Channel
The channel distorts and adds noise, and possibly interference, to the transmitted signal. Much of our success in developing communication technologies has resulted from being able to optimize communication strategies based on accurate mathematical models for the channel. Such models are typically statistical, and are developed with significant effort using a combination of measurement and computation. The physical characteristics of the communication medium vary widely, and hence so do the channel models. Wireline channels are typically well modeled as linear and time-invariant, while optical fiber channels exhibit nonlinearities. Wireless mobile channels are particularly challenging because of the time variations caused by mobility, and due to the potential for interference due to the broadcast nature of the medium. The link design also depends on system-level characteristics, such as whether or not the transmitter has feedback regarding the channel, and what strategy is used to manage interference.
Example: Consider communication between a cellular base station and a mobile device. The electromagnetic waves emitted by the base station can reach the mobile’s antennas through multiple paths, including bounces off streets and building surfaces. The received signal at the mobile can be modeled as multiple copies of the transmitted signal with different gains and delays. These gains and delays change due to mobility, but the rate of change is often slow compared to the data rate, hence over short intervals, we can get away with modeling the channel as a linear time-invariant system that the transmitted signal goes through before arriving at the receiver.
Demodulator
The demodulator processes the signal received from the channel to produce bit estimates to be fed to the channel decoder. It typically performs a number of signal processing tasks, such as synchronization of phase, frequency and timing, and compensating for distortions induced by the channel.
Example: Consider the simplest possible channel model, where the channel just adds noise to the transmitted signal. In our earlier example of sending ±s(t) to send 0 or 1, the demodulator must guess, based on the noisy received signal, which of these two options is true. It might make a hard decision (e.g., guess that 0 was sent), or hedge its bets, and make a soft decision, saying, for example, that it is 80% sure that the transmitted bit is a zero. There are a host of other aspects of demodulation that we have swept under the rug: for example, before making any decisions, the demodulator has to perform functions such as synchronization (making sure that the receiver’s notion of time and frequency is consistent with the transmitter’s) and equalization (compensating for the distortions due to the channel).
Channel decoder
The channel decoder processes the imperfect bit estimates provided by the demodulator, and exploits the controlled redundancy introduced by the channel encoder to estimate the information bits.
Example: The channel decoder takes the guesses from the demodulator and uses the redundancies in the channel code to clean up the decisions. In our simple example of repeating every bit three times, it might use a majority rule to make its final decision if the demodulator is putting out hard decisions. For soft decisions, it might use more sophisticated combining rules with improved performance.
While we have described the demodulator and decoder as operating separately and in sequence for simplicity, there can be significant benefits from iterative information exchange between the two. In addition, for certain coded modulation strategies in which channel coding and modulation are tightly coupled, the demodulator and channel decoder may be integrated into a single entity.
Source decoder
The source decoder processes the estimated information bits at the output of the channel decoder to obtain an estimate of the message. The message format may or may not be the same as that of the original message input to the source encoder: for example, the source encoder may translate speech to text before encoding into bits, and the source decoder may output a text message to the end user.
Example: For the example of a digital image considered earlier, the compressed image can be translated back to a pixel-by-pixel representation by taking the inverse spatial Fourier transform of the coefficients that survived the compression. We are now ready to compare analog and digital communication, and discuss why the trend towards digital is inevitable.
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