Coding theory: Difference between revisions

Revision as of 23:28, 12 November 2005

Revision as of 04:40, 18 November 2005

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is also a code word; and they are applied to the source bits in blocks; hence the name

Linear Block Codes. Although linearity is not a requirement, it is difficult to prove

that a code is a good one without this properityproperty.

Any linear block code, is represented at <math>(n,k,d_{min})</math> where

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we increase the dimensions, the number of near neighbors increases very rapidly.

The result is the the number of ways for noise to make the receiver choose

a neighbor (hence an error) grows as well. This is a fundementalfundamental limitation

of block codes, and indeed all codes. It may be harder to cause an error to

a single neighbor, but the number of neighbors can be large enough so the

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of the input bit, against the states of the convolution encoder, registers.

FundementallyFundamentally, convolutional codes do not offer more protection against noise than an

equivelentequivalent block code. In many cases, they generally offer greater simplicity of

implementation over a block code of equal power. The encoder is usually a simple

circuit which has state memory and some feedback logic, normally XOR gates. The decoder

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There are simplifications to reduce the computational load. They rely on searching only

the most likely paths. Although not optimum, they have generally found to give good results

in the lower noise environments. ModermModern microprocessors are capable of implementing these reduced

search algorithimsalgorithms at rate greater than 4000 codewords/s.

== Applications of Coding Theory ==