Polar Codes A Non-Trivial Approach to Channel Coding
This book explains the philosophy of the polar encoding and decoding technique. Polar codes are one of the most recently discovered capacity-achieving channel codes. What sets them apart from other channel codes is the fact that polar codes are designed m
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Orhan Gazi
Polar Codes A Non-Trivial Approach to Channel Coding
Springer Topics in Signal Processing Volume 15
Series editors Jacob Benesty, Montreal, Canada Walter Kellermann, Erlangen, Germany
More information about this series at http://www.springer.com/series/8109
Orhan Gazi
Polar Codes A Non-Trivial Approach to Channel Coding
123
Orhan Gazi Department of Electronic and Communication Engineering Çankaya University Etimesgut/Ankara Turkey
ISSN 1866-2609 ISSN 1866-2617 (electronic) Springer Topics in Signal Processing ISBN 978-981-13-0736-2 ISBN 978-981-13-0737-9 (eBook) https://doi.org/10.1007/978-981-13-0737-9 Library of Congress Control Number: 2018943249 © Springer Nature Singapore Pte Ltd. 2019 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, express or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. Printed on acid-free paper This Springer imprint is published by the registered company Springer Nature Singapore Pte Ltd. part of Springer Nature The registered company address is: 152 Beach Road, #21-01/04 Gateway East, Singapore 189721, Singapore
Contents
1 Information Theory Perspective of Polar Codes and Polar Encoding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.1 Information Theory Perspective of Polar Codes . . . . . . . . 1.1.1 The Philosophy of Polar Codes . . . . . . . . . . . . . . 1.1.2 Fundamental Idea of Polar Codes . . . . . . . . . . . . . 1.2 Polar Encoding Operation . . . . . . . . . . . . . . . . . . . . . . . . 1.3 Recursive Construction of Polar Encoder Structures . . . . . 1.4 Generator Matrix and Encoding Formula for Polar Codes .
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2 Decoding of Polar Codes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.
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