Constellation Shaping, Nonlinear Precoding, and Trellis Coding for Voiceband Telephone Channel Modems: with Emphasis on ITU-T Recommendation V.34 [Hardcover]

This book is an excellent reference for those working in the broad fields of communication theory, information theory, and modem design. It is essential for researchers in modulation and coding for voiceband telephone line modems; signal constellation design; nonlinear precoding for modems; and trellis coding.
The author presents the theory behind the new modulation and coding techniques included in ITU-T Recommendation V.34. Topics discussed include signal constellation shaping by shell mapping, nonlinear precoding, four-dimensional trellis codes, and fast equalizer training by using periodic sequences and FFT methods. In addition, several approaches that were considered but not accepted are presented including trellis shaping, trellis precoding, and modulus conversion.1. Basics of Lattice Theory.- 1.1. Definition of a Lattice.- 1.2. Examples of Lattices.- 1.3. Sublattices. Lattice Partitions, and Cosets.- 1.4. Binary Lattices and Coset Representatives.- 1.5. Fundamental Regions and Volumes, and Voronoi Regions.- 1.6. Point Spacing, Weight Distributions, and Theta Series.- 1.7. Fundamental Coding Gain.- 2. Performance Measures for Multidimensional Constellations.- 2.1. Introduction.- 2.2. Constellation Figure of Merit and Symbol Error Probabilities.- 2.3. Constituent 2D Constellations and Constellation Expansion Ratio.- 2.4. Peak-to-Average Power Ratio.- 2.5. Representing CFM(C) in Terms of Coding Gain and Shaping Gain.- 2.6. Coding and Shaping Factors of the Constellation Expansion Ratio.- 2.7. Factors of the Peak-to-Average Power Ratio.- 2.8. Optimum Tradeoffs of Shaping Gain with CERS and PAR.- 3. Principles of Convolutional and Trellis Codes.- 3.1. The Huffman D-Transform.- 3.2. Transfer Functions and Realizations.- 3.3. Description of a Convolutional Code by its Generator Matrix.- 3.4. Systematic Form of a Convolutional Code.- 3.5. The Parity Check Matrix and Syndromes.- 3.6. Inverse Check Matrix or Inverse Syndrome Former.- 3.7. The Code Trellis.- 3.lSv