ase M = 2, but the arguments developed are valid for all M. We first construct a binary tree of order l = IN, as shown in Fig. F1 (assuming here, for instance, l = 4). As the figure illustrates, the tree has 21 terminal nodes or "leaves" (here 24 = 16 terminal nodes). The tree also has 24 1 = 15 branching nodes. Each node is located on a uniquely defined path, labeled by the 0 and 1 signs at each splitting. For instance, the location of terminal node A is defined by the path labeled 1011. We call the node order the length of its path label (e.g., node A is of order four). The idea is to assign each of the codewords Ck (length 1k) to any of the nodes of the tree (branching or terminal), which is of order lk. Such an assignment is continued until there is no codeword left. Assume that there are only five codewords (N = 5), with lengths l = 1, l2 = 2, l3 = 3, and 14 = l5 = 4. As shown in Fig. F2, the codeword C1 could, thus, be assigned (for instance) to the order-1 node defined by the path 1. Because the code is a prefix code, C1 cannot be the prefix to any other codewords, meaning that this choice eliminates all the subsequent nodes found in the path beginning with 1 (connected in the figure by dashed lines). We continue by assigning C2 to any available order-2 node, and SO on until C5, as illustrated in the figure. Based on this example, it is easy to observe that each assignment of codeword Ck with length lk eliminates 21-1k terminal nodes. The total number of terminal nodes eliminated is, J.G. Proakis, Digital Communications, 4th edn. (New York: McGraw Hill, 2001). Appendix F Branching node Terminal node Figure F1 Binary tree of order l = IN. Figure F2 Binary tree for codewords C1, C2, C3, C4, and C5. therefore, 21-1k < 2', where 21 (to recall) is the total number of terminal nodes. The result of (F3) gives 2-"k 1, which is the Kraft-McMillan inequality. Appendix G (Chapter 9) Overview of data compression standards This appendix provides a brief overview of common data compression standards used for sounds, tex