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Information can be delivered from remote locations nearly instantaneously to much of the world. Digital communication theory, together with major advancements in computer, electronics, and semiconductor technologies, has made this feat possible. In a technical sense, communication can be defined as the transfer of information between different points in space, that is, between source and destination, or in the case of storage, between different points in time, from time t 1 to time t 2 . The first of these applications is well-illustrated by the cell phone, where for example Alice in Ann Arbor talks to Bob in Chicago. A digital video recorder (DVR), on the other hand, is a good illustration of a storage device, where a movie is downloaded in the morning to be watched later that evening. From a theoretical perspective, there is no need to differentiate between the transfer of information from one location to another and the storage and subsequent retrieval of information from one time to another. The same theory and analytic techniques are equally applicable to both situations, but we frame our discussion in terms of the former, which the reader may more generally think of as communication.
This textbook is devoted to the subject of digital communication. What does the word digital imply? In digital communication, the information transmitted or stored comes from a finite set of possible “messages.” In contrast, the set of possible messages in an analog communication system is of infinite size and can consist, for example, of the set of all continuous-time waveforms. When the set of messages is finite, we assume, without loss of generality, that each of these messages is a sequence of bits. For example, for a set of messages of size 2 N , message 1 could be labeled by the binary sequence 000…0, message 2 by 000…1, and message 2 N by 111…1, where each of these binary sequences contains N bits. Also note that information has relevance only when the sender is saying something that the recipient does not already know and can’t predict. 1 Knowledge of the binary sequence is sufficient to specify the corresponding message using either some deterministic algorithm or by table lookup
