I was going through binary communication systems whereby I came across the concept of information gain.Now, I assign probabilities to the transmitted symbols of a binary symmetric channel ie, the probability that I transmit a 0 is p(0) and if I transmit 1 is p(1). The channel which I am working on looks like :
Since Information gain is a concept governing the reduction in uncertainity when going down a branch, I think that we should be able to calculate the information gain while observing the output variable Y if I KNOW WHICH SYMBOL I TRANSMITTED, (or GIVEN THAT A SYMBOL HAS BEEN TRANSMITTED), SAY X0. Can anyone explain how can I do this? I am unable to figure out myself.