Decoding methods: Difference between revisions

Revision as of 06:12, 24 July 2008

Revision as of 06:15, 24 July 2008

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Now suppose that a codeword <math>x \in \mathbb{F}_2^n</math> is sent over the channel and the error pattern <math>e \in \mathbb{F}_2^n</math> occurs. Then <math>z=x+e</math> is received. Ordinary minimum distance decoding would lookup the vector <math>z</math> in a table of size <math>|C|</math> for the nearest match - iei.e. an element (not necessarily unique) <math>c \in C</math> with

:<math>d(c,z) \leq d(y,z)</math>