Decoding methods: Difference between revisions

Revision as of 21:49, 11 July 2008

Revision as of 06:12, 24 July 2008

Line 73:

==Syndrome decoding==

<!-- [[Syndrome decoding]] redirects here -->

'''Syndrome decoding''' is a highly efficient method of decoding a [[linear code]] over a ''noisy channel'' - iei.e. one on which errors are made. In essence, syndrome decoding is ''minimum distance decoding'' using a reduced lookup table. It is the linearity of the code which allows for the lookup table to be reduced in size.

The simplest kind of syndrome decoding is [[Hamming code]].

Line 113:

if and only if <math>x=y</math>. This is because the parity check matrix <math>H</math> is a generator matrix for the dual code <math>C^\perp</math> and hence is of full [[rank (linear algebra)|rank]].

== Partial response maximum likelihood ==