rce is shown in Figure 4.2. The average code length is calculated to be 2 bits/message, which is slightly larger than the entropy of 1.75 bits/message. Source coding efficiency is 1.75/2=87.5% By definition this is a suboptimal source coding scheme. A different binary representation is shown in Figure 4.3. The average code length is 1.75 bits/message now and is equal to the source entropy, resulting in a 100% efficient code. Knowledge of entropy informs the designer on the limit of source coding methods. This method of coding is called entropy coding. These codes are also called prefix-free codes, which means that no code is a prefix to another code. We will discuss source coding in more depth in Chapter 5. Another example is usage of ASCII 7-bit length binary for source coding the English alphabet as shown in Figure 4.4. The coding efficiency of 7 bits/message is significantly larger than the source entropy for English text as found in Example 4.3 as 4.176 bits/message. The coding efficiency is calculated to be 4.176/7.0=59.7%, which is quite low. In practice it is possible to design a source code with near entropy efficiency, as shown in Figure 4.5. This code is also prefix-free and is found using a method known as Huffman coding [3]. The average code length here is 4.205, resulting in a coding efficiency of Information Theory 100 0001 100 1010 101 0011 100 0010 100 1011 101 0100 100 0011 100 1100 101 0101 100 0100 100 1101 101 0110 100 0101 100 1110 101 0111 100 0110 100 1111 101 1000 100 0111 101 10000 101 1001 100 1000 101 0001 101 1010 100 1001 101 0010 Figure 4.4 ASCII coding for the English alphabet 001111101 101110 0011110 10010 11010 01110 11011 01111 001110 10110 00110 001111100 100110 101111 100111 001111110 001111111 Figure 4.5 A near entropy efficiency code for the English alphabet Broadband Telecommunications Technologies and Management 4.176/4.205 = 99.3%. This is a good illustration of Shannon source coding techniques and how highly efficient source codes may be found. A number of compression cod