(Solved): 6.) Rate distortion theory Let us assume a ternary source X with symbols equally probable 0,1,2, bu ...

6.) Rate distortion theory Let us assume a ternary source $X$ with symbols equally probable $0,1,2$, but only a binary representation $\hat{X}$, i.e., 0 and 1 . We assume the following distortion model, which we may draw in the form of an erasure channel or also mirrored to recognize the distorted representation. a) The figure on the left shows $P\left({\hat{X}}_i?X_j\right)$. Determine one of the components for the other graph, $P(X=0?\hat{X}=0)$. b) The rate distortion function may either be written as $I(X;\hat{X})=H(X)?H(X?\hat{X})\text{ or }I(X;\hat{X})=H(\hat{X})?H(\hat{X}?X).$ Choose a suitable formulation and determine $I(X;\hat{X})$.