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## Generalized multiple description coding with correlating transforms (2001)

Venue: | IEEE Trans. Inform. Theory |

Citations: | 82 - 2 self |

### Citations

12427 | Elements of Information Theory - Cover, Thomas - 1991 |

7739 |
Matrix Analysis
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(Show Context)
Citation Context ...ric. Notice the effect of transposing this matrix. Since and are symmetric, the transpose is ; thus, and commute. Diagonalizable matrices commute if and only if they are simultaneously diagonalizable =-=[57]-=-. Furthermore, for a matrix with distinct eigenvalues, the orthogonal transform that diagonalizes and leaves the diagonal in decreasing order is unique up to sign choices. On one hand, is diagonalized... |

884 | Vector Quantization.
- Gray
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(Show Context)
Citation Context ... performance of optimal fixed-rate MDSQ is and the performance of optimal entropy-constrained MDSQ is (10) The factors in parentheses are familiar from high-resolution quantization theory (see, e.g., =-=[41]-=- and the references therein). These features of high-rate MDSQ, however, tell us very little about how MDSQ performs at low rates. Later, in Section III-E, the performance of MD based on correlating t... |

579 |
Sphere Packings, Lattices and Groups
- Conway, Sloane
- 1993
(Show Context)
Citation Context ...The uniform scalar quantization of such a representation produces nonsquare partition cells. 11 These partition cells have higher normalized second moments than square cells, and are thus undesirable =-=[44]-=-. The insight attributed to Vaishampayan is that a correlating transform can be applied after quantization has been performed in an orthogonal basis representation. This ensures that the partition cel... |

489 |
Internet protocol, version 6 (ipv6) specification,”
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Citation Context ...re is nonzero. The emphasis in this paper is on situations in which long block codes cannot be used, which is often the case. For example, consider a network using Internet Protocol, Version 6 (IPv6) =-=[19]-=-. An IPv6 node is required to handle 576-byte packets without fragmentation, and it is recommended that larger packets be accommodated. 3 Accounting for packet head3 Without the “Jumbo Payload” option... |

357 | Wavelet transform that map integers to integers,” Applied and Computational Harmonic Analysis (ACHA),
- Calderbank, Daubechies, et al.
- 1998
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Citation Context ...ENDIX I PSEUDOLINEAR DISCRETE TRANSFORMS Invertible discrete-domain to discrete-domain transforms are alternatively described as reversible, integer-to-integer, or invertible in finite precision [53]–=-=[55]-=-. These transforms are based on factorizations of matrices which make information flow in a simple, regular way. Inversion can then be achieved by reversing the information flow. For example, one can ... |

352 |
Coding theorems for a discrete source with a fidelity criterion
- Shannon
- 1959
(Show Context)
Citation Context ...bounds to the achievable rate region for MD coding of any continuous-valued memoryless source with squared-error distortion. This is an extension of Shannon’s bounds on rate-distortion functions (see =-=[35]-=-, [60], [36]). C. Practical Codes The bounds of the previous section can be approached when a long sequence of source symbols is coded. In contrast, the focus in this paper is on simple codes for fini... |

306 |
Design of Multiple Description Scalar Quantizers.
- Vaishampayan, Domaszewicz
- 1993
(Show Context)
Citation Context ...alar quantizers to give two descriptions of a scalar source sample, with an additional central decoder that makes use of both descriptions. This approach was expounded and popularized by Vaishampayan =-=[37]-=-, though Reudink introduced very similar methods in earlier unpublished work [38]. The simplest example is to have scalar quantizers with nested thresholds, as shown in Fig. 3(a). Each quantizer outpu... |

262 | Gamal, “Achievable rates for multiple descriptions - Cover, El - 1982 |

247 | Rate-Distortion Theory.
- Berger
- 1971
(Show Context)
Citation Context ...e achievable rate region for MD coding of any continuous-valued memoryless source with squared-error distortion. This is an extension of Shannon’s bounds on rate-distortion functions (see [35], [60], =-=[36]-=-). C. Practical Codes The bounds of the previous section can be approached when a long sequence of source symbols is coded. In contrast, the focus in this paper is on simple codes for finite-length so... |

218 | Successive refinement of information,”
- Equitz, Cover
- 1991
(Show Context)
Citation Context ...; or channel 1 is always present. Successive refinement was first studied by Koshelev [23]–[25]. The conditions for perfect successive refinement—where (1) and (2) hold with equality—are described in =-=[26]-=-. The result follows from the tightness of the achievable region of [2] for the no excess rate sum case [21] (see also [27]). Finally, it should also be noted that there is a substantial literature on... |

199 | Quantized frame expansions with erasures
- Goyal, Kovacevic, et al.
- 2001
(Show Context)
Citation Context ...t. A recent surge of interest in MD coding seems to be due primarily to this application (see [1], [9]–[12]) and yet the present work was among the first to effectively use more than two packets [13]–=-=[17]-=-. Retransmission of lost packets, when feasible, is an effective technique for maintaining constant quality despite losses. The use of a retransmission protocol, such as TCP [18], requires at a minimu... |

164 | A study of vector quantization for noisy channels,” - Farvardin - 1990 |

131 |
On a Source-Coding Problem with Two Channels and Three Receivers.
- Ozarow
- 1980
(Show Context)
Citation Context ...ers (the side decoders) receive information only over their respective channels. The transmission rate over channel is denoted by , ; i.e., signaling over channel uses at most 1 We may infer from [3]–=-=[5]-=- and private communications that the problem originated with Gersho and Witsenhausen. Gersho proposed a scheme (unpublished [6]) that utilized the redundancy in coded speech waveforms to mitigate the ... |

125 |
Dynamic adaptation in an image transcoding proxy for mobile web browsing.
- Han, Bhagwat, et al.
- 1998
(Show Context)
Citation Context ...yless Gaussian Source The achievable rate-distortion region is completely known only for a memoryless Gaussian source with mean-squared error 4 This is not an arbitrary figure. Based on statistics in =-=[20]-=-, the average WWW image is only 3.9 kbytes; an image of this size would not be fragmented into more than eight packets. Of course, this depends on the sampling of the WWW and may change. (MSE) distort... |

111 |
Successive Refinement of Information: Characterization of the Achievable Rates
- Rimoldi
- 1994
(Show Context)
Citation Context ... successive refinement—where (1) and (2) hold with equality—are described in [26]. The result follows from the tightness of the achievable region of [2] for the no excess rate sum case [21] (see also =-=[27]-=-). Finally, it should also be noted that there is a substantial literature on the error sensitivity of compressed data and more generally on tradeoffs between source and channel coding. The reader is ... |

105 | CREW: Compression with Reversible Embedded Wavelets,” in - Zandi, Allen, et al. - 1995 |

98 |
Multiple Description Image Coding for Noisy Channels by Pairing Transform Coefficients.
- Wang, Orchard, et al.
- 1997
(Show Context)
Citation Context ...term MD correlating transform (MDCT) is used for the present technique. 2) Pairwise Correlating Transforms: A considerably different approach to MD coding was introduced by Wang, Orchard, and Reibman =-=[10]-=-. Instead of using MDSQ to produce two indexes that describe the same quantity, the MD character is achieved with a linear transform that introduces correlation between a pair of random variables; qua... |

92 |
New results in binary multiple descriptions
- Zhang, Berger
- 1987
(Show Context)
Citation Context ...ound is achieved by using truncated Reed–Solomon codes. A similar result holds in the more general setting of [7]. The situation with three channels and seven decoders was studied by Zhang and Berger =-=[8]-=-. The MD codes constructed in this paper apply to the generalized MD problem. Unfortunately, no tight achievability bounds are known for generalized MD coding. 2 Since the distortion metrics may diffe... |

88 |
Linear Algebra and Its Applications, 3rd ed.
- Strang
- 1988
(Show Context)
Citation Context ...ersing the calculations in (58) The existence of such a factorization follows from the fact that any nonsingular matrix can be reduced to an identity matrix by multiplication with elementary matrices =-=[56]-=-. Since our original matrix has determinant , it can be represented as the product of the following three types of elementary matrices: • , to subtract a multiple of row from row ; • , to exchange row... |

80 | Tradeoff between source and channel coding,
- Hochwald, Zeger
- 1997
(Show Context)
Citation Context ...ould also be noted that there is a substantial literature on the error sensitivity of compressed data and more generally on tradeoffs between source and channel coding. The reader is referred to [28]–=-=[32]-=- for a sampling of the results. B. Theoretical Bounds for a Memoryless Gaussian Source The achievable rate-distortion region is completely known only for a memoryless Gaussian source with mean-squared... |

71 |
Redudancy Rate-Distortion Analysis of Multiple Description Coding Using Pairwise Correlating Transforms.
- Orchard, Wang, et al.
- 1997
(Show Context)
Citation Context ...source coding is introduced. This is a generalization to more arbitrary transforms of a technique for two channels (or packets, or descriptions) introduced by Orchard, Wang, Vaishampayan, and Reibman =-=[1]-=-. The organization of the paper is as follows. First, MD coding and its connection to packet communication are described in the remainder of this section. Then, in Section II, a few theoretical and pr... |

71 | Multiple description transform coding of images.
- Goyal, Kovaceric, et al.
- 1998
(Show Context)
Citation Context ...r MD coding; their image coding results appear in [10]. (No image coding results appear in their later papers [1], [11].) Image coding results using the generalized framework presented here appear in =-=[15]-=-. These experiments indicate the expected behavior: at the expense of a slight increase in bit rate, image representations can be made more robust to packet losses. Conventional channel codes adding s... |

69 | Linear Algebra and its Applications, Third Edition, - Strang - 1988 |

67 | Source coding for multiple descriptions - Wolf, Wyner, et al. - 1980 |

62 | The rate-distortion region for multiple descriptions without excess rate
- Ahlswede
- 1985
(Show Context)
Citation Context ...te region later published in [2]. Ozarow’s contribution was to show the tightness of the El Gamal–Cover region for memoryless Gaussian sources and squared-error distortion [5]. Subsequently, Ahlswede =-=[21]-=- showed that the El Gamal–Cover region is tight in the “no excess rate sum” case (where there is equality in (1)), and Zhang and Berger [8] showed that this region is not tight when there is excess ra... |

54 | Optimal multiple description transform coding of Gaussian vectors
- Goyal, Kovačević
- 1998
(Show Context)
Citation Context ...levant. A recent surge of interest in MD coding seems to be due primarily to this application (see [1], [9]–[12]) and yet the present work was among the first to effectively use more than two packets =-=[13]-=-–[17]. Retransmission of lost packets, when feasible, is an effective technique for maintaining constant quality despite losses. The use of a retransmission protocol, such as TCP [18], requires at a m... |

54 | Sphere packings, lattices and groups, volume 290 of Grundlehren der Mathematischen Wissenschaften - Conway, Sloane - 1999 |

51 | Self-synchronizing Huffman codes - Ferguson, Rabinowitz - 1984 |

49 | M.: Multiple description transform coding: Robustness to erasures using tight frame expansions
- Goyal, Kovačević, et al.
- 1998
(Show Context)
Citation Context ...Vaishampayan use the term MD transform coding (MDTC) to refer to MDSQ applied to coefficients from an orthogonal transform. The same term could be used to describe the techniques developed here or in =-=[14]-=-, [16], [17]; however, to avoid confusion the term MD correlating transform (MDCT) is used for the present technique. 2) Pairwise Correlating Transforms: A considerably different approach to MD coding... |

42 | Gaussian Codes and Shannon Bounds for Multiple Descriptions.
- Zamir
- 1999
(Show Context)
Citation Context ...ch more impact if dedicated to reducing the side distortion than if dedicated to reducing the central distortion. The rate-distortion region is not completely known for any non-Gaussian source. Zamir =-=[34]-=- has found inner and outer bounds to the achievable rate region for MD coding of any continuous-valued memoryless source with squared-error distortion. This is an extension of Shannon’s bounds on rate... |

41 | Quantized frame expansions as source-channel codes for erasures using tight frame expansions
- Goyal, Kovacević, et al.
- 1998
(Show Context)
Citation Context ...mpayan use the term MD transform coding (MDTC) to refer to MDSQ applied to coefficients from an orthogonal transform. The same term could be used to describe the techniques developed here or in [14], =-=[16]-=-, [17]; however, to avoid confusion the term MD correlating transform (MDCT) is used for the present technique. 2) Pairwise Correlating Transforms: A considerably different approach to MD coding was i... |

39 | Asymptotic Analysis of Multiple Description Quantizers.
- Vaishampayan, Batllo
- 1998
(Show Context)
Citation Context ...gh rates, all the decay exponent tradeoffs discussed in Section II-B can be obtained. Furthermore, the factor by which the distortion product exceeds the bounds of Theorem 1 is approximately constant =-=[40]-=-. For and , the bound for large rates is approximately 6 There is no “central encoder,” but and effectively implement a quantizer with cells given by the intersections of the cells of the individual q... |

37 |
Design of EntropyConstrained Multiple-Description Scalar Quantizers.
- Vaishampayan, Domaszewicz
- 1994
(Show Context)
Citation Context ..., the central distortion is smaller—at the cost of higher side distortions—than for an MDSQ as in Fig. 3(a). The optimal design for fixed-rate MDSQ in [37] was extended to entropy-constrained MDSQ in =-=[39]-=-. One of the most satisfying aspects of the theory of MDSQ is that at high rates, all the decay exponent tradeoffs discussed in Section II-B can be obtained. Furthermore, the factor by which the disto... |

35 |
Dpcm system design for diversity systems with application to packetized speech.
- Ingle, Vaishampayan
- 1995
(Show Context)
Citation Context ...ain the analogy with the classical MD problem and because the source coding in that case is irrelevant. A recent surge of interest in MD coding seems to be due primarily to this application (see [1], =-=[9]-=-–[12]) and yet the present work was among the first to effectively use more than two packets [13]–[17]. Retransmission of lost packets, when feasible, is an effective technique for maintaining constan... |

30 | Asymptotic Performance of Multiple Description Transform Codes.
- Batllo, Vaishampayan
- 1997
(Show Context)
Citation Context ...in providing useful operating points for low base rates and redundancies. Applications of MDSQ are described in [9], [42], [12]. Joint optimization of an orthogonal transform and MDSQ is discussed in =-=[43]-=-. For the purposes of this paper, it is sufficient to note that an identity transform is optimal for a source vector with independent components. Note that Batllo and Vaishampayan use the term MD tran... |

30 | Optimal pairwise correlating transforms for multiple description coding - Wang, Orchard, et al. - 1998 |

30 | Error recovery for variables length codes - Maxted, Robinson - 1985 |

28 | Transform coding with backward adaptive updates
- Goyal, Zhuang, et al.
(Show Context)
Citation Context ... justified by high-resolution analysis. As long as the rate allocated to the lower variance component is at least about 1 bit/sample, an optimal rate allocation only negligibly reduces the distortion =-=[45]-=-. Fig. 6. Correlating transform structure for MD coding of a two-tuple source. and then computing the transform with intermediate roundings (15) The properties of are described in Appendix I. Though n... |

26 |
Multiple Description Source Coding with No Excess Marginal Rate.
- Zhang, Berger
- 1995
(Show Context)
Citation Context ...region is not tight when there is excess rate. The complementary situation, where (2) and (3) hold with equality, is called the “no excess marginal rate” case and was also studied by Zhang and Berger =-=[22]-=-. MD coding includes as a special case the better known successive refinement or multiresolution coding. The successive refinement problem can also be described by Fig. 1, but the interest is only in ... |

25 |
Capacity definitions and coding strategies for general channels with receiver side information
- Effros, Goldsmith
- 1998
(Show Context)
Citation Context ... For this reason, “description,” “channel,” and “packet” have been used interchangeably. However, this is not the only communication environment in which MD coding may be useful. Effros and Goldsmith =-=[52]-=- have studied the various notions of capacity for general time-varying channels. One of their results is that more information can be reliably received than can be reliably transmitted. With some thou... |

24 | Communication Networks: A First Course - Walrand, J - 1998 |

23 |
On Source Networks with Minimal Breakdown Degradation.
- Witsenhausen
- 1980
(Show Context)
Citation Context ...ecoders (the side decoders) receive information only over their respective channels. The transmission rate over channel is denoted by , ; i.e., signaling over channel uses at most 1 We may infer from =-=[3]-=-–[5] and private communications that the problem originated with Gersho and Witsenhausen. Gersho proposed a scheme (unpublished [6]) that utilized the redundancy in coded speech waveforms to mitigate ... |

22 | Beyond traditional transform coding - Goyal - 1998 |

18 |
Low-delay communication for Rayleigh fading channels: an application of the multiple description quantizer
- Yang, Vaishampayan
- 1995
(Show Context)
Citation Context ...perating points. (a) Central distortion h aP . (b) Central distortion h aP . UMDSQ in providing useful operating points for low base rates and redundancies. Applications of MDSQ are described in [9], =-=[42]-=-, [12]. Joint optimization of an orthogonal transform and MDSQ is discussed in [43]. For the purposes of this paper, it is sufficient to note that an identity transform is optimal for a source vector ... |

17 | Multiple description perceptual audio coding with correlating transforms
- Arean, Kovacevic, et al.
- 2000
(Show Context)
Citation Context ...tual Audio Coder (PAC) [50]. Experiments confirm that the new MD audio coder is robust and gracefully degrades as the number of lost packets increases. The implementation and results are described in =-=[51]-=-. Since the results cannot be adequately conveyed numerically or visually, the reader is invited to hear them. Audio files are provided on-line in aiff, wave, and next formats at http: //cm.bell-labs.... |

15 | MultipleDescription wavelet based image coding
- Servetto, Ramchandran, et al.
- 1998
(Show Context)
Citation Context ...the analogy with the classical MD problem and because the source coding in that case is irrelevant. A recent surge of interest in MD coding seems to be due primarily to this application (see [1], [9]–=-=[12]-=-) and yet the present work was among the first to effectively use more than two packets [13]–[17]. Retransmission of lost packets, when feasible, is an effective technique for maintaining constant qua... |

15 | To compress or not to compress - Buch, Burkert, et al. - 1996 |

14 |
Single and Multiple Description Transform Coding With Bases and Frames
- Goyal
- 2002
(Show Context)
Citation Context ... increase in the rate of decay of . The second way to interpret the tradeoff between central and side distortion begins with rearranging (5), under the assumption of equal side distortion , to obtain =-=[33]-=- Now separate the coding rate into a base rate and a redundancy . The base rate corresponds to the quality of the joint description and the redundancy is the additional rate added to make the side dis... |

14 |
Transform Coding with Integer-to-Integer Transforms
- Goyal
(Show Context)
Citation Context ..., where for minimum rate @& aHAthe optimal transform is unique up to reflections and permutations of coordinates. Uses for the extra design freedom in using discrete transforms are discussed in [47], =-=[48]-=-.sGOYAL AND KOVAČEVIĆ: GENERALIZED MULTIPLE DESCRIPTION CODING WITH CORRELATING TRANSFORMS 2209 formance. It can be shown that transforms of this form are in the optimal set only when or . Another spe... |

13 |
The perceptual audio coder
- Sinha, Johnson, et al.
- 1998
(Show Context)
Citation Context ...ith one or two components lost. Removing restrictions further by allowing a general R 2 R transform allows a further decrease in two-erasure distortion. coder: Bell Labs’ Perceptual Audio Coder (PAC) =-=[50]-=-. Experiments confirm that the new MD audio coder is robust and gracefully degrades as the number of lost packets increases. The implementation and results are described in [51]. Since the results can... |

9 |
Multilevel source coding and data transmission theorem
- Koshelev
- 1978
(Show Context)
Citation Context ...only in characterizing achievable . In other words, no attempt is made to estimate the source from channel 2 alone; or channel 1 is always present. Successive refinement was first studied by Koshelev =-=[23]-=-–[25]. The conditions for perfect successive refinement—where (1) and (2) hold with equality—are described in [26]. The result follows from the tightness of the achievable region of [2] for the no exc... |

9 | The multiple description rate region for high resolution source coding - Linder, Zamir, et al. - 1998 |

7 |
evaluation of the average distortion for discrete scheme of sequential approximation,” Probl
- “An
- 1981
(Show Context)
Citation Context ...in characterizing achievable . In other words, no attempt is made to estimate the source from channel 2 alone; or channel 1 is always present. Successive refinement was first studied by Koshelev [23]–=-=[25]-=-. The conditions for perfect successive refinement—where (1) and (2) hold with equality—are described in [26]. The result follows from the tightness of the achievable region of [2] for the no excess r... |

7 |
Ecient Error-Limiting Variable-Length Codes
- Neumann
- 1962
(Show Context)
Citation Context ...it should also be noted that there is a substantial literature on the error sensitivity of compressed data and more generally on tradeoffs between source and channel coding. The reader is referred to =-=[28]-=-–[32] for a sampling of the results. B. Theoretical Bounds for a Memoryless Gaussian Source The achievable rate-distortion region is completely known only for a memoryless Gaussian source with mean-sq... |

7 | The perceptual audio coder (PAC),” - Sinha, Johnston, et al. - 1998 |

6 |
The channel splitting problem and Modulo-PCM coding. Bell Labs Memo for Record (not archived
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- 1979
(Show Context)
Citation Context ...by , ; i.e., signaling over channel uses at most 1 We may infer from [3]–[5] and private communications that the problem originated with Gersho and Witsenhausen. Gersho proposed a scheme (unpublished =-=[6]-=-) that utilized the redundancy in coded speech waveforms to mitigate the effects of a channel breakdown. Witsenhausen recognized that the achievable distortions are better than one might guess, even f... |

5 |
The channel splitting problem with interpolative coders
- Reudink
- 1980
(Show Context)
Citation Context ...ional central decoder that makes use of both descriptions. This approach was expounded and popularized by Vaishampayan [37], though Reudink introduced very similar methods in earlier unpublished work =-=[38]-=-. The simplest example is to have scalar quantizers with nested thresholds, as shown in Fig. 3(a). Each quantizer outputs an index that can be used by itself to estimate the source sample. Using : , ,... |

4 | Manipulating rates, complexity, and error-resilience with discrete transforms
- Goyal, Vetterli
- 1998
(Show Context)
Citation Context ...sforms, where for minimum rate @& aHAthe optimal transform is unique up to reflections and permutations of coordinates. Uses for the extra design freedom in using discrete transforms are discussed in =-=[47]-=-, [48].sGOYAL AND KOVAČEVIĆ: GENERALIZED MULTIPLE DESCRIPTION CODING WITH CORRELATING TRANSFORMS 2209 formance. It can be shown that transforms of this form are in the optimal set only when or . Anoth... |

4 |
cosine transforms in signal processing
- Hong, Fourier, et al.
- 1993
(Show Context)
Citation Context .... APPENDIX I PSEUDOLINEAR DISCRETE TRANSFORMS Invertible discrete-domain to discrete-domain transforms are alternatively described as reversible, integer-to-integer, or invertible in finite precision =-=[53]-=-–[55]. These transforms are based on factorizations of matrices which make information flow in a simple, regular way. Inversion can then be achieved by reversing the information flow. For example, one... |

4 | Error protection of wavelet coded images using residual source redundancy - Sherwood, Zeger - 1997 |

2 |
Communication Networks: A First Course, 2nd ed
- Walrand
- 1998
(Show Context)
Citation Context ...than two packets [13]–[17]. Retransmission of lost packets, when feasible, is an effective technique for maintaining constant quality despite losses. The use of a retransmission protocol, such as TCP =-=[18]-=-, requires at a minimum that a feedback channel is available to indicate which packets have been successfully received. Even if feedback is available, many factors may preclude the retransmission of l... |

1 |
Minimizing the worst-case distortion in channel splitting
- Witsenhausen
- 1981
(Show Context)
Citation Context ...owered because the sum of the rates of the received channels must be at least one.) This bound is achieved by using truncated Reed–Solomon codes. A similar result holds in the more general setting of =-=[7]-=-. The situation with three channels and seven decoders was studied by Zhang and Berger [8]. The MD codes constructed in this paper apply to the generalized MD problem. Unfortunately, no tight achievab... |

1 | pairwise correlating transforms for multiple description coding - “Optimal - 1998 |

1 |
traditional transform coding
- “Beyond
- 1998
(Show Context)
Citation Context ...robustness is implied by a low variance of squared error or, equivalently, low expected fourth power of the Euclidean norm of the error. The balanced-rate transforms (38) give this desirable property =-=[49]-=-. Another benefit of the balanced-rate transforms is that the descriptions are identically distributed; the same entropy code can be applied to each, reducing memory requirements [48]. D. Modification... |

1 | Redundancy rae-disortion analysis of multiple description coding using pairwise correlating transforms - Orchard, Wang, et al. - 1997 |

1 | Tradeoff bewveen source and channel coding - Hochwald, Zeger - 1997 |

1 | Addendum to "Successive refinement of information - Equitz, Cover - 1993 |

1 | Corrections and additions to "Error recovery for variable length codes - Monaco, Lawlet - 1987 |