Generalized minimum-distance decoding: Difference between revisions

Revision as of 20:13, 27 June 2011

Revision as of 04:53, 2 August 2011

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: <math>\mathbb{E}[2X{_i^e + X{_i^?}}] \le {{2e_i} \over d}\qquad\qquad (2)</math>

Clearly, by definition <math>e' = \sum_{i}X{_i^e}</math> and <math>s' = \sum_{i}X{_i^?}</math>. FutherFurther, by the [[Linear|linearity]] of expectation, we get <math>\mathbb{E}[2e' + s'] \le {2 \over d}\sum_ie_i < D</math>. We consider two cases to prove (2) : <math>i'th</math> block is correctly decoded('''Case 1'''), <math>i'th</math> block is incorrectly decoded('''Case 2''')

'''Case 1:''' <math>(c_i = C_\text{in}(y_i'))</math>