Definition of a Digital Communication System

2.2 Definition of a Digital Communication System

The goal of communication systems is to efficiently convey information between two different locations.

A simplified model of a communication system is depicted below and describes the information flow in one direction. A convenient way of representing the information is through continuous-time signals or waveforms, such that $m (t)$ and $\hat{m} (t)$ correspond to the transmitted and recovered information, respectively, as indicated by:

m (t) \to Transmitter (Tx) \to s (t) \to Channel \to r (t) \to Receiver (Rx) \to \hat{m} (t) .

The channel is typically an analog system, such as an optic fiber, atmosphere (for wireless propagation), twisted copper-pairs, etc.

Due to historical reasons, there are two main categories of communication systems: analog and digital. The distinction between them can be related to the difference between analog and digital signals. For instance, in electronics, digital signals are characterized by having a finite set of amplitudes while analog signals do not have this restriction. Similarly, communication systems can be distinguished by the flexibility on the waveforms that are transmitted during a given interval of time $T_{sym}$ . Digital communication systems are defined as those that use waveforms $s (t)$ that convey information as numbers from a finite set of $M$ “symbols”. In contrast, an analog communication system can use arbitrary waveforms to convey information.

The mapping from symbols to waveforms can be a complicated one, but it is convenient to associate each waveform $s_{i} (t)$ to a unique symbol $m_{i}$ , with $m_{i}$ being a real or complex number. For example, assuming $M = 4$ , the transmitted waveform can be composed by concatenating

s (t) = [s_{3} (t) s_{1} (t) s_{4} (t) s_{3} (t) s_{2} (t) s_{1} (t) s_{1} (t) \dots],

with each waveform segment $s_{i} (t)$ lasting² $T_{sym}$ . The set ${m_{i}}, i = 1, \dots, M$ of possible symbols is called constellation. The previous $s (t)$ can be represented by the elements of ${m_{i}}$ that compose a sequence

m [n] = [m_{3} m_{1} m_{4} m_{3} m_{2} m_{1} m_{1} \dots]

(2.1)

with the implicit mapping from $m_{i}$ to $s_{i}$ .

It is assumed that $T_{sym}$ is in seconds, such that $R_{sym} = 1 ∕ T_{sym}$ is the number of symbols per second (also called bauds). The concepts of symbol and $T_{sym}$ are not needed when dealing with analog communication systems. In these systems, the source information is typically an analog waveform $m (t)$ that is converted to another analog signal $s (t)$ for transmission.

In digital communication, all sources of information are considered to be in a digital format. This is already the case when the information source is, for example, the text typed via a keyboard. If the information is originally conveyed by an analog waveform, an A/D conversion is required before a digital communication system can be used to transmit a digitized (and hopefully fairly accurate) version of this information. For example, the voice captured by a microphone in a voice over IP (VoIP) application has to be first digitized, often using a specialized ADC chip called codec.³ The A/D process is important because it impacts the quality of the overall digital communication system and is discussed in Chapter B.5.5.

In summary, even if the information source is originally an analog signal $m (t)$ , the strategy of using a digital communication system to transmit a digitized version of $m (t)$ has been increasingly popular due to advantages of digital communication systems over analog systems.

² Later this condition will be relaxed such that a symbol can have duration longer that $T_{sym}$ .

³ Codec stands for coder and decoder.