 4.1 shows the probability of an English letter appearing in the text. What is the information rate for a source that produces 100 letters every second? Table 4.1 Typical probability of occurrence of individual English letters 8.17% 0.15% 6.33% 1.49% 0.77% 9.06% 2.78% 4.03% 2.76% 4.25% 2.41% 0.98% 12.70% 6.75% 2.35% 2.23% 7.51% 0.15% 2.02% 1.93% 1.97% 6.09% 0.10% 0.07% 6.97% 5.98% Source entropy can be calculated to be 4.176 bits/letter. Source information rate is therefore 418 bps. Again a telecommunication network with a capacity of 418 bps will be sufficient to connect this source to a receiver of information. Source Coding Digital communications require representing of information from a source, with a series of binary bits, that is O's and 1's. Consider a source that produces two messages m and m with equal probability of 50%. The source entropy can be calculated from Equation 4.2 to be 1 bit/message. A binary repre- sentation, or source coding, for the messages m and m2 this source generates can be using '0' for m1 and '1' for M2. The average code length, A, a measure of how many bits are used on average for coding this source, is calculated from the following formula. This considers the probability of a message and the number of bits used to represent it: A = Epm (4.3) where pi is the probability and n; is number of binary bits used to represent message i. The average code length can also be calculated to be equal to 1 bit/message (50% X 1 + 50% X 1 = Source coding efficiency, defined as the ratio of entropy (H) to average code length (A), is equal to 100%. This is an optimal source coding scheme. Now consider the source from Example 4.1 which generates four messages, m1, m2, m3 and MA. The source entropy was calculated to be equal to 1.75 bits/message. One binary Broadband Telecommunications Technologies and Management 0.125 0.125 Average code length (A) Figure 4.2 One possible coding method 0.125 0.375 0.125 0.375 Average code length (A) Figure 4.3 An alternative coding method representation for this sou