Source Coding: Part I of Fundamentals of Source and Video Coding

Digital media technologies have become an integral part of the way we create, communicate, and consume information. At the core of these technologies are source coding methods that are described in this monograph. Based on the fundamentals of information and rate distortion theory, the most relevant techniques used in source coding algorithms are described: entropy coding, quantization as well as predictive and transform coding. The emphasis is put onto algorithms that are also used in video coding, which will be explained in the other part of this two-part monograph.

[1]  U. Grenander,et al.  Toeplitz Forms And Their Applications , 1958 .

[2]  Robert M. Gray,et al.  An Algorithm for Vector Quantizer Design , 1980, IEEE Trans. Commun..

[3]  ROBERT M. GRAY.  Asymptotically Optimal Quantizers , 2008 .

[4]  C. Jacobi.  Über ein leichtes Verfahren die in der Theorie der Säcularstörungen vorkommenden Gleichungen numerisch aufzulösen*). , 2022 .

[5]  P. F. Panter,et al.  Quantization distortion in pulse-count modulation with nonuniform spacing of levels , 1951, Proceedings of the IRE.

[6]  Michelle Effros,et al.  Suboptimality of the Karhunen-Loève Transform for Transform Coding , 2004, IEEE Trans. Inf. Theory.

[7]  Bruno O. Shubert,et al.  Random variables and stochastic processes , 1979 .

[8]  Lee D. Davisson,et al.  An Introduction To Statistical Signal Processing , 2004 .

[9]  S. P. Lloyd,et al.  Least squares quantization in PCM , 1982, IEEE Trans. Inf. Theory.

[10]  Tamás Linder,et al.  On the asymptotic tightness of the Shannon lower bound , 1994, IEEE Trans. Inf. Theory.

[11]  Khalid Sayood.  Lossless Compression Handbook , 2003 .

[12]  Philip A. Chou,et al.  Entropy-constrained vector quantization , 1989, IEEE Trans. Acoust. Speech Signal Process..

[13]  Simon Haykin,et al.  Optimally adaptive transform coding , 1995, IEEE Trans. Image Process..

[14]  David L. Neuhoff,et al.  Quantization , 2022, IEEE Trans. Inf. Theory.

[15]  Peter No,et al.  Digital Coding of Waveforms , 1986 .

[16]  Vivek K. Goyal,et al.  Transform coding with backward adaptive updates , 2000, IEEE Trans. Inf. Theory.

[17]  Robert M. Gray,et al.  High-resolution quantization theory and the vector quantizer advantage , 1989, IEEE Trans. Inf. Theory.

[18]  David A. Huffman,et al.  A method for the construction of minimum-redundancy codes , 1952, Proceedings of the IRE.

[19]  R. R. Clarke.  Transform coding of images , 1985 .

[20]  Mark Handley,et al.  SIP: Session Initiation Protocol , 1999, RFC.

[21]  Suguru Arimoto,et al.  An algorithm for computing the capacity of arbitrary discrete memoryless channels , 1972, IEEE Trans. Inf. Theory.

[22]  Glen G. Langdon,et al.  Arithmetic Coding , 1979 .

[23]  Serap A. Savari,et al.  Generalized Tunstall codes for sources with memory , 1997, IEEE Trans. Inf. Theory.

[24]  J G Daugman,et al.  Information Theory and Coding , 2005 .

[25]  Abraham Lempel,et al.  A universal algorithm for sequential data compression , 1977, IEEE Trans. Inf. Theory.

[26]  Vivek K Goyal.  High-rate transform coding: how high is high, and does it matter? , 2000, 2000 IEEE International Symposium on Information Theory (Cat. No.00CH37060).

[27]  Ian H. Witten,et al.  Arithmetic coding for data compression , 1987, CACM.

[28]  Itu-T and Iso Iec Jtc.  Advanced video coding for generic audiovisual services , 2010 .

[29]  Richard E. Blahut,et al.  Computation of channel capacity and rate-distortion functions , 1972, IEEE Trans. Inf. Theory.

[30]  D. J. Wheeler,et al.  A Block-sorting Lossless Data Compression Algorithm , 1994 .

[31]  Yair Shoham,et al.  Efficient bit allocation for an arbitrary set of quantizers [speech coding] , 1988, IEEE Trans. Acoust. Speech Signal Process..

[32]  T. Berger.  Rate-Distortion Theory , 2003 .

[33]  Jelena Kovacevic,et al.  Wavelets and Subband Coding , 2013, Prentice Hall Signal Processing Series.

[34]  Henrique S. Malvar,et al.  Signal processing with lapped transforms , 1992 .

[35]  Ricardo L. de Queiroz,et al.  LAPPED TRANSFORMS FOR IMAGE COMPRESSION , 1999 .

[36]  Athanasios Papoulis,et al.  Probability, Random Variables and Stochastic Processes , 1965 .

[37]  N. Ahmed,et al.  Discrete Cosine Transform , 1996 .

[38]  Henning Schulzrinne,et al.  RTP: A Transport Protocol for Real-Time Applications , 1996, RFC.

[39]  Heiko Schwarz,et al.  Probability Interval Partitioning Entropy Codes , 2010 .

[40]  Richard Clark Pasco,et al.  Source coding algorithms for fast data compression , 1976 .

[41]  R. Gallager.  Information Theory and Reliable Communication , 1968 .

[42]  Martin Vetterli,et al.  Wavelets, approximation, and compression , 2001, IEEE Signal Process. Mag..

[43]  Jorma Rissanen,et al.  Generalized Kraft Inequality and Arithmetic Coding , 1976, IBM J. Res. Dev..

[44]  Colmas Goldberg.  Information Rates of Gaussian Signals Under Criteria Constraining the Error Spectrum , 1964 .

[45]  Robert M. Gray,et al.  Toeplitz and Circulant Matrices: A Review , 2005, Found. Trends Commun. Inf. Theory.

[46]  Robert M. Gray,et al.  Toeplitz And Circulant Matrices: A Review (Foundations and Trends(R) in Communications and Information Theory) , 2006 .

[47]  Thomas Eriksson,et al.  Vector Quantization in Speech Coding. Variable Rate, Memory and Lattice Quantization , 1996 .

[48]  Aarnout Brombacher,et al.  Probability... , 2009, Qual. Reliab. Eng. Int..

[49]  Robert M. Gray,et al.  Linear Predictive Coding and the Internet Protocol , 2010 .

[50]  Robert M. Gray,et al.  Asymptotically optimal quantizers (Corresp.) , 1977, IEEE Trans. Inf. Theory.

[51]  Heiko Schwarz,et al.  Context-based adaptive binary arithmetic coding in the H.264/AVC video compression standard , 2003, IEEE Trans. Circuits Syst. Video Technol..

[52]  Iso/iec 14496-2 Information Technology — Coding of Audio-visual Objects — Part 2: Visual , 2022 .

[53]  A. N. Kolmogorov,et al.  Foundations of the theory of probability , 1960 .

[54]  Brian Parker Tunstall,et al.  Synthesis of noiseless compression codes , 1967 .

[55]  Bryan E. Usevitch,et al.  A Tutorial on Modern Lossy Wavelet Image Compression:of JPEG 2000 , 2001 .

[56]  Robert M. Gray,et al.  Random processes : a mathematical approach for engineers , 1986 .

[57]  Ian H. Witten,et al.  Arithmetic coding revisited , 1998, TOIS.

[58]  G. Golub,et al.  Eigenvalue computation in the 20th century , 2000 .

[59]  Michael W. Marcellin,et al.  JPEG2000 - image compression fundamentals, standards and practice , 2002, The Kluwer International Series in Engineering and Computer Science.

[60]  K. H. Barratt.  Digital Coding of Waveforms , 1985 .

[61]  Allen Gersho,et al.  Vector quantization and signal compression , 1991, The Kluwer international series in engineering and computer science.

[62]  J. Makhoul,et al.  Linear prediction: A tutorial review , 1975, Proceedings of the IEEE.

[64]  Pao-Chi Chang,et al.  Gradient algorithms for designing predictive vector quantizers , 1986, IEEE Trans. Acoust. Speech Signal Process..

[65]  JACOB BINIA,et al.  On the Epsilon -entropy and the rate-distortion function of certain non-Gaussian processes , 1974, IEEE Trans. Inf. Theory.

[66]  P. P. Vaidyanathan,et al.  The Theory of Linear Prediction , 2008, Synthesis Lectures on Signal Processing.

[67]  Robert G. Gallager,et al.  Variations on a theme by Huffman , 1978, IEEE Trans. Inf. Theory.

[68]  Sang Joon Kim,et al.  A Mathematical Theory of Communication , 2006 .

[69]  Vivek K. Goyal,et al.  Theoretical foundations of transform coding , 2001, IEEE Signal Process. Mag..

[70]  Herbert Gish,et al.  Asymptotically efficient quantizing , 1968, IEEE Trans. Inf. Theory.

[71]  Joel Max,et al.  Quantizing for minimum distortion , 1960, IRE Trans. Inf. Theory.

[72]  Thomas M. Cover,et al.  Elements of Information Theory , 2005 .

[73]  Aaron D. Wyner,et al.  Coding Theorems for a Discrete Source With a Fidelity CriterionInstitute of Radio Engineers, International Convention Record, vol. 7, 1959. , 1993 .

[74]  R. Gray.  Source Coding Theory , 1989 .