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An Outline of Informational GeneticsSoft Codes

An Outline of Informational Genetics: Soft Codes CHAP TER 10 10.1 INTRODUCING CODES DEFINED BY A SET OF CONSTRAINTS In Ch. 6, we defined an error-correcting code C(n, k) as a subset among the set S of n-symbol sequences over some finite alphabet of size q. The number of symbols k of the information message that each codeword represents is referred to as the number of dimensions of the code or, more briefly, as its dimension. The code being necessarily redundant implies the strict inequality k< n. There are basically two ways for defining such a code. One way is to give the list of its words; random coding, as used by Shannon and his followers in order to prove the fundamental theorem of channel coding, is a typical example of it. The trouble with a mere list of codewords is that the number of its elements exponentially grows in terms of the codeword length n: assuming a k Rn R n constant information rate R = k/n, 0 <R < 1, the number of codewords is q = q = (q ) , which makes the decoding process of such a code of prohibitive complexity when n is large enough for the code to be http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png

An Outline of Informational GeneticsSoft Codes

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Publisher
Springer International Publishing
Copyright
© Springer Nature Switzerland AG 2008
ISBN
978-3-031-00501-5
Pages
145 –152
DOI
10.1007/978-3-031-01629-5_10
Publisher site
See Chapter on Publisher Site

Abstract

CHAP TER 10 10.1 INTRODUCING CODES DEFINED BY A SET OF CONSTRAINTS In Ch. 6, we defined an error-correcting code C(n, k) as a subset among the set S of n-symbol sequences over some finite alphabet of size q. The number of symbols k of the information message that each codeword represents is referred to as the number of dimensions of the code or, more briefly, as its dimension. The code being necessarily redundant implies the strict inequality k< n. There are basically two ways for defining such a code. One way is to give the list of its words; random coding, as used by Shannon and his followers in order to prove the fundamental theorem of channel coding, is a typical example of it. The trouble with a mere list of codewords is that the number of its elements exponentially grows in terms of the codeword length n: assuming a k Rn R n constant information rate R = k/n, 0 <R < 1, the number of codewords is q = q = (q ) , which makes the decoding process of such a code of prohibitive complexity when n is large enough for the code to be

Published: Jan 1, 2008

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