 minimum number of bits TB required to code N. The resulting codeword length is M = HB + TB. At bottom are shown the total number of extended-source events, the mean codeword length L = (M), the extended-source entropy nH and the coding efficiency n = H/L. N = 4 games No of No of trailer No of required, Sequence Possibilities, bits, Probability, header M = HB Type type Probability, p1 p = Np Header bits, HB 0.89881955 0.89881955 0.89882 0.02429242 0.09716968 0.38868 0.00065655 0.00393931 0.02364 LWWW 1.7745 x 7.0979 x 10-5 0.00043 WWWW 4.7959 X 10-7 4.7959 x 10-7 0.00000 1.0000 X 10° 1.31156 Extended source entropy nH = 0.70226. Efficiency n = 53.544%. each of the above sequence types with the corresponding probabilities: p(LLLL) = C'(1-p) p(WWWW) = Cap4 p(LLLW) = C1p(1-p)3 (9.4) p(WWWL) = C1p3(1-p) p(LLWW) = Cap2(1-p)2, recalling that each of these types is associated with N = CK unique outcomes. Table 9.4 lists the data computed with p = 1/38 = 0.0263, the resulting probabilities being shown in decreasing order, with the sequence types referred to as A, B, C, D, and E. To label each of the sequence outcomes, we shall construct a variable-length block code made with the concatenation of a header block with a trailer block. The header block is coded with a uniquely decodable word of length HB, which indicates the sequence type (A, B, C, D, or E). The trailer block has the minimum number of bits TB required to code N. For instance, the outcome LLLL (type A) has the header 1 and an empty trailer. The outcome LLLW (type B) has the header 01 and a trailer of two bits (namely 00, 01, 10, and 11) which labels each of the four unique possibilities in the type-B sequence (namely LLLW, LLWL, LWLLL, and WLLL). The resulting codeword length is, therefore, M = HB + TB. Table 9.4 shows the mean codeword length L = (M) and the coding efficiency n = nH/L, where nH is the entropy of the extended source corresponding to the n independent outcomes of the n successive games. The results 9.3 Block codes indicate that our block code 