Informationen zum Autor Mohammad Rowshan, PhD, (Member, IEEE) received the B.Eng. degree (Hons.) in electrical engineering from the University of Nottingham in 2015 (ranked 1), the M.Sc. degree in electrical engineering from The Hong Kong University of Science and Technology in 2016, and the Ph.D. degree in electrical engineering from Monash University in 2021. He is currently an Engineering ECA Fellow with the School of Electrical Engineering and Telecommunications, University of New South Wales, Sydney, Australia, where he serves as a Researcher, a Lecturer, and a Supervisor/Mentor. He also serves as a reviewer of IEEE conferences and journals, and a TPC member of conferences. Emanuele Viterbo, PhD, is Professor in the Department of Electrical and Computer Systems Engineering, Monash University, Melbourne, Australia. He is a Fellow of the IEEE and an ISI Highly Cited Researcher (2009, Thompson Reuters). He has published extensively on a range of subjects related to channel coding and wireless communication. Klappentext Understand a cutting-edge new class of error correction codes with this introduction Channel coding is a pivotal technique employed to account for potential errors due to channel noise or interference by adding layers of redundancy to information prior to transmission or storage. Should errors appear in the transmitted sequence upon reaching its destination, they can be corrected with reference to the redundant layers. Polar codes are a new class of error correction codes that provably achieve the capacity of binary discrete memoryless channels. Their distinct advantages have led to their incorporation in the logical control channels of the fifth generation of wireless communications (5G). Possessing robust and competitive error correction capabilities for short and medium-length codes positions them strategically to fulfill a pivotal role in various communication systems as we move towards the sixth generation of wireless communication (6G) and beyond. Polar Codes provides a thorough, accessible overview of this new class of codes and its applications. Beginning with the foundational theories underlying polar codes, it guides readers through the construction of polar codes, their variants, and their encoding and decoding processes. The result is a must-have for coding researchers and professionals looking to develop an edge in the wireless communications of the future. Polar Codes readers will also find: Continuous connections between discussed concepts and current 5G standards Snippets of code in MATLAB/Python to illustrate key tools End of chapter problems and bibliographical notes to facilitate learning and provide references for further reading. Polar Codes is ideal for graduate students and researchers in coding and information theory, as well as engineers working in communications and related industries. Inhaltsverzeichnis About the Authors xv Preface xvii Acknowledgment xxi 1 Introduction 1 1.1 Reliable Transmission over Noisy Channels 2 1.2 Channel Models 4 1.2.1 Binary Symmetric Channel (BSC) 4 1.2.2 Binary Erasure Channel (BEC) 5 1.2.3 Additive White Gaussian Noise Channel (AWGN) 6 1.2.4 Fading Channel 7 1.3 Fundamentals of Information Theory 7 1.3.1 The Meaning of Information 8 1.3.2 Discrete Entropy 9 1.3.3 Properties of the Discrete Entropy 10 1.3.4 Mutual Information 11 1.3.5 Bhattacharyya Parameter 12 1.4 Channel Capacity and Channel Coding Theorem 13 1.5 Block Error Rate for Finite Length Codes 15 1.6 Shannon Limit on Power Efficiency 17 1.7 Time and Space Complexity 19 1.8 Historical Milestones in Channel Coding 20 1.9 Why Study Polar Codes? 24 1.9.1 How Do Polar Codes Compare with Other Codes? 25 Exercises 26 Bibli...

Autorentext

Mohammad Rowshan, PhD, (Member, IEEE) received the B.Eng. degree (Hons.) in electrical engineering from the University of Nottingham in 2015 (ranked 1), the M.Sc. degree in electrical engineering from The Hong Kong University of Science and Technology in 2016, and the Ph.D. degree in electrical engineering from Monash University in 2021. He is currently an Engineering ECA Fellow with the School of Electrical Engineering and Telecommunications, University of New South Wales, Sydney, Australia, where he serves as a Researcher, a Lecturer, and a Supervisor/Mentor. He also serves as a reviewer of IEEE conferences and journals, and a TPC member of conferences. Emanuele Viterbo, PhD, is Professor in the Department of Electrical and Computer Systems Engineering, Monash University, Melbourne, Australia. He is a Fellow of the IEEE and an ISI Highly Cited Researcher (2009, Thompson Reuters). He has published extensively on a range of subjects related to channel coding and wireless communication.

Klappentext

Understand a cutting-edge new class of error correction codes with this introduction Channel coding is a pivotal technique employed to account for potential errors due to channel noise or interference by adding layers of redundancy to information prior to transmission or storage. Should errors appear in the transmitted sequence upon reaching its destination, they can be corrected with reference to the redundant layers. Polar codes are a new class of error correction codes that provably achieve the capacity of binary discrete memoryless channels. Their distinct advantages have led to their incorporation in the logical control channels of the fifth generation of wireless communications (5G). Possessing robust and competitive error correction capabilities for short and medium-length codes positions them strategically to fulfill a pivotal role in various communication systems as we move towards the sixth generation of wireless communication (6G) and beyond. Polar Codes provides a thorough, accessible overview of this new class of codes and its applications. Beginning with the foundational theories underlying polar codes, it guides readers through the construction of polar codes, their variants, and their encoding and decoding processes. The result is a must-have for coding researchers and professionals looking to develop an edge in the wireless communications of the future. Polar Codes readers will also find:

• Continuous connections between discussed concepts and current 5G standards
• Snippets of code in MATLAB/Python to illustrate key tools

• End of chapter problems and bibliographical notes to facilitate learning and provide references for further reading. Polar Codes is ideal for graduate students and researchers in coding and information theory, as well as engineers working in communications and related industries.

  Inhalt

  About the Authors xv

  Preface xvii

  Acknowledgment xxi

  1 Introduction 1

  1.1 Reliable Transmission over Noisy Channels 2

  1.2 Channel Models 4

  1.2.1 Binary Symmetric Channel (BSC) 4

  1.2.2 Binary Erasure Channel (BEC) 5

  1.2.3 Additive White Gaussian Noise Channel (AWGN) 6

  1.2.4 Fading Channel 7

  1.3 Fundamentals of Information Theory 7

  1.3.1 The Meaning of Information 8

  1.3.2 Discrete Entropy 9

  1.3.3 Properties of the Discrete Entropy 10

  1.3.4 Mutual Information 11

  1.3.5 Bhattacharyya Parameter 12

  1.4 Channel Capacity and Channel Coding Theorem 13

  1.5 Block Error Rate for Finite Length Codes 15

  1.6 Shannon Limit on Power Efficiency 17

  1.7 Time and Space Complexity 19

  1.8 Historical Milestones in Channel Coding 20

  1.9 Why Study Polar Codes? 24

  1.9.1 How Do Polar Codes Compare with Other Codes? 25

  Exercises 26

  Bibliographic Notes 27

  Bibliography 28

  2 Linear Codes 29

  2.1 Generator and Parity-Check Matrices 29

  2.2 Distance, Weight, and Bounds 32

  2.3 Syndrome Decoding 35

  2.4 Repetition and Single Parity Check Codes 37

  2.5 Reed-Muller Codes 37

  2.5.1 Boolean Functions and Boolean Polynomials 38

  2.5.1.1 Evaluation of Monomials 38

  2.5.1.2 Boolean Products 40

  2.5.1.3 Boolean Polynomials 40

  2.5.2 Submatrix of Binary Walsh-Hadamard Matrix 41

  2.5.…