Author | Jones, Gareth A. author |
---|---|
Title | Information and Coding Theory [electronic resource] / by Gareth A. Jones, J. Mary Jones |
Imprint | London : Springer London : Imprint: Springer, 2000 |
Connect to | http://dx.doi.org/10.1007/978-1-4471-0361-5 |
Descript | XIII, 210 p. 5 illus. online resource |
1. Source Coding -- 1.1 Definitions and Examples -- 1.2 Uniquely Decodable Codes -- 1.3 Instantaneous Codes -- 1.4 Constructing Instantaneous Codes -- 1.5 Kraftโs Inequality -- 1.6 McMillanโs Inequality -- 1.7 Comments on Kraftโs and McMillanโs Inequalities -- 1.8 Supplementary Exercises -- 2. Optimal Codes -- 2.1 Optimality -- 2.2 Binary Huffman Codes -- 2.3 Average Word-length of Huffman Codes -- 2.4 Optimality of Binary Huffman Codes -- 2.5 r-ary Huffman Codes -- 2.6 Extensions of Sources -- 2.7 Supplementary Exercises -- 3. Entropy -- 3.1 Information and Entropy -- 3.2 Properties of the Entropy Function -- 3.3 Entropy and Average Word-length -- 3.4 Shannon-Fano Coding -- 3.5 Entropy of Extensions and Products -- 3.6 Shannonโs First Theorem -- 3.7 An Example of Shannonโs First Theorem -- 3.8 Supplementary Exercises -- 4. Information Channels -- 4.1 Notation and Definitions -- 4.2 The Binary Symmetric Channel -- 4.3 System Entropies -- 4.4 System Entropies for the Binary Symmetric Channel -- 4.5 Extension of Shannonโs First Theorem to Information Channels -- 4.6 Mutual Information -- 4.7 Mutual Information for the Binary Symmetric Channel -- 4.8 Channel Capacity -- 4.9 Supplementary Exercises -- 5. Using an Unreliable Channel -- 5.1 Decision Rules -- 5.2 An Example of Improved Reliability -- 5.3 Hamming Distance -- 5.4 Statement and Outline Proof of Shannonโs Theorem -- 5.5 The Converse of Shannonโs Theorem -- 5.6 Comments on Shannonโs Theorem -- 5.7 Supplementary Exercises -- 6. Error-correcting Codes -- 6.1 Introductory Concepts -- 6.2 Examples of Codes -- 6.3 Minimum Distance -- 6.4 Hammingโs Sphere-packing Bound -- 6.5 The Gilbert-Varshamov Bound -- 6.6 Hadamard Matrices and Codes -- 6.7 Supplementary Exercises -- 7. Linear Codes -- 7.1 Matrix Description of Linear Codes -- 7.2 Equivalence of Linear Codes -- 7.3 Minimum Distance of Linear Codes -- 7.4 The Hamming Codes -- 7.5 The Golay Codes -- 7.6 The Standard Array -- 7.7 Syndrome Decoding -- 7.8 Supplementary Exercises -- Suggestions for Further Reading -- Appendix A. Proof of the Sardinas-Patterson Theorem -- Appendix B. The Law of Large Numbers -- Appendix C. Proof of Shannonโs Fundamental Theorem -- Solutions to Exercises -- Index of Symbols and Abbreviations