{"product_id":"essentials-of-errorcontrol-coding-9780470029206","title":"Essentials of ErrorControl Coding","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eRapid advances in electronic and optical technology have enabled the implementation of powerful error-control codes, which are now used in almost the entire range of information systems with close to optimal performance.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e\u003cp\u003ePreface xiii\u003c\/p\u003e \u003cp\u003eAcknowledgements xv\u003c\/p\u003e \u003cp\u003eList of Symbols xvii\u003c\/p\u003e \u003cp\u003eAbbreviations xxv\u003c\/p\u003e \u003cp\u003e\u003cb\u003e1 Information and Coding Theory 1\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e1.1 Information 3\u003c\/p\u003e \u003cp\u003e1.1.1 A Measure of Information 3\u003c\/p\u003e \u003cp\u003e1.2 Entropy and Information Rate 4\u003c\/p\u003e \u003cp\u003e1.3 Extended DMSs 9\u003c\/p\u003e \u003cp\u003e1.4 Channels and Mutual Information 10\u003c\/p\u003e \u003cp\u003e1.4.1 Information Transmission over Discrete Channels 10\u003c\/p\u003e \u003cp\u003e1.4.2 Information Channels 10\u003c\/p\u003e \u003cp\u003e1.5 Channel Probability Relationships 13\u003c\/p\u003e \u003cp\u003e1.6 The A Priori and A Posteriori Entropies 15\u003c\/p\u003e \u003cp\u003e1.7 Mutual Information 16\u003c\/p\u003e \u003cp\u003e1.7.1 Mutual Information: Definition 16\u003c\/p\u003e \u003cp\u003e1.7.2 Mutual Information: Properties 17\u003c\/p\u003e \u003cp\u003e1.8 Capacity of a Discrete Channel 21\u003c\/p\u003e \u003cp\u003e1.9 The Shannon Theorems 22\u003c\/p\u003e \u003cp\u003e1.9.1 Source Coding Theorem 22\u003c\/p\u003e \u003cp\u003e1.9.2 Channel Capacity and Coding 23\u003c\/p\u003e \u003cp\u003e1.9.3 Channel Coding Theorem 25\u003c\/p\u003e \u003cp\u003e1.10 Signal Spaces and the Channel Coding Theorem 27\u003c\/p\u003e \u003cp\u003e1.10.1 Capacity of the Gaussian Channel 28\u003c\/p\u003e \u003cp\u003e1.11 Error-Control Coding 32\u003c\/p\u003e \u003cp\u003e1.12 Limits to Communication and their Consequences 34\u003c\/p\u003e \u003cp\u003eBibliography and References 38\u003c\/p\u003e \u003cp\u003eProblems 38\u003c\/p\u003e \u003cp\u003e\u003cb\u003e2 Block Codes 41\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e2.1 Error-Control Coding 41\u003c\/p\u003e \u003cp\u003e2.2 Error Detection and Correction 41\u003c\/p\u003e \u003cp\u003e2.2.1 Simple Codes: The Repetition Code 42\u003c\/p\u003e \u003cp\u003e2.3 Block Codes: Introduction and Parameters 43\u003c\/p\u003e \u003cp\u003e2.4 The Vector Space over the Binary Field 44\u003c\/p\u003e \u003cp\u003e2.4.1 Vector Subspaces 46\u003c\/p\u003e \u003cp\u003e2.4.2 Dual Subspace 48\u003c\/p\u003e \u003cp\u003e2.4.3 Matrix Form 48\u003c\/p\u003e \u003cp\u003e2.4.4 Dual Subspace Matrix 49\u003c\/p\u003e \u003cp\u003e2.5 Linear Block Codes 50\u003c\/p\u003e \u003cp\u003e2.5.1 Generator Matrix G 51\u003c\/p\u003e \u003cp\u003e2.5.2 Block Codes in Systematic Form 52\u003c\/p\u003e \u003cp\u003e2.5.3 Parity Check Matrix H 54\u003c\/p\u003e \u003cp\u003e2.6 Syndrome Error Detection 55\u003c\/p\u003e \u003cp\u003e2.7 Minimum Distance of a Block Code 58\u003c\/p\u003e \u003cp\u003e2.7.1 Minimum Distance and the Structure of the H Matrix 58\u003c\/p\u003e \u003cp\u003e2.8 Error-Correction Capability of a Block Code 59\u003c\/p\u003e \u003cp\u003e2.9 Syndrome Detection and the Standard Array 61\u003c\/p\u003e \u003cp\u003e2.10 Hamming Codes 64\u003c\/p\u003e \u003cp\u003e2.11 Forward Error Correction and Automatic Repeat ReQuest 65\u003c\/p\u003e \u003cp\u003e2.11.1 Forward Error Correction 65\u003c\/p\u003e \u003cp\u003e2.11.2 Automatic Repeat ReQuest 68\u003c\/p\u003e \u003cp\u003e2.11.3 ARQ Schemes 69\u003c\/p\u003e \u003cp\u003e2.11.4 ARQ Scheme Efficiencies 71\u003c\/p\u003e \u003cp\u003e2.11.5 Hybrid-ARQ Schemes 72\u003c\/p\u003e \u003cp\u003eBibliography and References 76\u003c\/p\u003e \u003cp\u003eProblems 77\u003c\/p\u003e \u003cp\u003e\u003cb\u003e3 Cyclic Codes 81\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e3.1 Description 81\u003c\/p\u003e \u003cp\u003e3.2 Polynomial Representation of Codewords 81\u003c\/p\u003e \u003cp\u003e3.3 Generator Polynomial of a Cyclic Code 83\u003c\/p\u003e \u003cp\u003e3.4 Cyclic Codes in Systematic Form 85\u003c\/p\u003e \u003cp\u003e3.5 Generator Matrix of a Cyclic Code 87\u003c\/p\u003e \u003cp\u003e3.6 Syndrome Calculation and Error Detection 89\u003c\/p\u003e \u003cp\u003e3.7 Decoding of Cyclic Codes 90\u003c\/p\u003e \u003cp\u003e3.8 An Application Example: Cyclic Redundancy Check Code for the Ethernet Standard 92\u003c\/p\u003e \u003cp\u003eBibliography and References 93\u003c\/p\u003e \u003cp\u003eProblems 94\u003c\/p\u003e \u003cp\u003e\u003cb\u003e4 BCH Codes 97\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e4.1 Introduction: The Minimal Polynomial 97\u003c\/p\u003e \u003cp\u003e4.2 Description of BCH Cyclic Codes 99\u003c\/p\u003e \u003cp\u003e4.2.1 Bounds on the Error-Correction Capability of a BCH Code: The Vandermonde Determinant 102\u003c\/p\u003e \u003cp\u003e4.3 Decoding of BCH Codes 104\u003c\/p\u003e \u003cp\u003e4.4 Error-Location and Error-Evaluation Polynomials 105\u003c\/p\u003e \u003cp\u003e4.5 The Key Equation 107\u003c\/p\u003e \u003cp\u003e4.6 Decoding of Binary BCH Codes Using the Euclidean Algorithm 108\u003c\/p\u003e \u003cp\u003e4.6.1 The Euclidean Algorithm 108\u003c\/p\u003e \u003cp\u003eBibliography and References 112\u003c\/p\u003e \u003cp\u003eProblems 112\u003c\/p\u003e \u003cp\u003e\u003cb\u003e5 Reed–Solomon Codes 115\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e5.1 Introduction 115\u003c\/p\u003e \u003cp\u003e5.2 Error-Correction Capability of RS Codes: The Vandermonde Determinant 117\u003c\/p\u003e \u003cp\u003e5.3 RS Codes in Systematic Form 119\u003c\/p\u003e \u003cp\u003e5.4 Syndrome Decoding of RS Codes 120\u003c\/p\u003e \u003cp\u003e5.5 The Euclidean Algorithm: Error-Location and Error-Evaluation Polynomials 122\u003c\/p\u003e \u003cp\u003e5.6 Decoding of RS Codes Using the Euclidean Algorithm 125\u003c\/p\u003e \u003cp\u003e5.6.1 Steps of the Euclidean Algorithm 127\u003c\/p\u003e \u003cp\u003e5.7 Decoding of RS and BCH Codes Using the Berlekamp–Massey Algorithm 128\u003c\/p\u003e \u003cp\u003e5.7.1 B–M Iterative Algorithm for Finding the Error-Location Polynomial 130\u003c\/p\u003e \u003cp\u003e5.7.2 B–M Decoding of RS Codes 133\u003c\/p\u003e \u003cp\u003e5.7.3 Relationship Between the Error-Location Polynomials of the Euclidean and B–M Algorithms 136\u003c\/p\u003e \u003cp\u003e5.8 A Practical Application: Error-Control Coding for the Compact Disk 136\u003c\/p\u003e \u003cp\u003e5.8.1 Compact Disk Characteristics 136\u003c\/p\u003e \u003cp\u003e5.8.2 Channel Characteristics 138\u003c\/p\u003e \u003cp\u003e5.8.3 Coding Procedure 138\u003c\/p\u003e \u003cp\u003e5.9 Encoding for RS codes CRS(28, 24), CRS(32, 28) and CRS(255, 251) 139\u003c\/p\u003e \u003cp\u003e5.10 Decoding of RS Codes CRS(28, 24) and CRS(32, 28) 142\u003c\/p\u003e \u003cp\u003e5.10.1 B–M Decoding 142\u003c\/p\u003e \u003cp\u003e5.10.2 Alternative Decoding Methods 145\u003c\/p\u003e \u003cp\u003e5.10.3 Direct Solution of Syndrome Equations 146\u003c\/p\u003e \u003cp\u003e5.11 Importance of Interleaving 148\u003c\/p\u003e \u003cp\u003eBibliography and References 152\u003c\/p\u003e \u003cp\u003eProblems 153\u003c\/p\u003e \u003cp\u003e\u003cb\u003e6 Convolutional Codes 157\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e6.1 Linear Sequential Circuits 158\u003c\/p\u003e \u003cp\u003e6.2 Convolutional Codes and Encoders 158\u003c\/p\u003e \u003cp\u003e6.3 Description in the D-Transform Domain 161\u003c\/p\u003e \u003cp\u003e6.4 Convolutional Encoder Representations 166\u003c\/p\u003e \u003cp\u003e6.4.1 Representation of Connections 166\u003c\/p\u003e \u003cp\u003e6.4.2 State Diagram Representation 166\u003c\/p\u003e \u003cp\u003e6.4.3 Trellis Representation 168\u003c\/p\u003e \u003cp\u003e6.5 Convolutional Codes in Systematic Form 168\u003c\/p\u003e \u003cp\u003e6.6 General Structure of Finite Impulse Response and Infinite Impulse Response FSSMs 170\u003c\/p\u003e \u003cp\u003e6.6.1 Finite Impulse Response FSSMs 170\u003c\/p\u003e \u003cp\u003e6.6.2 Infinite Impulse Response FSSMs 171\u003c\/p\u003e \u003cp\u003e6.7 State Transfer Function Matrix: Calculation of the Transfer Function 172\u003c\/p\u003e \u003cp\u003e6.7.1 State Transfer Function for FIR FSSMs 172\u003c\/p\u003e \u003cp\u003e6.7.2 State Transfer Function for IIR FSSMs 173\u003c\/p\u003e \u003cp\u003e6.8 Relationship Between the Systematic and the Non-Systematic Forms 175\u003c\/p\u003e \u003cp\u003e6.9 Distance Properties of Convolutional Codes 177\u003c\/p\u003e \u003cp\u003e6.10 Minimum Free Distance of a Convolutional Code 180\u003c\/p\u003e \u003cp\u003e6.11 Maximum Likelihood Detection 181\u003c\/p\u003e \u003cp\u003e6.12 Decoding of Convolutional Codes: The Viterbi Algorithm 182\u003c\/p\u003e \u003cp\u003e6.13 Extended and Modified State Diagram 185\u003c\/p\u003e \u003cp\u003e6.14 Error Probability Analysis for Convolutional Codes 186\u003c\/p\u003e \u003cp\u003e6.15 Hard and Soft Decisions 189\u003c\/p\u003e \u003cp\u003e6.15.1 Maximum Likelihood Criterion for the Gaussian Channel 192\u003c\/p\u003e \u003cp\u003e6.15.2 Bounds for Soft-Decision Detection 194\u003c\/p\u003e \u003cp\u003e6.15.3 An Example of Soft-Decision Decoding of Convolutional Codes 196\u003c\/p\u003e \u003cp\u003e6.16 Punctured Convolutional Codes and Rate-Compatible Schemes 200\u003c\/p\u003e \u003cp\u003eBibliography and References 203\u003c\/p\u003e \u003cp\u003eProblems 205\u003c\/p\u003e \u003cp\u003e\u003cb\u003e7 Turbo Codes 209\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e7.1 A Turbo Encoder 210\u003c\/p\u003e \u003cp\u003e7.2 Decoding of Turbo Codes 211\u003c\/p\u003e \u003cp\u003e7.2.1 The Turbo Decoder 211\u003c\/p\u003e \u003cp\u003e7.2.2 Probabilities and Estimates 212\u003c\/p\u003e \u003cp\u003e7.2.3 Symbol Detection 213\u003c\/p\u003e \u003cp\u003e7.2.4 The Log Likelihood Ratio 214\u003c\/p\u003e \u003cp\u003e7.3 Markov Sources and Discrete Channels 215\u003c\/p\u003e \u003cp\u003e7.4 The BCJR Algorithm: Trellis Coding and Discrete Memoryless Channels 218\u003c\/p\u003e \u003cp\u003e7.5 Iterative Coefficient Calculation 221\u003c\/p\u003e \u003cp\u003e7.6 The BCJR MAP Algorithm and the LLR 234\u003c\/p\u003e \u003cp\u003e7.6.1 The BCJR MAP Algorithm: LLR Calculation 235\u003c\/p\u003e \u003cp\u003e7.6.2 Calculation of Coefficients γi (u_, u) 236\u003c\/p\u003e \u003cp\u003e7.7 Turbo Decoding 239\u003c\/p\u003e \u003cp\u003e7.7.1 Initial Conditions of Coefficients αi−1(u_) and βi (u) 248\u003c\/p\u003e \u003cp\u003e7.8 Construction Methods for Turbo Codes 249\u003c\/p\u003e \u003cp\u003e7.8.1 Interleavers 249\u003c\/p\u003e \u003cp\u003e7.8.2 Block Interleavers 250\u003c\/p\u003e \u003cp\u003e7.8.3 Convolutional Interleavers 250\u003c\/p\u003e \u003cp\u003e7.8.4 Random Interleavers 251\u003c\/p\u003e \u003cp\u003e7.8.5 Linear Interleavers 253\u003c\/p\u003e \u003cp\u003e7.8.6 Code Concatenation Methods 253\u003c\/p\u003e \u003cp\u003e7.8.7 Turbo Code Performance as a Function of Size and Type of Interleaver 257\u003c\/p\u003e \u003cp\u003e7.9 Other Decoding Algorithms for Turbo Codes 257\u003c\/p\u003e \u003cp\u003e7.10 EXIT Charts for Turbo Codes 257\u003c\/p\u003e \u003cp\u003e7.10.1 Introduction to EXIT Charts 258\u003c\/p\u003e \u003cp\u003e7.10.2 Construction of the EXIT Chart 259\u003c\/p\u003e \u003cp\u003e7.10.3 Extrinsic Transfer Characteristics of the Constituent Decoders 261\u003c\/p\u003e \u003cp\u003eBibliography and References 269\u003c\/p\u003e \u003cp\u003eProblems 271\u003c\/p\u003e \u003cp\u003e\u003cb\u003e8 Low-Density Parity Check Codes 277\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e8.1 Different Systematic Forms of a Block Code 278\u003c\/p\u003e \u003cp\u003e8.2 Description of LDPC Codes 279\u003c\/p\u003e \u003cp\u003e8.3 Construction of LDPC Codes 280\u003c\/p\u003e \u003cp\u003e8.3.1 Regular LDPC Codes 280\u003c\/p\u003e \u003cp\u003e8.3.2 Irregular LDPC Codes 281\u003c\/p\u003e \u003cp\u003e8.3.3 Decoding of LDPC Codes: The Tanner Graph 281\u003c\/p\u003e \u003cp\u003e8.4 The Sum–Product Algorithm 282\u003c\/p\u003e \u003cp\u003e8.5 Sum–Product Algorithm for LDPC Codes: An Example 284\u003c\/p\u003e \u003cp\u003e8.6 Simplifications of the Sum–Product Algorithm 297\u003c\/p\u003e \u003cp\u003e8.7 A Logarithmic LDPC Decoder 302\u003c\/p\u003e \u003cp\u003e8.7.1 Initialization 302\u003c\/p\u003e \u003cp\u003e8.7.2 Horizontal Step 302\u003c\/p\u003e \u003cp\u003e8.7.3 Vertical Step 304\u003c\/p\u003e \u003cp\u003e8.7.4 Summary of the Logarithmic Decoding Algorithm 305\u003c\/p\u003e \u003cp\u003e8.7.5 Construction of the Look-up Tables 306\u003c\/p\u003e \u003cp\u003e8.8 Extrinsic Information Transfer Charts for LDPC Codes 306\u003c\/p\u003e \u003cp\u003e8.8.1 Introduction 306\u003c\/p\u003e \u003cp\u003e8.8.2 Iterative Decoding of Block Codes 310\u003c\/p\u003e \u003cp\u003e8.8.3 EXIT Chart Construction for LDPC Codes 312\u003c\/p\u003e \u003cp\u003e8.8.4 Mutual Information Function 312\u003c\/p\u003e \u003cp\u003e8.8.5 EXIT Chart for the SND 314\u003c\/p\u003e \u003cp\u003e8.8.6 EXIT Chart for the PCND 315\u003c\/p\u003e \u003cp\u003e8.9 Fountain and LT Codes 317\u003c\/p\u003e \u003cp\u003e8.9.1 Introduction 317\u003c\/p\u003e \u003cp\u003e8.9.2 Fountain Codes 318\u003c\/p\u003e \u003cp\u003e8.9.3 Linear Random Codes 318\u003c\/p\u003e \u003cp\u003e8.9.4 Luby Transform Codes 320\u003c\/p\u003e \u003cp\u003e8.10 LDPC and Turbo Codes 322\u003c\/p\u003e \u003cp\u003eBibliography and References 323\u003c\/p\u003e \u003cp\u003eProblems 324\u003c\/p\u003e \u003cp\u003e\u003cb\u003eAppendix A: Error Probability in the Transmission of Digital Signals 327\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003eAppendix B: Galois Fields GF(q) 339\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eAnswers to Problems 351\u003c\/p\u003e \u003cp\u003eIndex 357\u003c\/p\u003e","brand":"John Wiley \u0026 Sons Inc","offers":[{"title":"Default Title","offer_id":49402265796951,"sku":"9780470029206","price":64.55,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780470029206.jpg?v=1730479880","url":"https:\/\/bookcurl.com\/products\/essentials-of-errorcontrol-coding-9780470029206","provider":"Book Curl","version":"1.0","type":"link"}