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<math>\mathbb{E}[2X{_i^e + X{_i^?}}] \le {{2e_i} \over d}</math>............................................................. (2)
Clearly, by definition <math>e' = \sum_{i}X{_i^e}</math> and <math>s' = \sum_{i}X{_i^?}</math>. Futher, by the [http://en.wikipedia.org/wiki/Linear linearity] of expectation, we get <math>\mathbb{E}[2e' + s'] \le {2 \over d}\sum_ie_i</math> < <math>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_{in}(y_i'))</math>
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