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    5. The Art of Error Correcting Coding Second Edition

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    6. Information Theory and Network Coding (2008)

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      Information Theory and Network Coding (2008) Table of Contents 1 The Science of Information . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 Part I Components of Information Theory 2 Information Measures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 2.1 Independence and Markov Chains . . . . . . . . . . . . . . . . . . . . . . . . . 7 2.2 Shannon’s Information Measures . . . . . . . . . . . . . . . . . . . . . . . . . . 12 2.3 Continuity of Shannon’s Information Measures for Fixed Finite Alphabets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 2.4 Chain Rules . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 2.5 Informational Divergence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 2.6 The Basic Inequalities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 2.7 Some Useful Information Inequalities . . . . . . . . . . . . . . . . . . . . . . . 28 2.8 Fano’s Inequality . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32 2.9 Maximum Entropy Distributions . . . . . . . . . . . . . . . . . . . . . . . . . . 36 2.10 Entropy Rate of a Stationary Source . . . . . . . . . . . . . . . . . . . . . . . 38 Appendix 2.A: Approximation of Random Variables with Countably Infinite Alphabets by Truncation . . . . . . . . . . . . . . . . 41 Chapter Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43 Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45 Historical Notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50 3 TheI-Measure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51 3.1 Preliminaries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52 3.2 The I-Measure for Two Random Variables . . . . . . . . . . . . . . . . . . 53 3.3 Construction of the I-Measure μ* . . . . . . . . . . . . . . . . . . . . . . . . . 55 3.4 μ* Can Be Negative . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59 3.5 Information Diagrams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61 3.6 Examples of Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67 Appendix 3.A: A Variation of the Inclusion–Exclusion Formula . . . . 74 Chapter Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76 Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78 Historical Notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80 4 Zero-Error Data Compression . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81 4.1 The Entropy Bound . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81 4.2 Prefix Codes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86 4.2.1 Definition and Existence . . . . . . . . . . . . . . . . . . . . . . . . . . . 86 4.2.2 Huffman Codes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88 4.3 Redundancy of Prefix Codes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93 Chapter Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97 Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98 Historical Notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99 5 Weak Typicality . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101 5.1 The Weak AEP . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101 5.2 The Source Coding Theorem. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104 5.3 Efficient Source Coding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106 5.4 The Shannon–McMillan–Breiman Theorem . . . . . . . . . . . . . . . . . 107 Chapter Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109 Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110 Historical Notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112 6 Strong Typicality . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113 6.1 Strong AEP . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113 6.2 Strong Typicality Versus Weak Typicality . . . . . . . . . . . . . . . . . . 121 6.3 Joint Typicality . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122 6.4 An Interpretation of the Basic Inequalities . . . . . . . . . . . . . . . . . . 131 Chapter Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131 Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132 Historical Notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135 7 Discrete Memoryless Channels . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137 7.1 Definition and Capacity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141 7.2 The Channel Coding Theorem . . . . . . . . . . . . . . . . . . . . . . . . . . . . 149 7.3 The Converse . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152 7.4 Achievability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 157 7.5 A Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 164 7.6 Feedback Capacity. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 167 7.7 Separation of Source and Channel Coding . . . . . . . . . . . . . . . . . . 172 Chapter Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 175 Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 176 Historical Notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 181 8 Rate-Distortion Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 183 8.1 Single-Letter Distortion Measures . . . . . . . . . . . . . . . . . . . . . . . . . 184 8.2 The Rate-Distortion Function R(D) . . . . . . . . . . . . . . . . . . . . . . . 187 8.3 The Rate-Distortion Theorem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 192 8.4 The Converse . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 200 8.5 Achievability of RI (D) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 202 Chapter Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 207 Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 208 Historical Notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 209 9 The Blahut–Arimoto Algorithms . . . . . . . . . . . . . . . . . . . . . . . . . . 211 9.1 Alternating Optimization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 212 9.2 The Algorithms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 214 9.2.1 Channel Capacity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 214 9.2.2 The Rate-Distortion Function . . . . . . . . . . . . . . . . . . . . . . . 219 9.3 Convergence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 222 9.3.1 A Sufficient Condition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 222 9.3.2 Convergence to the Channel Capacity . . . . . . . . . . . . . . . . 225 Chapter Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 226 Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 227 Historical Notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 228 10 Differential Entropy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 229 10.1 Preliminaries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 231 10.2 Definition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 235 10.3 Joint Differential Entropy, Conditional (Differential) Entropy, and Mutual Information . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 238 10.4 The AEP for Continuous Random Variables . . . . . . . . . . . . . . . . 245 10.5 Informational Divergence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 248 10.6 Maximum Differential Entropy Distributions . . . . . . . . . . . . . . . . 249 Chapter Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 252 Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 255 Historical Notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 256 11 Continuous-Valued Channels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 257 11.1 Discrete-Time Channels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 257 11.2 The Channel Coding Theorem . . . . . . . . . . . . . . . . . . . . . . . . . . . . 260 11.3 Proof of the Channel Coding Theorem . . . . . . . . . . . . . . . . . . . . . 262 11.3.1 The Converse . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 262 11.3.2 Achievability. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 265 11.4 Memoryless Gaussian Channels . . . . . . . . . . . . . . . . . . . . . . . . . . . 270 11.5 Parallel Gaussian Channels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 272 11.6 Correlated Gaussian Channels . . . . . . . . . . . . . . . . . . . . . . . . . . . . 278 11.7 The Bandlimited White Gaussian Channel . . . . . . . . . . . . . . . . . . 280 11.8 The Bandlimited Colored Gaussian Channel . . . . . . . . . . . . . . . . 287 11.9 Zero-Mean Gaussian Noise Is the Worst Additive Noise . . . . . . . 290 Chapter Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 294 Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 296 Historical Notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 297 12 Markov Structures. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 299 12.1 Conditional Mutual Independence . . . . . . . . . . . . . . . . . . . . . . . . . 300 12.2 Full Conditional Mutual Independence . . . . . . . . . . . . . . . . . . . . . 309 12.3 Markov Random Field . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 314 12.4 Markov Chain . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 317 Chapter Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 319 Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 320 Historical Notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 321 13 Information Inequalities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 323 13.1 The Region Γ?n . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 325 13.2 Information Expressions in Canonical Form . . . . . . . . . . . . . . . . . 326 13.3 A Geometrical Framework . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 329 13.3.1 Unconstrained Inequalities . . . . . . . . . . . . . . . . . . . . . . . . . . 329 13.3.2 Constrained Inequalities . . . . . . . . . . . . . . . . . . . . . . . . . . . . 330 13.3.3 Constrained Identities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 332 13.4 Equivalence of Constrained Inequalities . . . . . . . . . . . . . . . . . . . . 333 13.5 The Implication Problem of Conditional Independence . . . . . . . 336 Chapter Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 337 Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 338 Historical Notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 338 14 Shannon-Type Inequalities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 339 14.1 The Elemental Inequalities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 339 14.2 A Linear Programming Approach. . . . . . . . . . . . . . . . . . . . . . . . . . 341 14.2.1 Unconstrained Inequalities . . . . . . . . . . . . . . . . . . . . . . . . . . 343 14.2.2 Constrained Inequalities and Identities . . . . . . . . . . . . . . . 344 14.3 A Duality . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 345 14.4 Machine Proving – ITIP . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 347 14.5 Tackling the Implication Problem. . . . . . . . . . . . . . . . . . . . . . . . . . 351 14.6 Minimality of the Elemental Inequalities . . . . . . . . . . . . . . . . . . . . 353 Appendix 14.A: The Basic Inequalities and the Polymatroidal Axioms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 356 Chapter Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 357 Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 358 Historical Notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 360 15 Beyond Shannon-Type Inequalities . . . . . . . . . . . . . . . . . . . . . . . . 361 15.1 Characterizations of Γ?2 , Γ?3 , and Γ?n . . . . . . . . . . . . . . . . . . . . . . 361 15.2 A Non-Shannon-Type Unconstrained Inequality . . . . . . . . . . . . . 369 15.3 A Non-Shannon-Type Constrained Inequality . . . . . . . . . . . . . . . 374 15.4 Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 380 Chapter Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 383 Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 383 Historical Notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 385 16 Entropy and Groups . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 387 16.1 Group Preliminaries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 388 16.2 Group-Characterizable Entropy Functions . . . . . . . . . . . . . . . . . . 393 16.3 A Group Characterization of Γ?n . . . . . . . . . . . . . . . . . . . . . . . . . . 398 16.4 Information Inequalities and Group Inequalities . . . . . . . . . . . . . 401 Chapter Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 405 Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 406 Historical Notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 408 Part II Fundamentals of Network Coding 17 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 411 17.1 The Butterfly Network . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 412 17.2 Wireless and Satellite Communications . . . . . . . . . . . . . . . . . . . . . 415 17.3 Source Separation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 417 Chapter Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 418 Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 418 Historical Notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 419 18 The Max-Flow Bound . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 421 18.1 Point-to-Point Communication Networks . . . . . . . . . . . . . . . . . . . 421 18.2 Examples Achieving the Max-Flow Bound . . . . . . . . . . . . . . . . . . 424 18.3 A Class of Network Codes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 427 18.4 Proof of the Max-Flow Bound . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 429 Chapter Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 431 Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 431 Historical Notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 434 19 Single-Source Linear Network Coding: Acyclic Networks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 435 19.1 Acyclic Networks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 436 19.2 Linear Network Codes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 437 19.3 Desirable Properties of a Linear Network Code . . . . . . . . . . . . . . 443 19.3.1 Transformation of a Linear Network Code . . . . . . . . . . . . 447 19.3.2 Implementation of a Linear Network Code . . . . . . . . . . . . 448 19.4 Existence and Construction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 449 19.5 Generic Network Codes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 460 19.6 Static Network Codes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 468 19.7 Random Network Coding: A Case Study . . . . . . . . . . . . . . . . . . . 473 19.7.1 How the System Works . . . . . . . . . . . . . . . . . . . . . . . . . . . . 474 19.7.2 Model and Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 475 Chapter Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 478 Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 479 Historical Notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 482 20 Single-Source Linear Network Coding: Cyclic Networks . . . . 485 20.1 Delay-Free Cyclic Networks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 485 20.2 Convolutional Network Codes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 488 20.3 Decoding of Convolutional Network Codes . . . . . . . . . . . . . . . . . . 498 Chapter Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 503 Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 503 Historical Notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 504 21 Multi-source Network Coding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 505 21.1 The Max-Flow Bounds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 505 21.2 Examples of Application . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 508 21.2.1 Multilevel Diversity Coding . . . . . . . . . . . . . . . . . . . . . . . . . 508 21.2.2 Satellite Communication Network . . . . . . . . . . . . . . . . . . . 510 21.3 A Network Code for Acyclic Networks . . . . . . . . . . . . . . . . . . . . . 511 21.4 The Achievable Information Rate Region . . . . . . . . . . . . . . . . . . . 512 21.5 Explicit Inner and Outer Bounds . . . . . . . . . . . . . . . . . . . . . . . . . . 515 21.6 The Converse . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 516 21.7 Achievability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 521 21.7.1 Random Code Construction . . . . . . . . . . . . . . . . . . . . . . . . 524 21.7.2 Performance Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 527 Chapter Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 536 Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 537 Historical Notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 539 Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 541 Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 561

      下载次数 2次 资源类型 技术书籍 上传时间 2013-11-16

    7. Coding Theory, A First Course

      标签:Coding Theory A First Course

      Coding Theory, A First Course 2004,Cambridge University Press Table of Contents 1. Introduction; 2. Error detection, correction and decoding; 3. Finite fields; 4. Linear codes; 5. Bounds in coding theory; 6. Constructions of linear codes; 7. Cyclic codes; 8. Some special cyclic codes; 9. Goppa codes.

      下载次数 0次 资源类型 技术书籍 上传时间 2013-11-16

    8. GPON(MOGPON)ONT模块(含原理图,PCB,测试数据)很强大

      标签:GPON MOGPON ONT

      GPON(MOGPON)ONT模块(含原理图,PCB,测试数据)很强大

      下载次数 7次 资源类型 技术书籍 上传时间 2013-11-16

    9. 通信中Viterbi算法和实现-硕士论文

      标签:通信 Viterbi算法

      通信中Viterbi算法和实现-硕士论文

      下载次数 0次 资源类型 技术书籍 上传时间 2013-11-16

    10. Understanding FFT Applications-ebook

      标签:Understanding FFT Applicationsebook

      Understanding FFT Applications-ebook

      下载次数 1次 资源类型 技术书籍 上传时间 2013-11-16

    11. 最新LDPC 译码器结构论文合集

      标签:LDPC 译码器

      最新LDPC 译码器结构论文合集 其中"A 640-Mbs 2048-bit programmable LDPC decoder chip.pdf"是经典, 全世界都在饮用这篇文章呢~~~~~~~~~~~~~~~~

      下载次数 1次 资源类型 技术书籍 上传时间 2013-11-16

    12. RF Imperfections in High-rate Wireless Systems: Impact and Digital Compensation

      标签:RF Imperfections Highrate Wireless Systems

      RF Imperfections in High-rate Wireless Systems: Impact and Digital Compensation (有书签和快捷方式) RF Imperfections in High-rate Wireless Systems Foreword xi Preface xiii 1. INTRODUCTION 1 1.1 Wireless communications 1 1.2 OFDM 3 1.3 MIMO 4 1.4 RF transceiver impairments 6 1.5 Outline of the book 9 2. MULTIPLE-ANTENNA OFDM SYSTEMS 11 2.1 Introduction 11 2.2 Channel modelling 11 2.2.1 Multipath propagation 12 2.2.2 Stochastic channel model 16 2.3 System modelling 18 2.3.1 MIMO 19 2.3.2 OFDM 22 2.3.3 MIMO OFDM 26 2.4 Conclusions 29 3. DESIGN AND IMPLEMENTATION OF A MIMO OFDM SYSTEM 31 3.1 Introduction 31 3.2 Transmission format and preamble design 32 3.2.1 IEEE 802.11a 32 3.2.2 MIMO OFDM 34 3.3 Frequency synchronisation 39 3.3.1 Influence of CFO 40 3.3.2 Algorithm description 42 3.3.3 Performance analysis 44 3.3.4 Numerical results 47 3.3.5 Summary 51 3.4 Channel estimation 52 3.4.1 Algorithm and performance analysis 52 3.4.2 Numerical results 58 3.4.3 Summary 62 3.5 Timing synchronisation 62 3.5.1 System description 63 3.5.2 Algorithm description 66 3.5.3 Numerical results 68 3.5.4 Summary and discussion 72 3.6 Multiple-antenna OFDM system implementation 73 3.6.1 Test system description 73 3.6.2 Baseband design 74 3.6.3 Measurement results 76 3.6.4 Comparison with simulation results 79 3.7 Conclusions 81 4. PHASE NOISE 83 4.1 Introduction 83 4.2 System and phase noise modelling 84 4.2.1 Oscillator modelling 85 4.2.2 Influence on signal model 88 4.3 Impact and distribution of the ICI term 91 4.3.1 System model 91 4.3.2 Bit-error probabilities 94 4.3.3 Properties of the ICI term 95 4.3.4 Simulation results 104 4.3.5 Summary 107 4.4 ICI-caused error term in MIMO OFDM 108 4.4.1 Transmitter phase noise 109 4.4.2 Receiver phase noise 110 4.4.3 Phase noise process 112 4.4.4 Numerical results 113 4.4.5 Summary and discussion 116 4.5 Compensation of the CPE 117 4.5.1 Maximum-likelihood estimator 117 4.5.2 MLE optimisation algorithm 119 4.5.3 Sub-optimal estimator 121 4.5.4 Cram?er-Rao lower bound 122 4.5.5 Numerical results 124 4.5.6 Summary 130 4.6 Compensation of the ICI 130 4.6.1 Suppression algorithm 131 4.6.2 Numerical results 134 4.6.3 Summary 136 4.7 Conclusions 137 5. IQ IMBALANCE 139 5.1 Introduction 139 5.2 System and IQ imbalance modelling 140 5.2.1 TX/RX front-end architecture 141 5.2.2 IQ mismatch 143 5.2.3 Influence on MIMO signal model 145 5.2.4 RX filter imbalance 148 5.3 Impact of IQ imbalance on system performance 150 5.3.1 Error in symbol detection 150 5.3.2 Probability of erroneous detection for M-QAM 152 5.3.3 Numerical results 159 5.3.4 Summary and discussion 163 5.4 Preamble based estimation and mitigation 163 5.4.1 Preamble design 164 5.4.2 TX IQ imbalance estimation 166 5.4.3 RX IQ imbalance estimation 167 5.4.4 TX and RX IQ imbalance estimation 168 5.4.5 Iterative TX and RX IQ imbalance estimation 170 5.4.6 Numerical results 172 5.4.7 Summary 177 5.5 Decision-directed mitigation 178 5.5.1 Adaptive filter based algorithm 178 5.5.2 Numerical results 180 5.6 Conclusions 182 6. NONLINEARITIES 185 6.1 Introduction 185 6.2 System and nonlinearities modelling 187 6.2.1 Nonlinearity modelling 187 6.2.2 Influence on signal model 192 6.3 Impact of nonlinearities on system performance 195 6.3.1 TX nonlinearities 196 6.3.2 RX nonlinearities 201 6.3.3 Numerical results 203 6.3.4 Summary and discussion 207 6.4 PAPR reduction by spatial shifting 208 6.4.1 Signal modelling 209 6.4.2 Spatial shifting 210 6.4.3 Combining SS and PS 211 6.4.4 Subcarrier grouping schemes 213 6.4.5 Side information/Transparency 213 6.4.6 Numerical results 215 6.4.7 Summary and discussion 217 6.5 RX-based correction of nonlinearities 219 6.5.1 Baseband amplitude clipping 220 6.5.2 Estimation of linear and nonlinear channel 221 6.5.3 Postdistortion 230 6.5.4 Iterative distortion removal 231 6.5.5 Simulation results 233 6.5.6 Summary 242 6.6 Conclusions 242 7. A GENERALISED ERROR MODEL 245 7.1 Introduction 245 7.2 Error model 246 7.2.1 TX and RX impairment model 247 7.2.2 Mapping of RF impairments 248 7.2.3 Nonstationarity of the impairments 250 7.2.4 Transmission structure 252 7.3 Performance evaluation 252 7.3.1 Preamble phase 253 7.3.2 Data phase 253 7.3.3 Probability of error 254 7.4 Numerical results 257 7.5 Conclusions 261 8. DISCUSSION AND CONCLUSIONS 263 8.1 Summary and conclusions 263 8.1.1 Synchronisation for MIMO OFDM systems 264 8.1.2 Multiple-antenna OFDM proof of concept 265 8.1.3 Behavioural RF impairment modelling 265 8.1.4 Performance impact of front-end imperfections 266 8.1.5 Mitigation approaches for RF impairments 267 8.1.6 A generalised error model 269 8.2 Scope of future research 270 8.2.1 Influence of RF impairments 270 8.2.2 Mitigation approaches 271 8.2.3 Towards mm-wave systems 272 Glossary 275 Appendices 281 A MSE in CFO estimation 281 B MSE in channel estimation 283 B.1 MSE in linear channel interpolation 283 B.2 MSE in linear channel extrapolation 284 C Measurement setup 287 C.1 Baseband 287 C.2 IF stages 289 C.3 Antennas 290 D Proof of Theorem 4.1 291 E Orthonormal polynomial basis 299 References 301 Index 315

      下载次数 9次 资源类型 技术书籍 上传时间 2013-11-16

    13. Digital Communications A Discrete Time Approach by Michael Rice

      标签:通信

      Digital Communications A Discrete Time Approach by Michael Rice Hardcover: 800 pages Publisher: Prentice Hall; 1 edition (April 21, 2008) Language: English ISBN-10: 0130304972 ISBN-13: 978-0130304971 Product Dimensions: 9.3 x 7.1 x 1.4 inches Product DescriptionThis text uses the principles of discrete-time signal processing to introduce and analyze digital communications – connecting continuous-time and discrete-time ideas. The text brings under one cover the theoretical and practical issues from discrete-time signal processing, discrete-time filter design, multi-rate discrete-time processing, estimation theory, signal space analysis, numerical algorithms – all focused on digital communications. A useful reference for programmers. From the Back CoverThis text uses the principles of discrete-time signal processing to introduce and analyze digital communications – connecting continuous-time and discrete-time ideas. The text brings under one cover the theoretical and practical issues from discrete-time signal processing, discrete-time filter design, multi-rate discrete-time processing, estimation theory, signal space analysis, numerical algorithms – all focused on digital communications. A useful reference for programmers.

      下载次数 45次 资源类型 技术书籍 上传时间 2013-11-16

    14. 数字调制基础.pdf

      标签:数字 数字调制 调制

      数字调制基础.pdf

      下载次数 1次 资源类型 技术书籍 上传时间 2013-11-16

    15. 采用uIP开放源码

      标签:采用uIP开放源码

      采用uIP开放源码 初步决定采用uIP开放源码。 代码量相对较少,我自己也没看过, 下面一个附件是参考文档,

      下载次数 0次 资源类型 技术书籍 上传时间 2013-11-16

    16. Digital Communication 2nd Edition (Edward A. Lee)

      标签:Digital Communication

      Digital Communication 2nd Edition (Edward A. Lee) 目录: PART I: THE BASICS INTRODUCTION 1 DETERMINISTIC SIGNAL PROCESSING 11 STOCHASTIC SIGNAL PROCESSING 48 LIMITS OF COMMUNICATION 97 PHYSICAL MEDIA AND CHANNELS 115 PART II: MODULATION AND DETECTION MODULATION 178 SIGNAL and RECEIVER DESIGN 279 NOISE 311 DETECTION 378 EQUALIZATION 442 ADAPTIVE EQUALIZATION 517 PART III: CODING SPECTRUM CONTROL 555 ERROR CONTROL 609 SIGNALSPACE CODING 650 PART IV: SYNCHRONIZATION PHASELOCKED LOOPS 700 CARRIER RECOVERY 725 TIMING RECOVERY 737 PART V: MULTIPLE ACCESS MULTIPLE ACCESS ALTERNATIVES 765 ECHO CANCELLATION 797 EXERCISE SOLUTIONS 825 PERMUTED INDEX 865

      下载次数 2次 资源类型 技术书籍 上传时间 2013-11-16

    17. A Software-Defined GPS and Galileo Receiver

      标签:SoftwareDefined GPS Galileo Receiver

      A Software-Defined GPS and Galileo Receiver About this textbook Satellite navigation receivers are used to receive, process, and decode space-based navigation signals, such as those provided by the GPS constellation of satellites. There is an increasing need for a unified open platform that will enable enhanced receiver development and design, as well as cost-effective testing procedures for various applications. This book and companion DVD provide hands-on exploration of new technologies in this rapidly growing field. One of the unique features of the work is the interactive approach used, giving readers the ability to construct their own Global Navigation Satellite Systems (GNSS) receivers. To construct such a reconfigurable receiver with a wide range of applications, the authors discuss receiver architecture based on software-defined radio (SDR) techniques. The presentation unfolds in a systematic, user-friendly style and goes from the basics to cutting-edge research. Additional features and topics include: * Presentation of basic signal structures used in GPS and Galileo, the European satellite navigation system * Design and implementation of a GPS signal generator * Presentation and analysis of different methods of signal acquisition—serial search; parallel-frequency space search; and parallel-code phase search—as well as code/carrier tracking and navigation data decoding * A complete GPS software receiver implemented using MATLAB code as well as GPS and GIOVE-A signal records—available on the companion cross-platform DVD—allowing readers to change various parameters and immediately see their effects * MATLAB-based exercises * A hands-on method of testing the material covered in the book: supplementary front-end hardware equipment—which may be purchased at http://ccar.colorado.edu/gnss—enables readers working on a Windows or LINUX system to generate real-world data by converting analog signals to digital signals * Supplementary course material for instructors available at http://gps.aau.dk/softgps * Bibliography of recent results and comprehensive index The book is aimed at applied mathematicians, electrical engineers, geodesists, and graduate students. It may be used as a textbook in various GPS technology and signal processing courses, or as a self-study reference for anyone working with satellite navigation receivers. Written for: Applied mathematicians, electrical engineers, geodesists, graduate students, or anyone working with satellite navigation receivers Keywords: GPS technology Galileo Global Navigation Satellite Systems (GNSS) MATLAB geodesy satellite navigation receivers satellite receiver architecture software-defined radio (SDR) techniques

      下载次数 3次 资源类型 技术书籍 上传时间 2013-11-16

    18. Edward Lee 的经典数字通信教材

      标签:Edward Lee

      Edward Lee 的经典数字通信教材 来自UC Berkeley 的 Edward Lee 的经典数字通信教材, 是1994年第二版的, 希望对大家有用

      下载次数 2次 资源类型 技术书籍 上传时间 2013-11-16

    19. OFDM同步技术研究(优秀博士论文答辩ppt)

      标签:OFDM同步技术

      OFDM同步技术研究(优秀博士论文答辩ppt) OFDM蜂窝无线移动通信系统中的同步技术研究.pdf(优秀博士论文答辩ppt) 主要内容: *OFDM蜂窝移动通信系统同步模型 *OFDM蜂窝移动通信中最大Doppler频移估计算法研究 *SISO-OFDM蜂窝移动通信中反向链路数据传输阶段的同步方案研究 *MIMO-OFDM蜂窝移动通信中反向链的同步方案研究 *全文总结与研究展望

      下载次数 2次 资源类型 技术书籍 上传时间 2013-11-16

    20. LTE Signaling: Troubleshooting and Optimization

      标签:LTE Signaling Troubleshooting and Optimization

      LTE Signaling: Troubleshooting and Optimization Ralf Kreher(Author), Karsten Gaenger (Author) Product Details Hardcover: 296 pages Publisher: Wiley (February 22, 2011) Language: English ISBN-10: 0470689005 ISBN-13: 978-0470689004 Review "A comprehensive reference on the call procedures of 4G RAN and Core networks, LTE (News - Alert) Signaling, Troubleshooting and Optimization describes the protocols and procedures of LTE.". (InfoTECH Spotlight - TMCnet, 16 March 2011) Product Description A comprehensive reference on the call procedures of 4G RAN and Core networks, LTE Signaling, Troubleshooting and Optimization describes the protocols and procedures of LTE. It explains essential topics from basic performance measurement counters, radio quality and user plane quality to the standards, architecture, objectives and functions of the different interfaces. The first section gives an overview of LTE/EPC network architecture, reference points, protocol stacks, information elements and elementary procedures. The proceeding parts target more advanced topics to cover LTE/EPC signalling and radio quality analysis. This book supplements the information provided in the 3GPP standards by giving readers access to a universal LTE/EPC protocol sequence to ensure they have a clear understanding of the issues involved. It describes the normal signaling procedures as well as explaining how to identify and troubleshoot abnormal network behavior and common failure causes. Enables the reader to understand the signaling procedures and parameters that need to be analyzed when monitoring UMTS networks Covers the essential facts on signaling procedures by providing first hand information taken from real LTE/EPC traces A useful reference on the topic, also providing sufficient details for test and measurement experts who need to analyze LTE/EPC signaling procedures and measurements at the most detailed level Contains a description of LTE air interface monitoring scenarios as well as other key topics up to an advanced level LTE Signaling, Troubleshooting and Optimization is the Long Term Evolution successor to the previous Wiley books UMTS Signaling and UMTS Performance Measurement.

      下载次数 5次 资源类型 技术书籍 上传时间 2013-11-16

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zlsx 2018-5-6
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