Source and Channel Coding: An Algorithmic Approach

1 Introduction.- 1.1 The Historical Context.- 1.2 Information and Coding.- 1.3 Bandwidth and Energy.- References.- 2 Source Coding Algorithms.- 2.1 Source Coding Preliminaries.- 2.2 Applications of Noiseless Source Coding.- 2.3 Rate-Distortion Theory.- 2.4 Predictive Source Coders.- 2.5 Some Other Rate-Distortion Approaches.- Problems.- References.- 3 Error Control Coding.- 3.1 Fundamentals of Coding.- 3.2 Linear Block Codes.- 3.3 Syndrome Decoding.- 3.4 Bounds on Performance.- 3.5 Cyclic Codes.- 3.6 Decoding Cyclic Codes.- 3.7 Algebra of Finite Fields.- 3.8 The BCH Codes.- 3.9 Decoding BCH Codes.- 3.10 Reed-Solomon Codes: Algebra in Non-Binary Fields.- 3.11 Codes for Burst Error Correction.- 3.12 Automatic Repeat Request Protocols.- Problems.- References.- 4 Trellis Codes.- 4.1 Convolutional Codes.- 4.2 Trees, Trellises and the Viterbi Algorithm.- 4.3 Continuous Phase Modulation Codes.- 4.4 Set-Partition Coding.- 4.5 Intersymbol Interference Decoding.- Problems.- References.- 5 Reduced Trellises.- 5.1 Truncation of the Impulse Response.- 5.2 Partition of the Path Map Alphabet.- 5.3 Pulse Response Simplification.- Problems.- References.- 6 Sequential Coding Algorithms.- 6.1 Basics of Sequential Coding.- 6.2 Important Channel Decoding Algorithms.- 6.3 Calculation of the Search Region Boundaries.- 6.4 Number of Paths Searched.- 6.5 Other Analyses of Sequential Decoding.- 6.6 Algorithm Steps.- 6.7 Source Coding Revisited.- Problems.- References.- 7 Architectures for Coding Algorithms.- 7.1 Parallel Architectures and Algorithms.- 7.2 Architectures for the M-Algorithm.- 7.3 Architectures for the Viterbi Algorithm.- Problems.- References.- APPENDICES.- A Signal Space Theory.- B Introduction to Algebra.- C Mathematical Details of the Stop and Drop Lines.