Essentials of Error-Control Coding Techniques (eBook)

Hideki Imai (Herausgeber)

eBook Download: EPUB

2014 | 1. Auflage
348 Seiten
Elsevier Science (Verlag)
978-1-4832-5937-6 (ISBN)

Infos

Essentials of Error-Control Coding Techniques presents error-control coding techniques with an emphasis on the most recent applications. It is written for engineers who use or build error-control coding equipment. Many examples of practical applications are provided, enabling the reader to obtain valuable expertise for the development of a wide range of error-control coding systems. Necessary background knowledge of coding theory (the theory of error-correcting codes) is also included so that the reader is able to assimilate the concepts and the techniques. The book is divided into two parts. The first provides the reader with the fundamental knowledge of the coding theory that is necessary to understand the material in the latter part. Topics covered include the principles of error detection and correction, block codes, and convolutional codes. The second part is devoted to the practical applications of error-control coding in various fields. It explains how to design cost-effective error-control coding systems. Many examples of actual error-control coding systems are described and evaluated. This book is particularly suited for the engineer striving to master the practical applications of error-control coding. It is also suitable for use as a graduate text for an advanced course in coding theory.

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1

Introduction

Hideki Imai

Publisher Summary

This chapter focuses on error-control coding. Errors are classified as one of three types, namely, random errors, burst errors, and byte errors. Random errors occur independently on each symbol. Burst errors occur intensively in a period of data. Byte errors occur in a small block of data. In some cases, mixtures of two of the three types can occur. For each type of error, there exist codes that can effectively detect and/or correct errors of that type. However, a code designed to detect or correct one type of error cannot necessarily be effective for other types. Error-control coding has become an essential part in most of the digital communication and recording systems. As the amount of digital data that must be transmitted or stored reliably increases, error-control coding is becoming more and more important. Because of advances in solid-state electronics technology, codes with large error-correction capability and high efficiency are widely used. In particular, coding systems that employ two codes combined together to obtain better performance, for example, concatenated codes, are often employed.

1.1. Digital Techniques and Error-Control Coding

1.2. Error-Control Coding in Communications

1.2.1. Applications to Satellite Communications

1.2.2. Applications to Broadcasting

1.2.3. Applications to Other Communication Systems

1.3. Error-Control Coding in Computers

1.3.1. Applications to Logic Circuits

1.3.2. Applications to Semiconductor Memory Systems

1.3.3. Applications to Magnetic Recording Systems

1.3.4. Applications to Optical Disk Systems

1.4. Error-Control Coding in Audio-Video Systems

1.4.1. Applications to Audio Systems

1.4.2. Applications to Video Systems

1.5. Future Prospects of Error-Control Coding

Bibliography

1.1 Digital Techniques and Error-Control Coding

As of 1989, the number of communication or audio-video systems that treat voice or image signals as digital data is rapidly increasing. The material that computers process or store is digital data as well. One of the important characteristics of digital signals is that they are more reliable in a noisy environment than analog signals. Since the detector for digital data may only decide whether each symbol is a 0 or a 1, digital symbols can often be detected perfectly, provided the noise is weak.

However, when the noise is not weak, the detector may make an erroneous decision, that is, it may decide that a symbol is a 1 although it was originally a 0. But if the data are coded, that is, some appropriate check (redundant) symbols are annexed to the data symbols, the decoder can correct or detect certain errors. Thus, when a signal is represented as digital data, we can make the signal detection more reliable by adding check symbols to the data symbols. This technique is called error-control coding.

A vast amount of research has been done so far on the theory of error-control coding. But it is not until recently that this technique has been applied widely to digital communication and storage systems. Today, error-control coding is used in many digital systems, and its role is becoming more and more important. This is because error-control codes have become easy to implement owing to advances in solid-state electronic technology and because the amount of digital data that must be transmitted or stored reliably has greatly increased. In some areas, error-control coding is essential to practical system design.

When choosing an appropriate error-control code for a digital communication or recording system, a number of factors must be considered. The first of these is the type of errors that occur in the system. Errors are classified as one of three types, namely, random errors, burst errors, and byte errors. Random errors occur independently on each symbol. Burst errors occur intensively in a period of data. Byte errors occur in a small block of data. In some cases, mixtures of two of the three types may occur. For each type of error, there exist codes that can effectively detect and/or correct errors of that type. However, a code designed to detect or correct one type of error will not necessarily be effective for other types.

The next things to be considered are the required error-correction or -detection capability, the allowable number of redundant symbols, and the size, complexity, and speed of the decoder. Naturally, a trade-off among the preceding must be made. This is shown conceptually in Fig. 1.1. The vertical axis represents the error-correction (or -detection) capability, while the transverse axis represents the code rate, which is related inversely to the amount of redundancy required. The closer to the origin the point in Fig. 1.1 is, the better the code is.

Fig. 1.1 General characteristics of codes.

Generally, a code with large error-correction capability has low code rate. This relationship is indicated by the two lines in Fig. 1.1 representing two classes of codes, namely code classes A and B. Since code class B has a code with higher code rate than code class A for a given error-correction capability, code class B is more efficient in that it is less redundant and thus has less waste than code class A. However, efficient codes usually need a complicated decoder which operates at a relatively low speed. Thus, if a simple or fast decoder is required, efficiency must be sacrificed to a certain extent. Figure 1.1 also shows the limit of theoretically realizable codes. We cannot have a code beyond this limit no matter how large a decoder we install. Therefore, the problem of selecting a code boils down to finding a point in Fig. 1.1 that fulfills the requirements for error-correction capability, code rate, size, and speed of the decoder. Table 1.1 lists typical error-control codes.

Table 1.1

Typical Error-Control Codes

Random

Self-orthogonal convolutional codes

Small

BCH codes

Convolutional codes with Viterbi decoding

Convolutional codes with sequential decoding

Concatenated codes (Reed—Solomon + convolutional)

Large

Burst

Iwadare codes

Small

Fire codes

Reed—Solomon codes

Doubly coded Reed—Solomon codes

Large

Byte

Reed—Solomon codes

In addition to the selection of the code, we must choose among three error-control schemes: (1) correct any errors at the decoder according to a given rule (FEC: forward error correction), (2) request a retransmission of erroneous data block (ARQ: automatic repeat request), (3) estimate the true value of erroneous data from correct data by utilizing the statistical characteristics of the data. This is determined by the required reliability of the decoded data, the allowable delay time for reception of the decoded data, the amount of hardware that can be put at the sending and receiving ends, and so on.

In the following sections, we derive the requirements for error-control coding and show examples of codes actually used in the areas of communications, computers, and audio-video systems.

1.2 Error-Control Coding in Communications

At first, error-control coding was studied as a means to improve the bit error performance of digital communication systems, but not until quite recently has it become an important part of the digital communication systems.

1.2.1 Applications to Satellite Communications

In satellite communications, the channel noise can be regarded as additive white Gaussian; thus the errors are mostly random. Since the transmitter power and the size of the antennas of a spacecraft are limited, it is desirable to use a code with large error-correction capability to compensate for the low signal-to-noise ratio. This is because we can reduce the required transmitting power per bit ratio to obtain a given bit-error rate by using an error-correcting code. However, since the available bandwidth for transmission is also limited, the code rate must not be too low. Furthermore, for a system where the transmission speed is very high, we cannot use a code that needs a complicated decoder.

Self-orthogonal convolutional codes, which are decoded by a simple decoder, were mainly used for satellite communications. However a ½ rate convolutional code with Viterbi decoding, which produces larger error-correction...

Produkt-Details

• Erscheint lt. Verlag: 28.6.2014
• Sprache: englisch
• Themenwelt: Mathematik / Informatik ► Informatik ► Datenbanken
• Themenwelt: Mathematik / Informatik ► Informatik ► Theorie / Studium
• Themenwelt: Technik ► Bauwesen
• ISBN-10: 1-4832-5937-4 / 1483259374
• ISBN-13: 978-1-4832-5937-6 / 9781483259376