Decoding methods: Difference between revisions

Revision as of 09:12, 5 August 2015

Revision as of 03:14, 30 March 2016

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:<math>Hz = H(x+e) =Hx + He = 0 + He = He</math>

To perform ML decoding in a [[Binary symmetric channel]], one has to look-up a precomputed table of size <math>2^{n-k}</math>, mapping <math>He</math> to <math>e</math>.<br/>

Under the assumption that no more than <math>t</math> errors were made during transmission, the receiver looks up the value <math>He</math> in a table of size

Note that this is already of significantly less complexity than that of a [[standard array |Standard array decoding]].

UnderHowever, under the assumption that no more than <math>t</math> errors were made during transmission, the receiver can looks up the value <math>He</math> in a further reduced table of size

:<math>

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</math>

only (for a binary code). The table is against pre-computed values of <math>He</math> for all possible error patterns <math>e \in \mathbb{F}_2^n</math>.

Knowing what <math>e</math> is, it is then trivial to decode <math>x</math> as:

:<math>x = z - e </math>