Constellation Shaping, Nonlinear Precoding, and Trellis Coding for Voiceband Telephone Channel Modems

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.- 3.8. Weight Distributions and Error Correction Properties.- 3.9. Trellis Coded Modulation (TCM).- 3.10. Brief Review of the Viterbi Decoding Algorithm.- 3.11. The Fundamental Coding Gain of a Trellis Code.- 4. Trellis Shaping.- 4.1. Trellis Shaping Based on Lattice Partitions.- 4.2. Trellis Shaping on Regions.- 5. Nonlinear Precoding Methods to Remove Intersymbol Interference.- 5.1. Tomlinson/Harashima Precoding.- 5.2. LTF/Motorola/GDC Precoding.- 5.3. Precoding and Noise Whitening.- 6. Trellis Precoding.- 6.1. Trellis Precoding Based on Shaping on Regions.- 6.2. Trellis Precoding Based on Lattice Partitions and Linear Codes.- 6.3. Experimental Performance Results.- 7. Mapping Data to Channel Symbol Frames by a Modulus Encoder.- 7.1. The AT&T Fractional Bit Rate Modulus Converter.- 7.2. The V.90 Modulus Encoder.- 8. Constellation Shaping by Shell Mapping.- 8.1. General System Description.- 8.2. Ring Weights and the Number of Frames of Each Weight.- 8.3. Lexicographical Ordering of Ring Frames.- 8.4. The Decoding Algorithm.- 8.5. The Encoding Algorithm.- Appendix 8.A. Justification for the Motorola Weight Function.- Appendix 8.B. Shell Mapping Program.- 9. The Four Dimensional Constellation Used by Itu-T V.34 Modems.- 9.1. The 2D Constellation and its Partitioning.- 9.2. Framing.- 9.3. The 4D Constellation.- 10. The Combined Precoding and Trellis Coding Scheme for V.34.- 10.1. The Nonlinear Precoder.- 10.2. The Trellis Encoders.- 10.3. Viterbi Decoding of 4D Trellis Codes.- 10.4. More Details on the Wei 16-State Code.- 10.5. Using the Modulo Encoder to Make y(n) a Trellis Sequence.- 10.6. Superframe Synchronization.- 10.7. Receiver Operation.- 11. Fast Equalizer Adjustment by Using A Periodic Training Sequence.- 11.1. The V.34 Periodic Training Sequence.- 11.2. The Optimal Fractionally Spaced Equalizer.- 11.3. Finding the Initial Equalizer Taps by Using the FFT.- References.