all image blocks are coded and transmitted in absolute magnitude order. The resulting ordered-by-magnitude transmission is accomplished without sacrificing coding efficiency by using partition priority coding (PPC a new source coding method that allows the transmission of an ordered data source without coding overhead due to prioritization. Using this approach, coding and transmission are adaptive to the characteristics of each individual image, and therefore, very efficient. Another advantage of this approach is its high progression effectiveness. Since the largest transform coefficients that capture the most important characteristics of images are coded and transmitted first, this method is well suited for progressive image transmission (PIT). Further compression of the image data is achieved by utilizing multiple distribution entropy coding (MDEC. MDEC is a new coding technique based on arithmetic coding. Experiments are presented where the new DCT approach was tested. It is shown that it compares favorably with previously reported DCT and subband image codecs and is also very effective for PIT.

关键词： Discrete cosine transforms Image coding Discrete transforms Source coding Image communication entropy coding Arithmetic Testing Codecs

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