Talk:Fano's inequality

Probability of communication error
Shouldn't the definition of the probability of communication error be:


 * $$P(e)= \sum_{j\not=i} P(y_j, x_i)$$

instead of:


 * $$P(e)=\sup_i \sum_{j\not=i} P(y_j|x_i)$$

This way, the total probability mass of generating a message x and receiving a different message y is calculated. What is currently written, calculates the probability of error that is largest for a particular message. However, this does not take into account the fact that the probability of generating this message could be very small.

Where can I find the proof of the "Alternative formulation"?
$SUBJ — Preceding unsigned comment added by Lockywolf (talk • contribs) 11:26, 30 September 2015 (UTC)