Chapter Questions
Find binary Huffman codes for the sources shown in Figure 5.$$\begin{array}{l|cccccccc}\hline \text { Symbol } & \text { A } & \text { B } & \text { C } & \text { D } & \text { E } & \text { F } & \text { G } & \text { H } \\\hline \text { Prob. (1 }{ }^{\text {st }} \text { source) } & \frac{1}{8} & \frac{1}{8} & \frac{1}{8} & \frac{1}{8} & \frac{1}{8} & \frac{1}{8} & \frac{1}{8} & \frac{1}{8} \\\text { Prob. (2 }{ }^{\text {nd }} \text { source) } & 0.1 & 0.2 & 0.1 & 0.3 & 0.05 & 0.1 & 0.05 & 0.1 \\\text { Prob. (3 } 3^{\text {rd }} \text { source) } & 0.15 & 0.15 & 0.15 & 0.15 & 0.1 & 0.1 & 0.1 & 0.1 \\\hline\end{array}$$
Find ternary and quaternary (three and four code symbols) Huffman codes for the sources shown in Figure 5.
Find the smallest number of code symbols necessary to construct an instantaneous code of average length $L \leq 1.5$ for each of the three sources of Figure 5.
Find all binary Huffman codes for the source consisting of symbols $A, B, C, D$ if $A$ is twice more frequent $\operatorname{than} B$ and $B$ is twice more frequent than either of $C$ and $D$.
Describe binary Huffman codes of sources with equiprobable symbols(1) if the number of source symbols is a power of 2 ,(2) if it is not a power of 2.
Describe binary Huffman codes of sources satisfying $p_1<p_{n-1}+p_n$ (where $p_1 \geq p_2 \geq \cdots \geq p_n$ are the source probabilities). Compare with Exercise 2E.