Decoding methods: Difference between revisions

Revision as of 11:08, 24 November 2006

Revision as of 01:05, 17 December 2006

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'''Syndrome decoding''' is a highly efficient method of decoding a [[linear code]] over a ''noisy channel'' - ie 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.

Suppose that <math>C\subset \mathbb{F}_2^n</math> is a linear code of length <math>n</math> and minimum distance <math>d</math> with [[parity check matrix]] <math>H</math>. Then clearly <math>C</math> is capable of correcting uptoup to

:<math>t=\lfloor\frac{d-1}{2}\rfloor</math>