r 4. It is easily established that the PDF of the trit codewords is the same as that of the bit (or conventional Morse) codewords.13 Table 8.3 also shows the source entropy in either base-2 (bit/symbol) or base-3 (trit/symbol) logarithms. By convention, entropy in logarithm base M will be called here HM. Consistently, it is defined according to: (8.2) Recalling that logM X : Inx/lnM, where In is the natural logarithm, the relation between base-M entropy and conventional (base-2) entropy is the following: In(M)HM==In(2)H2. (8.3) Looking at Table 8.3, the calculations for base 2 and base 3 source entropies yield H2 = 4.185 bit/symbol (English-language entropy) and H3 = 2.640 trit/symbol, respec- tively. The next step in our analysis is to define a way to measure how efficient a given code is in using the most concise codewords, regardless of the logarithmic base. This issue is addressed in the next section, which will also use our new Morse code by way of an illustrative example. Mean code length and coding efficiency Let's introduce the mean codeword length (also called expected length) according to the definition (8.4) where 1(x) is the codeword length corresponding to symbol x from source X. With a binary code, the unit of L is bit/symbol. This defines the mean or expected codeword length as effective code entropy. We shall, again, use the ternary Morse code as an illustrative example. In this case, L is in units of trit/symbol. Columns 6 and 7 in Table 8.3 detail the calculation of the mean codeword length, as based on the above definition, the ternary codewords previously introduced (Column 2) and the distribution p(x). As Table 8.3 shows, the mean codeword length is L = 3.544 trit/symbol. Since L has the dimensions of entropy, we can compare it with the codeword source, using the ratio n = H3/L, with 13 This is because the joint and conditional probabilities of the Morse/blank digrams x/y satisfy p(y = blank /x) = p(x) and p(y = blank, x) : p(x), with p(y = blank) = 1. More accurately the unit of the mean cod