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Fundamentals of Classical and Modern Error-Correcting Codes by Shu Lin, Juane Li is a scholarly article available to read on EtoBox.

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Finite fields have been applied to construct error-correcting codes for reliable information transmission and data storage since the late 1950s. These codes are commonly called algebraic codes, which have nice structures and large minimum distances. The most well-known classical algebraic codes are BCH and RS codes presented in Chapters 5 and 6 which can be decoded with the elegant hard-decision Berlekamp-Massey iterative algorithm. Over the past 60 years, BCH and RS codes have been widely applied in many communication and datastorage systems and they are still operating nowadays. Since the rediscovery of LDPC codes in the late 1990s , extensive research has been done in constructing modern LDPC codes using algebraic methods. It was found that finite fields are also very effective for constructing modern LDPC codes with distinctive structures that not only simplify encoding and decoding implementations but also provide good error performance in both waterfall and error-floor regions.In this chapter, we present three flexible methods for constructing three types of QC-LDPC codes based on finite fields. The first two types of QC-LDPC codes are constructed based on two arbitrary subse

Author
Shu Lin, Juane Li
Publisher
Cambridge University Press
Published
2021
Language
EN
ISBN
9781009067928

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