Data Transportation and Protection

A new breed of engineer is developing in our contemporary society. These engineers are concerned with communications and computers, economics and regulation. These new engineers apply themselves to data-to its pack aging, transmission, and protection. They are data engineers. Formal curricula do not yet exist for their dedicated development. Rather they learn most of their tools "on the job" and their roots are in computer engineering, communications engineering, and applied mathe matics. There is a need to draw relevant material together and present it so that those who wish to become data engineers can do so, for the betterment of themselves, their employer, their country, and, ultimately, the world-for we share the belief that the most effective tool for world peace and stability is neither politics nor armaments, but rather the open and timely exchange of information. This book has been written with that goal in mind. Today numerous signs encourage us to expect broader information exchange in the years to come. The movement toward a true Integrated Services Digital Network (ISDN) is perhaps the clearest of these. Also, the development offormal protocol layers reflects both a great deal of brilliance and compromise and also the desire for a common language among data engineers.

Contenu

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 Bene-Waksman Permutation Network.- 13.7. The Perfect Shuffle Network Revisited.- References.- 14. Network Reliability and Survivability.- References.