2 problems

Let $\mathcal{Y}^*=\bigcup_{k\in\mathbb{N}\setminus\{0\}}\mathcal{Y}^k$ be the set of nonempty finite strings over $\mathcal{Y}$, let $\{Y_k:k\in\mathbb{N}\}$ be the Markov chain a…

Let $P_{X_k}^{+}$ and $P_{X_k}^{-}$ denote the distributions of the observations at layer $k$ conditioned on the source bit being $1$ and $0$, respectively. Fix…