32 225 792 840 4.97902 X 10-34 129 024 480 6.4242 X 10-26 3.14784 X 10-24 LLLL LLLL LLLW WWWW WWWW WWWW WWWW WWWW 1.34568 X 10-35 64 512 240 8.6813 X 10-28 4.25383 X 10-26 LLLL LLLL LLWW WWWW WWWW WWWW WWWW WWWW LLLL LLLL LWWW WWWW WWWW WWWW WWWW WWWW 3.63698 X 10-37 1.0201 X 10-29 4.99863 X 10-28 28 048 800 9.82966 X 10-39 10 518 300 1.0339 X 10-31 5.06618 X 10-30 LLLL LLLL WWWW WWWW WWWW WWWW WWWW WWWW 8.942 X 10-34 4.29214 X 10-32 LLLL LLLW WWWW WWWW WWWW WWWW 2.65667 X 10-40 3 365 856 LLLL LLWW WWWW WWWW WWWW WWWW WWWW WWWW 7.18018 X 10-42 6.5066 X 10-36 3.05811 X 10-34 906 192 LLLL LWWW WWWW WWWW WWWW WWWW WWWW WWWW 1.94059 X 10-43 201 376 3.9079 X 10-38 1.79762 X 10-36 5.24483 X 10-45 35 960 1.886 X 10-40 8.4719 X 10-39 LLLL WWWW WWWW WWWW WWWW WWWW WWWW WWWW 1.41752 X 10-46 4 960 7.0309 X 10-43 3.02329 X 10-41 LLLW WWWW WWWW WWWW WWWW WWWW WWWW WWWW 3.83114 X 10-48 1.9002 X 10-45 7.60099 X 10-44 LLWW WWWW WWWW WWWW WWWW WWWW WWWW WWWW 1.03544 X 10-49 3.3134 X 10-48 1.22597 X 10-46 LWWW WWWW WWWW WWWW WWWW WWWW WWWW WWWW WWWW WWWW WWWW WWWW WWWW WWWW 2.7985 10-51 2.7985 X 10-51 8.95519 X 10-50 4 294 967 296 1.0000 X 1000 5.771800335 Extended source entropy nH = 5.618081. Efficiency n = 97.34%. 9.3 Block codes Number of games n Figure 9.8 Coding efficiency of variable-length block code describing a sequence of n roulette game outcomes. The data corresponding to n = 2k (where k is an integer) are shown in dark. The continuous curve corresponds to the envelope of ideal Huffman coding, as computed up to n : 9 and extrapolated beyond n = 9. of trailer bits, which progressively reduces the maximum compression effect obtained each time that n = 2k. Concerning the curve envelope (n = 9), which is also plotted in Fig. 9.8, see further. The above example illustrates that block coding can be quite efficient and yield high data compression, but care should be given to find the optimum sequence length, if it exists. A relevant question is: how does block coding compare with Huffman coding? The second solution, which we 