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An Outline of Informational GeneticsAn Outline of Error-Correcting Codes

An Outline of Informational Genetics: An Outline of Error-Correcting Codes CHAP TER 6 An Outline of Error-Correcting Codes 6.1 INTRODUCTION This chapter provides an introduction to error-correcting codes, considered as tools for making reliable communication through unreliable channels. A lot of works were devoted to error-correcting codes but only a few of them are actually accounted for below. Even when dealing with well-known codes, the approach for presenting them is rather unconventional: much of the vocabulary and notation used in this text departs from the standard ones, which have their origin in the history of the discipline rather than in a logical development. Our starting point will be an analysis of mere repetition, which is a rather crude error-correcting means. Then more elaborated error-correcting codes will be introduced. Interestingly, this approach will enable us to meet and understand practically important families of error-correcting codes, including the most efficient ones. We need first to describe the basic communication problem and the kind of channels which will be considered. 6.2 COMMUNICATING A MESSAGE THROUGH A CHANNEL 6.2.1 DEFINING A MESSAGE A message consists of an arbitrary sequence of elements, referred to as symbols, taken from some alphabet, i.e., some finite collection of signs. For instance, the previous sentence is made of http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png

An Outline of Informational GeneticsAn Outline of Error-Correcting Codes

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Publisher
Springer International Publishing
Copyright
© Springer Nature Switzerland AG 2008
ISBN
978-3-031-00501-5
Pages
79 –115
DOI
10.1007/978-3-031-01629-5_6
Publisher site
See Chapter on Publisher Site

Abstract

CHAP TER 6 An Outline of Error-Correcting Codes 6.1 INTRODUCTION This chapter provides an introduction to error-correcting codes, considered as tools for making reliable communication through unreliable channels. A lot of works were devoted to error-correcting codes but only a few of them are actually accounted for below. Even when dealing with well-known codes, the approach for presenting them is rather unconventional: much of the vocabulary and notation used in this text departs from the standard ones, which have their origin in the history of the discipline rather than in a logical development. Our starting point will be an analysis of mere repetition, which is a rather crude error-correcting means. Then more elaborated error-correcting codes will be introduced. Interestingly, this approach will enable us to meet and understand practically important families of error-correcting codes, including the most efficient ones. We need first to describe the basic communication problem and the kind of channels which will be considered. 6.2 COMMUNICATING A MESSAGE THROUGH A CHANNEL 6.2.1 DEFINING A MESSAGE A message consists of an arbitrary sequence of elements, referred to as symbols, taken from some alphabet, i.e., some finite collection of signs. For instance, the previous sentence is made of

Published: Jan 1, 2008

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