2019
This chapter describes the principal idea of channel coding by considering some well-known codes representing the two main code families: block codes and convolutional codes. The codes are combined, or concatenated, in different ways to build larger and more efficient codes by using small constituent codes. The idea with channel coding is to add redundancy in a controlled way such that it is possible to correct some of the errors at the receiver side. The main idea of error-correcting codes is that a sequence of symbols representing the pure information should be represented by data with a higher dimensionality, in such a way that errors can be corrected. In most communication systems, there are both an error-correcting code and an error-detecting code. The chapter provides a brief discussion on error-detection codes, represented by cyclic redundancy check (CRC) codes.
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Yi Lou, Niaz Ahmed · Textbooks in telecommunication engineering · 2021
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2015
Channel coding is implemented through various algebraic structures, which can be in the form of parity-check matrix as used in linear block codes, Galois field structures as used in cyclic codes, filter structures as used in convolutional codes, or constellation structures as used in trellis coded modulation. This chapter first focuses on feed-forward error correction (FEC) codes, briefly introduces some basic concepts of Galois fields, and then describes binary cyclic codes. It shows that the correction capability of general cyclic codes can only be determined by an enumerative list of the code weights after a code has been generated. A BCH code can have its correction capability designed by theory, with the term BCH to honor its inventors Hocquenghem, Bose and Ray-Chaudhuri. A discrete symbol input endows a convolutional encoder with Markovian properties, which can be characterized by a state diagram, trellis diagram, and transfer function.
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Andres Kwasinski, Vinay Chande · 2022
This chapter focuses on reviewing forward error correction techniques, i.e. error-correcting codes that add redundant bits to the transmitted bit stream and related decoding techniques to detect and correct errors at the receiver. Linear block codes operate on blocks of input bits or symbols, for which they generate a block of bits or symbols at the output. While block codes operate by processing blocks of input symbols, convolutional codes conceptually work on streams of input symbols. It is frequently useful in joint source–channel coding (JSCC) applications to be able to modify the characteristics of a linear channel code, often called the mother code . Channel codes related by a rate-compatibility property are useful in JSCC because they provide a simple method to adapt the channel coding rate, while still using the same decoder in all cases.
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Monica Borda · 2011
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tomaso erseghe · Research Padua Archive (University of Padua) · 2016
This book deals with the subject of channel coding and forward error correction techniques, providing a complete, but introductory, overview on modern coding/decoding techniques, as well as on the theoretical bases on which they lay. It is meant for master degree students with a background in both probability and communication techniques. The book is designed to present the material in an accessible but rigorous manner. It comprehensively covers both practical and theoretical aspects, and aims at explaining the link existing between coding concepts and the underlying communication channel. However, it is not fully organized as a standard textbook, but, rather, it is a collection of records corresponding to well defined concepts in channel coding, in such a way to constitute a blueprint for a course. A number of suggested further readings are provided along the book, for the interested reader who wishes to delve into a specific subject. The book is organized in five parts. The first three parts are devoted to coding and decoding criteria and techniques. The final two parts are instead devoted to assessing the theoretical limits of coding.
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Tolga M. Duman · Cambridge University Press eBooks · 2025
This dynamic textbook provides students with a concise and accessible introduction to the fundamentals of modern digital communications systems. Building from first principles, its comprehensive approach equips students with all of the mathematical tools, theoretical knowledge, and practical understanding they need to excel. It equips students with a strong mathematical foundation spanning signals and systems, probability, random variables, and random processes, and introduces students to key concepts in digital information sources, analog-to-digital conversion, digital modulation, power spectra, multi-carrier modulation, and channel coding. It includes over 85 illustrative examples, and more than 270 theoretical and computational end-of-chapter problems, allowing students to connect theory to practice, and is accompanied by downloadable Matlab code, and a digital solutions manual for instructors. Suitable for a single-semester course, this succinct textbook is an ideal introduction to the field of digital communications for senior undergraduate students in electrical engineering.
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Henrik Schulze, Christian Lüders · 2005
This chapter contains sections titled: General Principles Convolutional Codes Reed–Solomon Codes Bibliographical Notes Problems
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Jerry D. Gibson · Synthesis lectures on communications · 2023
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Te Sun Han · Applications of mathematics · 2003
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Carmelo Decanis, Simone Piana, Softly Decoded Block Code · 2013
The local loop market deregulation and the increased data traffic demand have been the main drivers behind the development of 1 st generation Broadband Wireless Access (BWA) systems. Ericsson has developed a 1 st generation BWA in the 24 to 31 GHz bands exploiting a TDM/TDMA/FDD scheme and supporting voice and data services. An efficient MAC protocol provides fast dynamic allocation of the capacity, exceeding 30 Mb/s net throughput. Approach to 2 nd generation systems has started already, with main goals of throughput enhancement and enabling of low cost equipment. Such systems will be still based on a point-to-multipoint cellular architecture providing highquality access (BER < 10-11), at net throughput exceeding 115 Mb/s in 28 MHz. In this paper, after a short overview of 1 st generation system features, requirements, architecture and performances of 2 nd generation systems are described. Main results of investigations upon some key implementation aspects are also reported. The modulation scheme adopted is a four levels constant envelope (C-QPSK), also known as Tamed Frequency Modulation (TFM), allowing 37.5 Mb/s in 28 MHz symmetric RF channels, while enabling very high system gain. Key system features of this product are summarized in table 1.
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Elsevier eBooks · 2014
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P. Sweeney · Institution of Engineering and Technology eBooks · 1999
Channel coding is a signal-processing technique which makes the representation of information bits interdependent and introduces redundancy into the sequences so that noise averaging and error protection can be achieved. It originates from the development of information theory by Shannon ' in the late 1940s which showed that any channel of known characteristics has a calculable capacity for information transfer. Provided that capacity is not being exceeded, it should be possible to achieve reliable communications with an error rate which can be reduced to any desired level by increasing the length of the codes used. The passage of 50 years since Shannon's discoveries has not yielded practicable coding schemes which allow theoretical channel capacity and error rates to be achieved. There are certain recently discovered codes which appear to provide the closest approach to the Shannon performance, but mainstream practice is content to adopt more modest aims. These could include the reduction of error rates to be suitable for a particular application or to allow the extension of operations to difficult areas. A common objective would be to reduce the power requirements for acceptable error rates, since high power brings with it several expensive problems including effects induced by nonlinear power devices. In this cost-conscious age, it is unlikely that cost-effective solutions to digital communications can be achieved without coding.
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Neri Merhav, Neri Merhav · 2008
We demonstrate that there is an intimate relationship between the magnetic properties of Derrida’s random energy model (REM) of spin glasses and the problem of joint source–channel coding in Information Theory. In particular, typical patterns of erroneously decoded messages in the coding problem have “magnetization ” properties that are analogous to those of the REM in certain phases, where the non–uniformity of the distribution of the source in the coding problem, plays the role of an external magnetic field applied to the REM. We also relate the ensemble performance (random coding exponents) of joint source–channel codes to the free energy of the REM in its different phases.
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Martin J. Wainwright, Emin Martinian · 2007
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Song-Nam Hong · 2020
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2001
Subject Mathematical and Statistical Physics Collection: Oxford Scholarship Online
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K-K Wong, Lajos Hanzo · ePrints Soton (University of Southampton) · 1992
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Imre Csiszár · 1970
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Luigi Paura · 2011
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