ented by ''', whereas 'Z' an infrequently letter is represented by '-_..' Information theory provides the theoretical background to calculate the optimal code length for representing a message. This design is efficient in that it allows for faster message transmission and therefore lower average operational cost per message. Source Entropy As discussed earlier, knowledge of a message's information size is needed in order to design and dimension a network to connect a source to a sink. At times a source generates a range of messages with different probabilities and therefore information size (such as different letters of the alphabet). To dimension the necessary network, the designer needs to know the average information size. To calculate this, all possible messages and their corresponding probabilities are considered to calculate average source information. This average source information is called 'source entropy' and is the first of the contributions made by Shannon. Source entropy is denoted by H, and has a unit of bits/message. It is the sum of individual messages' information content weighted by their corresponding probability. For a source that produces M different messages, entropy is calculated from the following equation: (4.2) where pi is the probability message i is generated. A related definition of importance to tele- communications dimensioning is the average source information rate, or entropy rate, which is defined as the average amount of information generated per second. This figure is important to an operator as it informs the necessary size of the telecommunications network. Example 4.2 The entropy for the source of Example 4.1 can be calculated as: [(1/8)*log2(1/8)]-[(1/8)*log2(1/8)] H = 1.75 bits/message Information Theory If this source generates one message every second then the source information rate is 1.75 bits per second (bps). Theoretically, a telecommunications link with a capacity of 1.75 bps will be sufficient to connect this source to a receiver of information. Example 4.3 Table