G.G. Langdon and J. Rissanen, "Compression of black-white images with arithmetic coding", IEEE Trans. Communications, 29 (6), 858-867, June 1981.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....bit planes. It generates the input to the BAC block based on statistics (state information bits that are maintained across the bit planes) of the data coded previously. BAC: The BPC outputs are entropy coded using BAC to generate the code stream. The MQ coder, which is a derivative of the coder [11], 12] has been proposed to implement the BAC. The algorithm is multiplication free. Predetermined probability values are supplied by the standard and are stored in a look up table. The adaptation state machine is also supplied by the standard. File formatting and layer formation: For each of ....

G. L. Langdon, Jr. and J. Rissanen, "Compression of black-white images with arithmetic coding," IEEE Trans. Commun., vol. COM-29, pp. 858--867, June 1981.

....data compression, where the two mafn approaches are [4] are modebased (e.g. Arithmetic Coding (AC) or adaptive Huffman coding) and dictionary based (e.g. Lempel Ziv (LZ) coding) where the adaptivity comes from dynamically updating, respectively, the model and the dictionary. In the AC algorithm [1], in the simpler case of a binary source, the encoder has to update the probabilities of the 0 s and 1 s. If the source is stationary and the model is correct then AC can provide a performance very close to the first order entropy. However, in real life environments, where sources need not be ....

G. G. Langdon and J. Rissancn, "Compression of black-white images with arithmetic coding," IEEE Trans. on Comm., vol. COM-29, pp. 858 867, Jun. 1981.

....the feature image. The method is near lossless because the amount of changes is controlled only isolated noise pixels are reversed. 2. Context based compression Binary images are favorable source for context based image compression because of the spatial dependencies between neighboring pixels [7,8]. In context based compression, the pixels are coded on the basis of their probability estimates in respect to the context. The context is deftned by the combination of the color values of already coded neighboring pixels within the template. JBIG is the current international standard for ....

Langdon G.G., Rissanen J., Compression of blackwhite images with arithmetic coding. IEEE Trans. Communications 29 (6): 858-867, 1981.

....discussions of a particular arithmetic code for an arbitrary source having an alphabet of K letters. This code is referred to as a K ar t arithmetic code, to distinguish it from the more widely used (and perhaps more widely understood) arithmetic codes designed for binary source alphabets [32] [47] [48] Although ultimately the code is to be applied to the scalar quantization problem for a memoryless source, the discussion in these first sections does not assume independence of source letters; this is to make the material useful to those interested in high performance entropy coding in the ....

....Thus, carry trapping must be disabled as long as the carry control field contains a carry trap bit. This consideration leads to the two state carry trapping mechanism as indicated in Figure 3.19. This method of controlling the propagation of carry overs was devised by Langdon and Rissanen [47], and may have been based on a similar technique devised by Rubin [60] 3.6 Performance of Arithmetic Coding Applied to Quantization 75 rate distortion function uniform quantization with ideal entropy coding uniform quantization with arithmetic coding uniform quantization with ideal ....

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Langdon, G., and Rissanen, J.J., "Compression of Black-White Images with Arithmetic Coding," IEEE Trans. Commun., vol. COM-29, no. 6, pp. 858-867, June 1981.

....and the PMF to be specified independently for each pixel encoded. The PMF can be conditioned on anything that the decoder will have access to prior to the time of decoding. One of the first published applications of arithmetic coding was a scheme for lossless compres sion of binary images [69], which is depicted in Figure 4.1.1. Pixels (which can be either black or white) are scanned in raster order and fed to an arithmetic coder, along with a corresponding estimate of the conditional PMF. The arithmetic coder then produces a compact sequence of bits from which the original image may ....

....the size of the alphabet of x for any of the neighborhoods shown in Figure 4.1.2 is small enough that it is feasible to estimate the conditional PMF for each x by counting x specific occurrences of the values of y. Several variations of such a count based estimation procedure are described in [69]. Count based PMF estimation is not appropriate for greyscale images, because the number of conditioning states becomes prohibitively large for even moderate size neighborhoods. Also, that method of estimation when applied to scalar observations does not exploit the relationship between nearby ....

Glen G. Langdon and Jorma J. Rissanen. Compression of black-white images with arithmetic coding. IEEE Trans. Comm., COM-29:858-867, June 1981.

....some novel methods for choosing the optimal resolution order combination without an exhaustive search or even a pre scan of the data. As a final introductory note, the algorithms described in this paper are adaptive. Adaptive Markov models, most often used in conjunction with arithmetic coding [3], start with no information about the source, accept data sequentially, are presented with each symbol in the sample only once, and modify the way they compress in response to the history. Adaptive algorithms are attractive in that it is unnecessary to perform a pre scan of the data, and no side ....

....in that it is unnecessary to perform a pre scan of the data, and no side information need be sent. 2. PRELIMINARIES Before proceeding, we need to introduce the terms state weight, which is simply the number of contexts in a Markov modeller and permutation, which is an ordered set of integers [3], p = fp 1 #p 2 # Delta Delta Delta#p ng, where n is the model order. The source to be coded is given by x t = x 1 #x 2 # Delta Delta Delta#x t , where x i is the i th symbol, and we define the order n context of x at symbol t using permutation p as the sequence x t;p 1 #x t;p 2 # ....

G. Langdon and J. Rissanen, "Compression of black-white images with arithmetic coding," IEEE Transactions on Communications, vol. 29, pp. 858--867, 1981.

....are usually the vast majority) to zero. The data stream then consists of two parts: the transmission of a sparse binary map indicating the locations of the non zero pixels (coded using either run length encoding [2] or arithmetic coding [4] followed by the quantized values. Arithmetic coding [10] is more powerful than runlength coding and gives better results at the expense of greater computation. The basic idea behind binary arithmetic coding is to use a finite state machine, whose state is determined by previously coded pixels, to estimate the probability that the next pixel will be a ....

....g ij (m# n) f ij (m# n) f ij (m# n) i# j 2f(0# 1)# (1# 0)# (1# 1)g# (6) which can then be coded instead of the original subbands. The second method is based on the arithmetic coding algo (a) Lena (256 Theta 256) b) Barb (512 Theta 512) Fig. 1. The Original Images rithm given in [10] and uses the predicted values to guess at which of the highpass pixels will be non zero after deadzone quantization. If the prediction is fairly good, then the guess will improve the prediction as to whether or not the next pixel will be a 1 , allowing the binary map to be coded at a lower ....

G. G. Langdon and J. Rissanen, "Compression of black-white images with arithmetic coding," IEEE Trans. Commun.,vol. 29, pp. 858--867, June 1981.

....be transparent for data superimposing, and 1 stands for the foreground color. Binary images can be efficiently compressed using context based statistical modeling and arithmetic coding. The image is processed pixel by pixel in raster scan order starting from the top leftmost pixel of the image [15]. The probabilities of the black and white pixels are conditioned on the combination of already coded neighboring pixels defined by a template, see Fig. 1. The above approach is adopted in the international standard JBIG [11,12] and the emerging standard JBIG2 [13,14] Furthermore, JBIG2 segments ....

G.G. Langdon, J. Rissanen, "Compression of black-white images with arithmetic coding", IEEE Trans. Communications, 29 (6), 858-867, June 1981.

....that improved performance can be obtained by using a variable decay rate scheme that uses the derivative of the per symbol codelength sequence to control the rate of decay. 1. INTRODUCTION Consider the task of compressing a non stationary memoryless source. We know that arithmetic coding [1][2] can compress the source to a rate corresponding to the entropy of the probability model of the source, so that determining the probability model is the central problem. If we constrain ourselves to adaptive algorithms that process data sequentially, are presented with each symbol in the sample ....

G. Langdon and J. Rissanen, "Compression of blackwhite images with arithmetic coding," IEEE Transactions on Communications, vol. 29, pp. 858--867, 1981.

....allows the application of binary adaptation to M ary alphabets. Decomposition makes binary alphabets and adaptation attractive because Shannon s notion of entropy provides that the binary decomposition of any M ary alphabet does not change the entropy value. Early binary adaptation techniques [8, 7], were developed as universal parts for building and then combining with a coder and a context model designed for each particular application. Other adapters appear in [12, 11, 10] With binary adapters, a multiple outcome event is transformed to a decision tree of binary events. Each leaf of the ....

....SSS adap constrains the LPS count to values 3, 4, and 5. When the LPS count reaches 6, the LPS count is halved to 3, and the total count is halved as well. The algorithm LPS3:5;1 is so called because the LPS count range is 3 to 5, and the count increment is 1. This algorithm is described in [8]. With value LPSct as the current count for the LPS symbol, and TOTct as the total count, their current count ratio is the value pLPS, the probability of the less probable symbol. The probability estimate pLPS is: pLPS = LPSct TOT ct : We describe LPS3:5;1 by means of a program snippit. We ....

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G. G. Langdon, Jr. and J. J. Rissanen. \Compression of black-white images with arithmetic coding ". IEEE Trans. Commun., vol. COM-29, no. 6:pp. 858-867, June. 1981.

....remaining constraint is that the statistical model may be conditioned only on preceding pixels in the chosen ordering. The conditioning structure of the statistical model we consider is patterned after the grayscale extension [10] of the causal neighborhood context model originally proposed in [7] for binary images. Speci cally, for every pixel location in the sequence, a set of nearby but strictly preceding pixel locations is speci ed as a conditioning context. We consider the simplest case, wherein the pixels are encoded in raster order and the set of conditioning pixels is speci ed ....

G. G. Langdon and J. J. Rissanen. Compression of black-white images with arithmetic coding. IEEE Trans. Comm., COM-29:858-867, June 1981.

....is maintained in a register until a byte is completed. At this moment, the codeword byte is emitted. However, in this case, a carry generated in the computation of c i 1 could propagate over the discarded part of c i . To limit the carry propagation, several stuffing bits are introduced [12] [14] [18] module OUT) Arithmetic coding ensures that no future value of C can exceed the current value of C A. Consequently, once a carry over has propagated into a given code string position no other carry over will reach the same code string position. This way, considering that the output codeword ....

....the value of C i is updated its integer part is assimilated and then it is transmitted in blocks of 8 bits. When a code byte of hexadecimal value FF is transmitted, a stuff bit is inserted into the code string. The stuff bit has the same weight as the least significant bit in the FF byte [12] [14] [18] Bits shifted out of the left end of the Low register during alignment are queued in an extension of the register. As the maximum shift that can be performed over the value stored 12 8 2 CODE BYTE 1 CODE BYTE 0 # 17 bit # 9 bit OUT BYTE 0 8 8 2 S 2 I 2 S 1 I 1 S 0 I 0 OUT 8 ....

G.G. Langdon, J. Rissanen, Compression of Black-White Images with Arithmetic Coding, IEEE Trans. on Communications, pp. 858-867. (1981).

....parameters (as suggested in Table 7.2) namely, blending surface order (these models are described in Chapter 6) MINIMUM PSNR, MINIMUM AREA, and the number of quantization levels, QUANT LEVELS, for the control point representation. We use a 3rd order context model adaptive arithmetic coding [14, 21] to encode the control points bitstream. We applied the Burrows Wheeler Transform [41] followed by the same 78 Figure 7.4: Result for RTP: PSNR = 30.76 dB, bitrate = 0.47 bpp. arithmetic coding to encode the partitioning information. A description of these encoding techniques and an analysis of ....

....entropy encoder tries to achieve the lowest average bit per symbol possible. The theoretical lower bound for the average bit per symbol is given by the zero order entropy of the source, assuming memoryless source [33] For the purpose of encoding a memoryless source, we can use arithmetic coding [14] or Hu man coding [12] Arithmetic coding encodes the entire sequence into a binary number as opposed to Hu man coding which uses optimal variable length code association with each symbol. Hu man coding is only optimal (average bit length close to the entropy) when the symbol probabilities are ....

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G. G. Langdon, Jr. and J. Rissanen. Compression of Black-White Images with Arithmetic Coding. IEEE Transactions on Communications, 29(6):858-867, 1981.

....reference block from the previous frame and also outputs the motion vector. The DCT coefficients are quantized and then run length coded (RLC) to redundance in long sequences of zeroes. In addition, the statistically based variable length code (VLC) such as the Huffman code or arithmetic code [24], is applied to exploit any remaining data redundancy. For compression systems using intra frame coding only, the ME block is not needed. In this paper, we use the spatial domain to refer to the raw pixel data format before encoding or after decoding. Sometimes for the purpose of contrast, we ....

G.G. Langdon and J. Rissanen," Compression of Black-White Images with Arithmetic Coding," IEEE Transactions on Communications, June 1981, pp.858-67.

....as a new class. If it matches with a representative component in the codebook, the component is encoded (see Section 2.4.9) and is added to the equivalence class with which it matched. 2.4. 9 Image coding Images are compressed using the binary context model introduced by Langdon and Rissanen [LR81] A context which corresponds to a bit mask is applied at each position in the image to be encoded. The context is formed by using the pixel values from the image, and for each context, a count is recorded and used to predict black (c b ) and white (c w ) pixels in that context. The number of ....

....required to specify M given L k is minimised. This distance metric is called the cross entropy between pairs of images, and can be approximated by compressing one component relative to another. The entropy model we use is the context based compression model proposed by Langdon and Rissanen [LR81] and further developed by Moffat [Mof91] 6.2.1 Cross entropy To calculate the cross entropy between two components, we use the pairwise compression of components introduced in Chapter 2. A clairvoyant context can be used to estimate the information content of each pixel, because it is not ....

Glen G. Langdon and Jorma J. Rissanen. Compression of black-white images with arithmetic coding. IEEE Transactions on Communications, 29(6):858-- 867, June 1981.

....suitability of the probability distribution that is used. CAE assumes that a high degree of local correlation exists in the image. Hence, conditional probabilities are introduced. For a given pixel, the probability distribution is conditioned upon the values of the pixels in a local neighbourhood [29]. The shape and size of the neighbourhood is represented by a template (see Figure 2 for the template used for intra mode coding) The size of the template is typically 10 pixels leading to 1024 different contexts [5] A context is an integer specifying the value of each pixel within the template. ....

G. Langdon and J. Rissanen. Compression of black-white images with arithmetic coding. IEEE Trans. Communications, COM-29(6):858--867, June 1981.

....coding environment, with special attention to the interaction between shape coding and other coding tools (texture and motion coding) 2 Context based Arithmetic Encoding (CAE) The bitmap based approach considered here draws its source from text compression techniques. Langdon and Rissanen [8] proposed an efficient method based on finite state machines and arithmetic coding. The idea is quite simple: the image is coded pixel by pixel in a scanline order. For each pixel, the state of the finite state machine is defined by the values of pixels within a template. This template typically ....

G. Langdon Jr. and J. Rissanen. Compression of black-white images with arithmetic coding. IEEE Trans. on Comm., 29(6):858--867, 1981.

....of those methods by narrowing the range of possible models. Much of the current research in arithmetic coding concerns finding approximations that increase coding speed without compromising compression efficiency. The most common method is to use an approximation to the multiplication operation [10,27,29,43]; in this paper we present an alternative approach using table lookups and approximate probability estimation. Another disadvantage of arithmetic coding is that it does not in general produce a prefix code. This precludes parallel coding with multiple processors. In addition, the potentially ....

....images, an important problem with a natural two symbol alphabet, often produces probabilities close to 1, indicating the use of arithmetic coding to obtain good compression. Historically, much of the arithmetic coding research by Rissanen, Langdon, and others at IBM has focused on bilevel images [29]. The Q Coder [2,27,33,41,42,43] is a binary arithmetic coder; work by Rissanen and Mohiuddin [50] and Chevion et al. 10] extends some of the Q Coder ideas to multi symbol alphabets. In most other text and image compression applications, a multi symbol alphabet is more natural, but even then we ....

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G. G. Langdon & J. Rissanen, "Compression of Black-White Images with Arithmetic Coding," IEEE Trans. Comm.COM--29 (1981), 858--867.

....: 179 6.4 Experimental results : 186 6.5 Conclusions and future work : 190 6. 1 Introduction The most successful methods for lossless compression of data, such as arithmetic coding [55, 116, 80], Lempel Ziv coding [120] or dynamic Huffman coding [35, 54, 111] are all adaptive (see [6] for an extensive review of lossless compression) While the initial work on entropy coding (e.g. Huffman coding) relied on knowing, or measuring, the source distribution, adaptive schemes make no prior ....

....(AC) or adaptive Huffman coding) and dictionarybased (e.g. Lempel Ziv (LZ) coding) where the adaptivity comes from dynamically updating, respectively, the model and the dictionary. We refer to [6] for an extensive survey of lossless compression techniques. We will concentrate on the AC algorithm [55, 80, 116] as it is closer to some of the main ideas in our work. In the simpler case of a binary source, the encoder has to update the probabilities of the 0 s and 1 s. If the source is stationary and the model is correct then AC can provide a performance very close to the first order entropy. However, in ....

[Article contains additional citation context not shown here]

G. G. Langdon and J. Rissanen. Compression of black-white images with arithmetic coding. IEEE Trans. on Comm., COM-29(6):858--867, Jun. 1981. 196

....that the amount of information required to specify M given L k is minimized. This distance metric is called the cross entropy between pairs of images, and can be approximated by compressing one mark relative to another. The entropy model we use is the context based compression model proposed by Langdon Rissanen (1981) and further developed by Moffat (1991) There are two principal issues to investigate when studying template matching methods: their susceptibility to different kinds of noise, and how they respond to errors in the initial registration. Because of the computation intensive nature of the ....

Langdon, G.G. and Rissanen, J. (1981) "Compression of black-white images with arithmetic coding," IEEE Trans Communications COM-29(6): 858--867; June.

....entry. As a consequence, restored values are not limited to only those appearing explicitly in a codebook. The technique is more than a lookup table; it uses the available information to synthesize the missing value. 4. APPLICATION TO LOSSLESS COMPRESSION OF GRAYSCALE IMAGES Langdon and Rissanen [7] have described an efficient reversible compression scheme for binary images. In their system, each pixel is arithmetically encoded using a PMF that is conditioned on a nearby set of previously encoded pixels, i.e. on a neighborhood of pixels that precede it in CODE BITS GRAYSCALE PIXEL VALUES ....

Glen Langdon and Jorma Rissanen. Compression of black-white images with arithmetic coding. IEEE Trans. Comm., COM-29:858--867, June 1981.

....sorts of coding methods developed for the (lossless) compression of bilevel images. Run length coding as described in the preceding section is one possibility which offers a good trade off between coding efficiency and complexity. However, sacrificing speed the context based modeling introduced in [2] and successfully implemented in the JBIG 3 standard offers a more effective coding strategy. Essentially, this approach is based on a model using conditional probabilities where the conditioning context is created with the help of a socalled template. A template is usually made up of ....

G. G. Langdon and J. J. Rissanen, "Compression of Black-White Images with Arithmetic Coding", IEEE Trans. on Comm., Vol. 29, No.6, pp.858--867, 1981.

....this article, is the speed at which the current interval can be updated. In the basic algorithm outlined in Section 1 and in the work of Witten, Neal, and Cleary, up to two multiplications and one division are needed for each symbol encoded. Work by Rissanen, Langdon, Mohiuddin, and others at IBM [5,16,18,22,27] eliminates the division altogether and focuses on approximating the multiplication by combinations of additions and shifts. In [13] we present an alternative approach in which we approximate an arithmetic coder by a finite state automaton with a small number of states. Since the arithmetic ....

G. G. Langdon & J. Rissanen, "Compression of Black-White Images with Arithmetic Coding," IEEE Trans. Comm.COM--29 (1981), 858--867.

....statistical dependencies between objects. In image processing it is well known that pixels are highly correlated with their neighbours. In data compression the use of higher order Markov models can exploit some of the statistical dependencies between items to be encoded. Langdon and Rissanen [11] proposed the use of higher order Markov models in connection with arithmetic coding for the exact compression of binary images and their proposal has formed the basis for the algorithms used by the JBIG binary image compression standard. Todd et al. 12] extended the approach of Langdon and ....

Glen G. Langdon Jr. and Jorma Rissanen, "Compression of black-white images with arithmetic coding", IEEE Transaction on Communication, vol. COM-29, pp. 858--867, 1981.

....more characters than those used in images. In text compression, the best methods make predictions based on up to three or four preceding characters [1] while with black white images the most effective contexts tend to have a radius of just a few pixels, giving a much more localized context [2, 3]. One possibility for textual image compression is to perform optical character recognition (OCR) on the text and transmit (or store) Computer Science, University of Waikato, Hamilton, New Zealand. ihw waikato.ac.NZ; Phone 64 (7) 838 4246; Fax 64 (7) 838 4155. the ASCII codes for the ....

....this option is lossy. However, the basic image based Groups 3 and 4 compression methods are lossless. A more advanced kind of lossless coding uses context to predict upcoming pixels. A context model conditions the probability distribution of a pixel being 0 or 1 on the values of preceding pixels [2]. For example, experiments have shown that a good template is the 10 pixel one of Figure 5a. A black dot marks each pixel included in the template and a bullseye marks the position of the pixel about to be coded. The light gray pixels are ones whose values are not yet known by the decoder and so ....

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G.G. Langdon and J. Rissanen. Compression of black-white images with arithmetic coding. IEEE Trans Information Theory, IT-6:158--167, June 1981.

....if the encoding and decoding are carried out with different computer architectures due to the assumption that the operations in the Eq. 2.22) can be carried out with infinite precision. These issues have been solved by the use of finite precision integer arithmetic and are discussed in [8] and [9]. Since the algorithm can be adapted without changing the underlying principle, they will not be discussed further. The performance of the arithmetic coder, or any entropy coder, is highly dependent on its ability to accurately estimate the symbol probabilities in order to optimally partition the ....

G. Langdon and J. Rissanen, "Compression of Black--White Images with Arithmetic Coding," IEEE Trans. on Comm., vol. 29, pp. 858--867, Jun. 1981.

....data structure. The main part of our pre coder finally supplies the elements of each source with a context , i.e. an appropriate model for the actual coding process in the arithmetic coder. Here we combine the two preceding methods with a contextbased modeling which was initially introduced in [9] and later on successfully implemented in the JBIG z standard [1] It offers a very efficient, adaptive and flexible coding strategy for the removal of higher order redundancies with a rather modest demand of computational resources. 1) Partitioning: The theoretical basis of partitioning is ....

G. G. Langdon and J. J. Rissanen, "Compression of Black-White Images with Arithmetic Coding", IEEE Trans. on Comm., Vol. 29, No.6, pp.858--867, 1981.

....The DPCM trellis thus defined provides a basis for an algorithm to perform soft decision quantization for the prediction error in DPCM under the near lossless criterion. III The Context Model As in [5] we code the quantized prediction errors using an arithmetic coder. It is well known (e.g. [10]) that employing conditional probability models based on contexts can provide significant performance improvements over a simple memoryless probability model. In [5] contexts were based on the previous coded neighboring pixels in the horizontal, vertical, and diagonal directions, i.e. at time ....

G. G. Langdon, Jr. and J. Rissanen, "Compression of black-white images with arithmetic coding," IEEE Trans. on Communications, vol. COM-29, pp. 858--867, Jun. 1981.

....probabilities directly in the coding process, or with some multiplication and division, use the counts value themselves directly in the coding process. There are many ways to incorporate the count ratio and scaled count techniques into the arithmetic code. Perhaps the first such is described in [lr81], where adapter SSS adap provides the coding parameter needed by the shift coder also described in [lr81] Several techniques are reported in the IBM Technical Disclosure Bulletin. For mary (m symbol) alphabets, and arithmetic adapter coder is described by Goertzel in File Compressor [goe87] ....

....themselves directly in the coding process. There are many ways to incorporate the count ratio and scaled count techniques into the arithmetic code. Perhaps the first such is described in [lr81] where adapter SSS adap provides the coding parameter needed by the shift coder also described in [lr81]. Several techniques are reported in the IBM Technical Disclosure Bulletin. For mary (m symbol) alphabets, and arithmetic adapter coder is described by Goertzel in File Compressor [goe87] The standard distributions employed by statisticians and others, such as the Poisson, Gaussian, or ....

[Article contains additional citation context not shown here]

G. Langdon and J. Rissanen, "Compression of Black-white images with arithmetic coding", IEEE Trans commm., vol COM-29, no 6, 858-867, June 1981.

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G.G. Langdon and J. Rissanen, "Compression of black-white images with arithmetic coding", IEEE Trans. Communications, 29 (6), 858-867, June 1981.

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G.G. Langdon, J. Rissanen, Compression of black -- white images with arithmetic coding, IEEE Transactions on Communications 29 (6) (1981) 858 -- 867. June.

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Langdon G.G., Rissanen J., Compression of blackwhite images with arithmetic coding. IEEE Trans. Communications 29 (6): 858-867, 1981.

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Langdon GG, Rissanen J (1981) "Compression of black-white images with arithmetic coding", IEEE Trans. Communications 29: 858-867.

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G.G. Langdon, J. Rissanen, "Compression of black-white images with arithmetic coding", IEEE Trans. Communications, 29 (6), 858-867, June 1981.

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G. G. Langdon and J. Rissanen, "Compression of black-white images with arithmetic coding," IEEE Trans. Commun. 29#6#, 858--867 #1981#.

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G. Langdon Jr and J. Rissanen. Compression of black--white images with arithmetic coding. IEEE Transactions on Communications, 29(6):858--867, 1981.

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Langdon G.G., Rissanen J., Compression of blackwhite images with arithmetic coding. IEEE Trans. Communications 29 (6): 858-867, 1981.

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G. G. Langdon and J. Rissanen, "Compression of black-white images with arithmetic coding," IEEE Trans. Commun., vol. COMM-29, pp. 858--867, June 1981.

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G.G. Langdon Jr. and J.J. Rissanen, "Compression of black-white images with arithmetic coding," IEEE Trans. Communications, vol. 29(6), pp. 858--867, June 1981. 21

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G. Langdon and J. Rissanen, "Compression of black-white images with arithmetic coding," IEEE Trans. Commun., vol. COM-6, pp. 158--167, 1981.

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G. G. Langdon and J. Rissanen, "Compression of black-white images with arithmetic coding," IEEE Trans. Commun. 29#6#, 858--867 #1981#.

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Glen G. Langdon, Jr. and Jorma Rissanen, \Compression of Black-White Images with Arithmetic Coding ", IEEE Trans. Communications, vol COM-29, No. 6, June 1981, 858-867.

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Jr. Glen G. Langdon and Jorma Rissanen, "Compression of blackwhite images with arithmetic coding," IEEE Transactions on Communications, vol. COM-29, no. 6, pp. 858--867, June 1981.

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G. G. Langdon and J. Rissanen, "Compression of black-white images with arithmetic coding," IEEE Trans. Comm., vol. COM-29, pp. 858--867, June 1981.

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