number of symbols received. A possible codeword assignment to each symbol, including that of the -node, is shown for each step. See Fig. 10.3 for the corresponding coding trees up to step k = 6. The entropy and coding efficiency are plotted in Fig. 10.4. Symbol k = 1 k = 2 k = 3 k = 4 k = 5 k = 6 k = 7 k = 8 k = 9 k = 10 k = 11 k = 12 Source entropy H (bit/symbol) 0.918 1.921 1.792 2.128 2.405 2.419 2.646 2.550 2.751 mean codeword length L (bit/word) 1.333 2.200 2.000 2.285 2.625 2.777 2.800 2.727 3.000 Coding efficiency n (%) 33.33 68.87 85.71 87.36 89.62 93.10 91.64 87.10 94.52 93.51 91.72 10.3 Adaptive Huffman coding Number of message symbols k Figure 10.4 Evolution of entropy H and coding efficiency n in adaptive Huffman coding as a function of the number of symbols received k, which corresponds to the example in Fig. 10.3 and Tables 10.3 and 10.4. In case (a), the -node's current codeword acts as a signal to the decoder that a new symbol must be entered in the tree (initially, the -node codeword is set to zero). The previous -node is split into a new -node and a new leaf for this symbol. The other information concerns the symbol description, for instance its ASCII value. In case (b), the weight of the symbol's terminal node (leaf) simply needs to be incremented by one unit, which is sufficient to recompute the coding tree. Note that the information in case (b) is pure payload (previously-seen symbol transmission), while that in case (a) is both payload and overhead (new symbol transmission with definition). The data listed in Table 10.4 represent the information provided by the encoder to the decoder for the message string GOODTOSEEYOU, as based on the codewords of Table 10.3, to be sequentially used by the decoder for coding-tree updating and decoding. The table also shows the number of information bits that the encoder outputs at each step. Assume that a fixed- length codeword with n bits is required to define a new symbol, for instance n = 7 for the reduced ASCII code. As this table indicates, the seven-b