HlX] =0.3 log2(0.3)-0.3log2 (0.3)-0.21082 (0.2)-0.1 log2(0.1)-0.1 log2 (0.1) = 2.17 bits per symbol Since this source is not uniform, its entropy is less than log2 (5) = 2.32 bits. Consider the problem of encoding this data source with binary codes. There are five symbols, so each one can be encoded with three bits (23 82 5). We illustrate the code with a binary tree Code words start at the root of the tree (top) and proceed to a leaf (bottom). For instance, the sequence aabec is encoded as 000 000 001 100 010 (the "dots" are shown only for exposition and are not transmitted) This seems wasteful, however, since only five of the eight possible code words would be used. We can prune the tree by eliminating the three unused leafs and shortening the remaining branch: HlX] =0.3 log2(0.3)-0.3log2 (0.3)-0.21082 (0.2)-0.1 log2(0.1)-0.1 log2 (0.1) = 2.17 bits per symbol Since this source is not uniform, its entropy is less than log2 (5) = 2.32 bits. Consider the problem of encoding this data source with binary codes. There are five symbols, so each one can be encoded with three bits (23 82 5). We illustrate the code with a binary tree Code words start at the root of the tree (top) and proceed to a leaf (bottom). For instance, the sequence aabec is encoded as 000 000 001 100 010 (the "dots" are shown only for exposition and are not transmitted) This seems wasteful, however, since only five of the eight possible code words would be used. We can prune the tree by eliminating the three unused leafs and shortening the remaining branch