Discrete mathematics has now established its place in most undergraduate mathematics courses. This textbook provides a concise, readable and accessible introduction to a number of topics in this area, such as enumeration, graph theory, Latin squares and designs. It is aimed at second-year undergraduate mathematics students, and provides them with many of the basic techniques, ideas and results. It contains many worked examples, and each chapter ends with a large number of exercises, with hints or solutions provided for most of them. As well as including standard topics such as binomial coefficients, recurrence, the inclusion-exclusion principle, trees, Hamiltonian and Eulerian graphs, Latin squares and finite projective planes, the text also includes material on the ménage problem, magic squares, Catalan and Stirling numbers, and tournament schedules.

6. 5 137 7 Performance of BTCs and 139 their Applications 7. 1 Introduction 139 7. 2 Some Results from the Literatures 139 7. 3 Applications of Block Turbo Codes. 142 7. 3. 1 Broadband Wireless Access Standard 144 7. 3. 2 Advanced Hardware Architectures (AHA) 145 7. 3. 3 COMTECH EF DATA 147 7. 3. 4 Turbo Concept 149 7. 3. 5 Paradise Data Com 150 Summary 7. 4 151 8 Implementation Issues 153 8. 1 Fixed-point Implementation of Turbo Decoder 153 8. 1. 1 Input Data Quantization for DVB-RCS Turbo Codes 155 8. 1. 2 Input Data Quantization for BTC 157 8. 2 The Effect of Correction Term in Max-Log-MAP Algorithm 159 8. 3 Effect of Channel Impairment on Turbo Codes 163 8. 3. 1 System Model for the Investigation of Channel Impairments 163 8. 3. 2 Channel SNR Mismatch 164 8. 3. 2. 1 Simulation Results 165 8. 3. 3 Carrier Phase Recovery 170 8. 3. 3. 1 The Effect of Phase Offset on the Performance of RM Turbo Codes 170 8. 3. 3. 2 The Effect of Preamble Size on the Performance of RM Turbo Codes 170 8. 3. 3. 3 Simulation Results 170 8. 4 Hardware Implementation of Turbo Codes 171 8. 5 Summary 175 9 177 Low Density Parity Check Codes 9. 1 Gallager Codes: Regular Binary LDPC Codes 177 9. 2 Random Block Codes 178 9. 2. 1 Generator Matrix 179 9. 2.

This work presents applications of numerical semigroups in Algebraic Geometry, Number Theory, and Coding Theory. Background on numerical semigroups is presented in the first two chapters, which introduce basic notation and fundamental concepts and irreducible numerical semigroups.

We have all experienced delays and frustrations as a result of the notorious ‘computer glitch.’ However, the more dependent we become on computational systems in our daily lives, the more we must ensure that they are safe, reliable and user-friendly.

Dieses Buch führt kompakt in einige Kerngebiete der Diskreten Mathematik ein. Es behandelt zunächst grundlegende Konzepte aus der Kombinatorik und der Graphentheorie und fokussiert anschließend in seinem methodischen Teil auf probabilistische und algebraische Techniken sowie Themen aus der Ramseytheorie. So wird den Lesenden klar, dass die Diskrete Mathematik eine spannende Disziplin mit eigenen Fragestellungen ist, die zahlreiche interessante Bezüge zu den klassischen Anfängervorlesungen hat.

The Complexity Theory Companion is an accessible, algorithmically oriented, research-centered, up-to-date guide to some of the most interesting techniques of complexity theory.

Algorithmic Principles of Mathematical Programming investigates the mathematical structures and principles underlying the design of efficient algorithms for optimization problems. Recent advances in algorithmic theory have shown that the traditionally separate areas of discrete optimization, linear programming, and nonlinear optimization are closely linked. This book offers a comprehensive introduction to the whole subject and leads the reader to the frontiers of current research.