Decoding methods: Difference between revisions

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Hx = Hy does not imply x = y (this is obvious since if x and y are both codewords then Hx = Hy = 0, but equivalent errors will also give the same syndrome)
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:<math>x = z - e </math>
 
Notice that this will always give a unique (but not necessarily accurate) decoding result since
 
: <math>Hx = Hy</math>
 
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 ==