Fast list Viterbi decoding and application for source-channel coding of images

A list Viterbi algorithm (LVA) finds the n best paths in a trellis. We propose a new implementation of the tree-trellis LVA. Instead of storing all paths in a single sorted list, we show that it is more efficient to use several lists, where all paths of the same list have the same metric. For an integer metric, both the time and space complexity of our implementation are linear in n. Experimental results show that our implementation is much faster than all previous LVAs. This allows us to consider a large number of paths in acceptable time, which significantly improves the performance of a popular progressive source-channel coding system that protects embedded data with a concatenation of an outer error detecting code and an inner error correcting convolutional code.

[1]  R. Fossum,et al.  On Picard groups of algebraic fibre spaces , 1973 .

[2]  W. Fulton.  Introduction to Toric Varieties. , 1993 .

[3]  William A. Pearlman,et al.  A new, fast, and efficient image codec based on set partitioning in hierarchical trees , 1996, IEEE Trans. Circuits Syst. Video Technol..

[4]  Kenneth Zeger,et al.  Progressive image coding for noisy channels , 1997, IEEE Signal Processing Letters.

[5]  Ralf Hinze,et al.  Constructing Red−Black Trees , 1999 .

[6]  Hanspeter Kraft,et al.  Geometrische Methoden in der Invariantentheorie , 1984 .

[7]  D. Mumford.  The red book of varieties and schemes , 1988 .

[8]  Hanspeter Kraft,et al.  Local Properties of Algebraic Group Actions , 1989 .

[9]  Jarosław Włodarczyk,et al.  Maximal Quasiprojective Subsets and the Kleiman-Chevalley Quasiprojectivity Criterion , 1999 .

[10]  Biing-Hwang Juang,et al.  Fundamentals of speech recognition , 1993, Prentice Hall signal processing series.

[11]  Jürgen Hausen,et al.  PRODUCING GOOD QUOTIENTS BY EMBEDDING INTO TORIC VARIETIES by , 2002 .

[12]  J. S. Sadowsky.  A maximum likelihood decoding algorithm for turbo codes , 1997, GLOBECOM 97. IEEE Global Telecommunications Conference. Conference Record.

[13]  Frank K. Soong,et al.  A Tree.Trellis Based Fast Search for Finding the N Best Sentence Hypotheses in Continuous Speech Recognition , 1990, HLT.

[14]  Carl-Erik W. Sundberg,et al.  List and soft symbol output Viterbi algorithms: extensions and comparisons , 1995, IEEE Trans. Commun..

[15]  Mihai Halic.  Families of toric varieties , 2002 .

[16]  Hideyasu Sumihiro,et al.  Equivariant completion II , 1975 .

[17]  A. Białynicki-Birula,et al.  Three theorems on existence of good quotients , 1997 .

[18]  A. Bialnickibirula,et al.  On Projectivity of Good Quotients , 1995 .

[19]  Juergen Hausen.  A Hilbert-Mumford-Criterion for SL2-Actions , 2002 .

[20]  A. A'Campo-Neuen,et al.  Quotients of divisorial toric varities , 2000 .

[21]  Alexander Grothendieck,et al.  Éléments de géométrie algébrique : II. Étude globale élémentaire de quelques classes de morphismes , 1961 .

[22]  Jürgen Hausen,et al.  A generalization of Mumford's geometric invariant theory , 2001, Documenta Mathematica.

[23]  Andrzej Białynicki-Birula,et al.  On complete orbit spaces of SL(2) actions, II , 1988 .

[24]  Arne Svensson,et al.  Multi-Rate Convolutional Codes , 1998 .

[25]  G. G. Stokes.  "J." , 1890, The New Yale Book of Quotations.

[26]  Jon Callas,et al.  OpenPGP Message Format , 1998, RFC.

[27]  Carl-Erik W. Sundberg,et al.  List Viterbi decoding algorithms with applications , 1994, IEEE Trans. Commun..

[28]  Andrew J. Sommese,et al.  Quotients by C ∗ × C ∗ Actions , 1985 .

[29]  C. S. Seshadri.  Quotient Spaces Modulo Reductive Algebraic Groups , 1972 .

[30]  隅広 秀康,et al.  Equivariant Completion (代数幾何学の研究) , 1973 .

[31]  Jürgen Hausen,et al.  Equivariant Embeddings into Smooth Toric Varieties , 2000, Canadian Journal of Mathematics.

[32]  D. Birkes,et al.  Orbits on Linear Algebraic Groups , 1971 .