I am reading Yeung's Information theory and network coding. In Examples 3.12, 3.13, and 3.14, the author uses schematic diagrams for the random variables. This is Example 3.13:
This is definition of $Z$:
In Example 3.13, how do I understand this schematic diagram? What are these switches, these boxes? $p_{1}(y|x),p_{2}(y|x)$ are transition matrices. What are transition matrices? Or can you recommand places where I can learn about these?
This is pretty standard in info theory. Basically the transition matrix enumerates the conditional distributions for the channel. Let $X \in {\cal X}=\{x_1,\ldots,x_k\},$ and $Y \in {\cal Y}=\{y_1,\ldots,y_n\},$ then $$ M=\left[ \begin{array}{ccc} p(y_1|x_1)& \ldots & p(y_n|x_1) \\ p(y_1|x_2)& \ldots & p(y_n|x_2) \\ \vdots & \ldots & \vdots \\ p(y_1|x_1)& \ldots & p(y_n|x_k) \\ \end{array} \right] $$ is the transition matrix.
As for the diagram, based on the value of a random variable $Z$ which equals 1 with probability $\lambda$ and equals 2 with probability $\overline{\lambda}=1-\lambda,$ the conditional distribution is equal to $M_1=[p_1(y_j|x_i)]$ or $M_2=[p_2(y_j|x_i)],$ respectively.