Enumeration encoding and decoding algorithms for pyramid cubic lattice and trellis codes

A pyramid source code is a code that assigns equal-length binary strings to all reproduction codevectors of equal (weighted) /spl epsiv//sub 1/ norm. A pyramid source encoding is partitioned into two concatenated mappings; the first from source word to reproduction codeword within a codebook; the second from the reproduction codevector to a binary string. The first mapping allows distortion and is accomplished using lattice quantization or trellis-coded quantization. The second mapping is noiseless and is denoted as enumeration. Efficient pyramid enumeration encoding and decoding algorithms are presented, for use with fixed-rate or variable-rate pyramid lattice and trellis codes.

[1]  N. J. A. Sloane,et al.  Sphere Packings, Lattices and Groups , 1987, Grundlehren der mathematischen Wissenschaften.

[2]  N. J. A. Sloane,et al.  Voronoi regions of lattices, second moments of polytopes, and quantization , 1982, IEEE Trans. Inf. Theory.

[3]  Nariman Farvardin,et al.  A structured fixed-rate vector quantizer derived from a variable-length scalar quantizer - II: Vector sources , 1993, IEEE Trans. Inf. Theory.

[4]  Michel Barlaud,et al.  Pyramidal lattice vector quantization for multiscale image coding , 1994, IEEE Trans. Image Process..

[5]  Michael W. Marcellin,et al.  On entropy-constrained trellis coded quantization , 1994, IEEE Trans. Commun..

[6]  Thomas M. Cover,et al.  Enumerative source encoding , 1973, IEEE Trans. Inf. Theory.

[7]  Allen Gersho,et al.  On the structure of vector quantizers , 1982, IEEE Trans. Inf. Theory.

[8]  Michael W. Marcellin,et al.  Trellis coded quantization of memoryless and Gauss-Markov sources , 1990, IEEE Trans. Commun..

[9]  Jerry D. Gibson,et al.  Uniform and piecewise uniform lattice vector quantization for memoryless Gaussian and Laplacian sources , 1993, IEEE Trans. Inf. Theory.

[10]  Nariman Farvardin,et al.  Trellis-based scalar-vector quantizer for memoryless sources , 1994, IEEE Trans. Inf. Theory.

[11]  N. J. A. Sloane,et al.  A fast encoding method for lattice codes and quantizers , 1983, IEEE Trans. Inf. Theory.

[12]  Thomas R. Fischer,et al.  A pyramid vector quantizer , 1986, IEEE Trans. Inf. Theory.

[13]  G. David Forney,et al.  Lattice and trellis quantization with lattice- and trellis-bounded codebooks - High-rate theory for memoryless sources , 1993, IEEE Trans. Inf. Theory.

[14]  Rosa Lancini,et al.  Video coding scheme using DCT-pyramid vector quantization , 1995, IEEE Trans. Image Process..

[15]  Jerry D. Gibson,et al.  An algorithm for uniform vector quantizer design , 1984, IEEE Trans. Inf. Theory.

[16]  J. D. Gibson,et al.  Image coding with uniform and piecewise-uniform vector quantizers , 1995, IEEE Trans. Image Process..

[17]  Thomas R. Fischer,et al.  Geometric source coding and vector quantization , 1989, IEEE Trans. Inf. Theory.

[18]  Huey-Chen Tseng,et al.  Transform and Hybrid Transform/DPCM Coding of Images Using Pyramid Vector Quantization , 1987, IEEE Trans. Commun..

[19]  Jerry D. Gibson,et al.  Distributions of the Two-Dimensional DCT Coefficients for Images , 1983, IEEE Trans. Commun..

[20]  Min Wang,et al.  Entropy-constrained trellis-coded quantization , 1992, IEEE Trans. Inf. Theory.

[21]  Nariman Farvardin,et al.  Subband Image Coding Using Entropy-Coded Quantization over Noisy Channels , 1992, IEEE J. Sel. Areas Commun..

[22]  G. David Forney,et al.  Coset codes-I: Introduction and geometrical classification , 1988, IEEE Trans. Inf. Theory.