Non-Binary Error Control Coding for Wireless Communication and Data Storage

Comprehensive introduction to non-binary error-correction coding techniques Non-Binary Error Control Coding for Wireless Communication and Data Storage explores non-binary coding schemes that have been developed to provide an alternative to the Reed Solomon codes, which are expected to become unsuitable for use in future data storage and communication devices as the demand for higher data rates increases. This book will look at the other significant non-binary coding schemes, including non-binary block and ring trellis-coded modulation (TCM) codes that perform well in fading conditions without any expansion in bandwidth use, and algebraic-geometric codes which are an extension of Reed-Solomon codes but with better parameters. Key Features: Comprehensive and self-contained reference to non-binary error control coding starting from binary codes and progressing up to the latest non-binary codes Explains the design and construction of good non-binary codes with descriptions of efficient non-binary decoding algorithms with applications for wireless communication and high-density data storage Discusses the application to specific cellular and wireless channels, and also magnetic storage channels that model the reading of data from the magnetic disc of a hard drive. Includes detailed worked examples for each coding scheme to supplement the concepts described in this book Focuses on the encoding, decoding and performance of both block and convolutional non-binary codes, and covers the K tter-Vardy algorithm and Non-binary LDPC codes This book will be an excellent reference for researchers in the wireless communication and data storage communities, as well as development/research engineers in telecoms and storage companies. Postgraduate students in these fields will also find this book of interest.

Comprehensive introduction to non-binary error-correction codingtechniquesNon-Binary Error Control Coding for Wireless Communicationand Data Storage explores non-binary coding schemes that havebeen developed to provide an alternative to the ReedSolomon codes, which are expected to become unsuitable for use infuture data storage and communication devices as the demand forhigher data rates increases. This book will look at the othersignificant non-binary coding schemes, including non-binary blockand ring trellis-coded modulation (TCM) codes that perform well infading conditions without any expansion in bandwidth use, andalgebraic-geometric codes which are an extension of Reed-Solomoncodes but with better parameters.Key Features:* Comprehensive and self-contained reference to non-binary errorcontrol coding starting from binary codes and progressing up to thelatest non-binary codes* Explains the design and construction of good non-binary codeswith descriptions of efficient non-binary decoding algorithms withapplications for wireless communication and high-density datastorage* Discusses the application to specific cellular and wirelesschannels, and also magnetic storage channels that model the readingof data from the magnetic disc of a hard drive.* Includes detailed worked examples for each coding scheme tosupplement the concepts described in this book* Focuses on the encoding, decoding and performance of both blockand convolutional non-binary codes, and covers theKötter-Vardy algorithm and Non-binary LDPC codesThis book will be an excellent reference for researchers in thewireless communication and data storage communities, as well asdevelopment/research engineers in telecoms and storage companies.Postgraduate students in these fields will also find this book ofinterest.

AcknowledgementsPrefaceChapter 1 - Information, Channel Capacity and ChannelModelling* Introduction1.2. Measure of Information1.3. Channel Capacity1.4 Channel Modelling1.5. Definition of a communications channel and itsparameters1.6. Multiple Input Multiple Output (MIMO) Channel1.8. Magnetic Storage Channel Modelling1.9. SummaryReferencesChapter 2 - Basic Principles of Non-Binary Codes2.1. Introduction to Algebraic Concepts2.2. Algebraic Geometry2.3. ConclusionsChapter 3 - Non-Binary Block Codes3.1. Introduction3.2. Fundamentals of Block Codes3.3. Bose-Chaudhuri-Hocquenghem (BCH) CodesExample 3.3. Constructing a non-binary BCH code over GF(4) oflength n = 15 symbols3.4. Reed-Solomon CodesExample 3.4: Constructing a non-binary BCH code over GF(16) oflength n = 15 symbols3.5. Decoding Reed-Solomon Codes3.6. Coded Modulation3.7. ConclusionsReferencesChapter 4 - Algebraic-Geometric Codes4.1. Introduction4.2. Construction of Algebraic-Geometric Codes4.3. Decoding Algebraic-Geometric Codes4.4. Majority Voting4.5. Calculating the Error Magnitudes.4.6. Complete Hard-Decision Decoding Algorithm for HermitianCodes.4.8. Simulation Results4.9. ConclusionsReferencesChapter 5 - List Decoding5.1. Introduction5.2. List Decoding of Reed-Solomon Codes using theGuruswami-Sudan algorithm5.3. Soft-Decision List Decoding of Reed-Solomon codes using theKötter-Vardy Algorithm.5.4. List Decoding of Algebraic-Geometric Codes5.5. Determining the Corresponding Coefficients5.6. Complexity reduction Interpolation5.7. General Factorisation5.8. Soft-Decision List Decoding of Hermitian Codes5.9. ConclusionsReferencesChapter 6 - Non-Binary Low Density Parity Check Codes6.1. Introduction6.2. Construction of Binary LDPC Codes - Random andStructured Methods6.3. Decoding of Binary LDPC Codes using the Belief PropagationAlgorithm.6.4. Construction of Non-Binary LDPC Codes defined over FiniteFields6.5. Decoding Non-Binary LDPC Codes with the Sum ProductAlgorithm6.6.ConclusionsReferencesChapter 7 - Non-Binary Convolutional CodesReferencesChapter 8 - Non-binary Turbo codes8.1. Introduction8.2. The turbo encoder8.3. The Turbo Decoder8.4. Non-Binary Turbo Codes8.5. ConclusionReferences