1. DataIts Representation and Manipulation. - 1. 1. Introduction. - 1. 2. Number Systems. - 1. 3. Negabinary Numbers. - 1. 4. The Factorial Number System. - 1. 5. The Gray Code. - 1. 6. A Look at Boolean Functions. - References. - 2. Counting and Probability. - 2. 1. Counting. - 2. 2. Generating Functions. - 2. 3. Permutations. - 2. 4. Combinations. - 2. 5. Recurrence Relations/Difference Equations. - 2. 6. Probability. - 2. 7. Generating Functions in Probability Theory. - 2. 8. The Bernoulli Source. - 2. 9. Some Important and Famous Problems. - 2. 10. Random Mappings. - 2. 11. Redundancy and the Perfect Voter. - 2. 12. Bias. - 2. 13. Maximum Likelihood Estimation. - References. - 3. The Natural Numbers and Their Primes. - 3. 1. Introduction. - 3. 2. Finding Primes: I. - 3. 3. The Euclidean Algorithm. - 3. 4. Congruences. - 3. 5. Residue Sets. - 3. 6. Reduced Residue Sets. - 3. 7. The Euler-Fermat Theorem. - 3. 8. Wilson's Theorem. - 3. 9. The Function ?. - 3. 13. 1. An Example of the Split-Search Algorithm. - 3. 14. The Chinese Remainder Theorem. - 3. 15. Finding Primes: II. - References. - 4. Basic Concepts in Matrix Theory. - 4. 1. Introduction. - 4. 2. Concept of a Field and a Group. - 4. 3. Basic Definitions. - 4. 4. Matrix Operations. - 4. 5. Partitioned Matrices. - 4. 6. Inverses of Matrices. - References. - 5. Matrix Equations and Transformations. - 5. 1. Introduction. - 5. 2. Linear Vector Spaces. - 5. 3. Gram-Schmidt Process. - 5. 4. Solutions of Equations. - 5. 5. Solutions of Overdetermined Systems. - 5. 6. Normal Matrices. - 5. 7. Discrete Transforms. - References. - 6. Matrix Representations. - 6. 1. Introduction. - 6. 2. Eigenvalue Problem. - 6. 3. Diagonal Representation of Normal Matrices. - 6. 4. Representations of Nondiagonable Matrices. - 6. 5. Circulant Matrix and Its Eigenvectors. - 6. 6. Simple Functions of Matrices. - 6. 7. Singular ValueDecomposition. - 6. 8. Characteristic Polynomials. - 6. 9. Minimal Polynomial. - 6. 10. Powers of Some Special Matrices. - 6. 11. Matrix Norms. - References. - 7. Applications of Matrices to Discrete Data System Analysis. - 7. 1. Introduction. - 7. 2. Discrete Systems. - 7. 3. Discrete Convolution. - 7. 4. Discrete Deconvolution. - 7. 5. Linear Constant-Coefficient Difference Equations. - 7. 6. Matrix Representation of an Nth-Order Constant-Coefficient Difference Equation. - 7. 7. Solutions of an Nth-Order Difference Equation Using a State Model Representation. - 7. 8. Transfer Functions: An Introduction to Z Transforms. - 7. 9. Observability Problem. - References. - 8. Random and Pseudorandom Sequences. - 8. 1. Introduction. - 8. 2. Markov Chains. - 8. 3. m-Sequences (Hershey 1982). - References. - 9. Source Encoding. - 9. 1. Introduction. - 9. 2. Generalized Bernoulli Source. - 9. 3. Unique Decodability. - 9. 4. Synchronizable Codes. - 9. 5. Information Content of a Bernoulli Source. - 9. 6. The Huffman Code. - 9. 6. 1. Connell's Method of Coding. - 9. 7. Source Extension and Its Coding. - 9. 8. Run Length Encoding. - 9. 9. Encoding to a Fidelity Criterion. - References. - 10. Information Protection. - 10. 1. Classical Cryptography. - 10. 2. Public Key Cryptography. - 10. 3. Secret Sharing Systems. - References. - 11. Synchronization. - 11. 1. Introduction. - 11. 2. Epoch Synchronization. - 11. 3. Phase Synchronization. - References. - 12. The Channel and Error Control. - 12. 1. Introduction. - 12. 2. A Channel Model. - 12. 3. The Simplest Hamming Code. - 12. 4. The Hamming CodeAnother Look. - 12. 5. The z-Channel and a Curious Result. - 12. 6. The Data Frame Concept. - 12. 7. A Curious Problem. - 12. 8. Estimation of Channel Parameters. - References. - 13. Space Division Connecting Networks. - 13. 1. Introduction. - 13. 2. Complete Permutation Networks. -13. 3. The Clos Network. - 13. 4. A Rearrangeable Connecting Network and Paull's Algorithm. - 13. 5. The Perfect Shuffle and the Omega Network. - 13. 6. The Beneš-Waksman Permutation Network. - 13. 7. The Perfect Shuffle Network Revisited. - References. - 14. Network Reliability and Survivability. - References. Language: English