Block code: Difference between revisions

Revision as of 14:36, 13 September 2005

Revision as of 18:07, 23 September 2005

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===Practical definition===

BlockA '''block code''' is the primary type of [[channel coding]] which was used in earlier [[Mobilemobile communication]] systems. Simply it adds [[redundancy]] in soorder that at the receiver, one can decode with (theoretical) probability of zero errors, provided that the [[Rateinformation rate]] (R)amount of transported [[information]] in [[bit]]s per sec) would not exceed the [[Channelchannel Capacitycapacity]].

The main characterisation of a block code is that it is a ''fixed length'' channel code (unlike source coding schemes such as [[Huffman coding]], and unlike channel coding methods like [[convolutional code|convolutional encoding]]). Typically, a block code takes a ''k''-digit information word, and transforms this into an ''n''-digit codeword.

===Theoretical definition===

In [[information theory]], a '''block code''' is a [[code]] which encodes strings formed from an alphabet set <math>S</math> into code words by encoding each letter of <math>S</math> separately. Let <math>(k_1,k_2,\ldots,k_m)</math> be a sequence of [[natural numbers]] each less than <math>|S|</math>. If <math>S={s_1,s_2,\ldots,s_n}</math> and a particular word <math>W</math> is written as <math>W=s_{k_1}s_{k_2}\ldots s_{k_m}</math>, then the code word corresponding to <math>W</math>, namely <math>C(W)</math>, is

<math>C(W) = C(s_{k_1})C(s_{k_2})\ldots C(s_{k_m})</math>.