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used to send the signal from the transmitter to the receiver. In wireless transmission, the channel may be the atmosphere (free space). On the other hand, telephone channels usually employ a variety of physical media, including wire lines,optical fiber cables, and wireless (microwave radio). Whatever the physical medium used for transmission of the information, the essential feature is that the transmitted signal is corrupted in a random manner by a variety of possible mechanisms, such as additive thermal noise generated by electronic devices,manmade noise, ., automobile ignition noise,and atmospheric noise,..electrical lightning discharges during thunderstorms. At the receiving end of a digital munications system, the digital demodulator processes the channelcorrupted transmitted waveform and reduces the waveforms to a sequence of numbers that represent estimates of the transmitted data symbols (binary or Mary). This sequence of numbers is passed to the channel decoder, which attempts to reconstruct the original information sequence from knowledge of the code used by the channel encoder and the redundancy contained in the received data. A measure of how well the demodulator and decoder perform is the frequency with which errors occur in the decoded sequence. More precisely,the average probability of a biterror at the output of the decoder is a measure of the performance of the demodulatordecoder bination. In general, the probability of error is a function of the codc characteristics, the types of waveforms used to transmit the information over the channci, the transmitter power, the characteristics of the channel, ., the amount of noise, the nature of the interference, etc., and the method of demodulation and decoding. These items and their effect on performance will be discussed in detail in subsequent chapters. As a final step, when an analog output is desired, the source decoder accepts the output sequence from the channel decoder and, from knovtledge of the source encoding method used, attempts to reconstruct the original signal from the source. Due to channel decoding errors and possible distortion introduced by the source encoder and, perhaps, the source decoder, the signal at the output of the source decoder is an approximation to the original source difference or some function of the difference between the original signal and the reconstructed signal is a measure of the distortion introduced by the digital munication system. 12 COMMUNICATION CHANNELS AND THEIR CHARACTERISTICS As indicated in the preceding discussion, the munication channel provides the connection between the transmitter and the receiver. The physical channel may be a pair of wires that carry the electrical signal, or an optical fiber thai carries the information on a modulated light beam, or an underwater ocean channel in which the information is transmitted acoustically, or free space over which the informationbearing signal is radiated by use of an antenna. Other media that can be characterized as munication channels are data storage media, such as magic tape, magic disks, and optical disks. One mon problem in signal transmission through any channel is additive noise. In general, additive noise is generated internally by ponents such as resistors and solidstate devices used to implement the munication is sometimes called thermal noise. Other sources of noise and interference may arise externally to the system, such as interference from other users of the channel. When such noise and interference occupy the same frequency band as the desired signal, its effect can be minimized by proper design of the transmitted signal and its demodulator at the receiver. Other types of signal degradations (hat may be encountered in transmission over the channel are signal attenuation, amplitude and phase distortion, and multipath distortion. The effects of noise may be minimized by increasing the power in the transmitted signal. However, equipment and other practical constraints limit the power level in the transmitted signal. Another basic limitation is the available channel bandwidth. A bandwidth constraint is usually due to the physical limitations of the medium and the electronic ponents used to implement the transmitter and the receiver. These two limitations result in constraining the amount of data that can be transmitted reliably over any munications channel as we shall observe in later chapters. Below, we describe some of the important characteristics of several munication channels. Wireline Channels The telephone work makes extensive use of wire lines for voice signal transmission, as well as data and video wire lines and coaxial cable are basically guided electromagic channels that provide relatively modest bandwidths. Telephone wire generally used to connect a customer to a central office has a bandwidth of several hundred kilohertz (kHz). On the other hand, coaxial cable has a usable bandwidth of several megahertz (MHz). Figure 121 illustrates the frequency range of guided electromagic channels, which include waveguides and optical fibers. Signals transmitted through such channels are distored in both amplitude and phase and further corrupted by additive noise. Twistedpair wireline channels arc also prone to crosstalk interference from physically adjacent channels. Becausc wireline channels carry a large percentage of our daily munications around the country and the world, much research has been performed on the characterization of their transmission properties and on methods for mitigating the amplitude and phase distortion encountered in signal transmission. In Chapter 9, we describe methods for designing optimum transmitted signals and their demodulation: in Chapters 10 and 11, we consider the design of channel equalizers that pensate for am