e details of their respective code-length assignments. We observe from Table 8.5 that the binary code has the smallest mean codeword length relative to the source entropy, i.e., L**(x) = 4.577 bit/symbol, yielding the highest coding efficiency of n = 91.42%. This result is better than the value of n = 83.70% found for a fixed-length binary code with 5 bit/symbol (such as ASCII reduced to lower-case or upper-case letters). Moving from binary to ternary is seen to decrease the coding efficiency to n = 84.37%. The efficiency increases somewhat with the quaternary code (n = 84.63%.), but apart from such small irregularities due to the integer truncation effect, it decreases with increasing M. For M = 26, the efficiency has dropped to = 72.63%. This last result is substantially lower than the value of n = 89.0%, which we found earlier for fixed-length, 26-ary coding having one character/symbol. The conclusion of this exercise is that the Shannon code does not necessary yield better efficiencies than a fixed-length code, against all expectations. In the example of the English-character source, the Shannon code is better with binary codewords, but it is Information coding Table 8.5 Shannon codes for the English-character source, using binary, ternary, quaternary, and 26-ary codewords. Binary coding Ternary coding Ideal Ideal length length length length length length plog2(p) l*(x) l**(x) l**(x)p(x) plog3(x) l*(x) l**(x) l**(x)p(x) 0.127 0.378 2.9771 0.381 0.239 1.8783 0.254 0.091 0.314 3.4623 0.363 0.198 2.1845 0.272 0.082 0.295 3.6126 0.327 0.186 2.2793 0.245 0.075 0.280 3.7413 0.299 0.177 2.3605 0.224 0.070 0.268 3.8408 0.279 0.169 2.4233 0.209 0.067 0.261 3.904 0.267 0.165 2.4632 0.200 0.063 0.251 3.9928 0.251 0.158 2.5192 0.188 0.061 0.246 4.0394 0.304 0.155 2.5486 0.182 0.060 0.243 4.0632 0.299 0.153 2.5636 0.179 0.043 0.195 4.5438 0.214 0.123 2.8668 0.129 0.040 0.185 4.6482 0.199 0.117 2.9327 0.120 0.028 0.144 5.1628 0.167 0.091 3.2573 0.112 0.028 0.144 5.1628 0.167 0.091 3.2573 0.112 0.024 0.129 5.3851 0.144 0.08