Past exam of the mathematics course of the University of Cambridge / 2024 / iii / Paper 224 / 2 / b / Solution

The code-distribution correspondence starts from the Kraft inequality. For codeword lengths $L(x)$ putConversely, a probability mass function determines ideal lengths $-{\log }_{2}R(x)$, up to integer rounding. For the source law $P_n$,using nonnegativity of Kullback-Leibler divergence and $K\le 1$.