Past exam of the information theory course of the University of Oxford / 2021 / 2 / a

The displayed prefix code has expected codeword length $3/2$ ternary digits per source symbol. Instead assignThis is a ternary prefix code: the first two codewords end at distinct tree children of the tree root, and the other two start with $2$ and end at distinct tree children below it. No codeword is a prefix of another. Its expected codeword length isThe reduction is $1/4$ trit per source symbol, which already disproves optimality of the displayed code. The ternary Huffman coding construction below will produce this same improved code tree.