Digital Communication

Source Encoder

As already discussed, the source encoder converts the message signal into a sequence of information bits. The information bit rate depends on the nature of the message signal (e.g., speech, audio, video) and the application requirements. Even when we fix the class of message signals, the choice of source encoder is heavily dependent on the setting. For example, video signals are heavily compressed when they are sent over a cellular link to a mobile device, but are lightly compressed when sent to an high definition television (HDTV) set. A cellular link can support a much smaller bit rate than, say, the cable connecting a DVD player to an HDTV set, and a smaller mobile display device requires lower resolution than a large HDTV screen. In general, the source encoder must be chosen such that the bit rate it generates can be supported by the digital communication link we wish to transfer information over. Other than this, source coding can be decoupled entirely from link design (we comment further on this a bit later).

Example: A laptop display may have resolution 1024×768 pixels. For a grayscale digital image, the intensity for each pixel might be represented by 8 bits. Multiplying by the number of pixels gives us about 6.3 million bits, or about 0.8 Mbyte (a byte equals 8 bits). However, for a typical image, the intensities for neighboring pixels are heavily correlated, which can be exploited for significantly reducing the number of bits required to represent the image, without noticeably distorting it. For example, one could take a two-dimensional Fourier transform, which concentrates most of the information in the image at lower frequencies and then discard many of the high frequency coefficients. There are other possible transforms one could use, and also several more processing stages, but the bottomline is that, for natural images, state of the art image compression algorithms can provide 10X compression (i.e., reduction in the number of bits relative to the original uncompressed digital image) with hardly any perceptual degradation. Far more aggressive compression ratios are possible if we are willing to tolerate more distortion. For video, in addition to the spatial correlation exploited for image compression, we can also exploit temporal correlation across successive frames.

Channel encoder 

The channel encoder adds redundancy to the information bits obtained from the source encoder, in order to facilitate error recovery after transmission over the channel. It might appear that we are putting in too much work, adding redundancy just after the source encoder has removed it. However, the redundancy added by the channel encoder is tailored to the channel over which information transfer is to occur, whereas the redundancy in the original message signal is beyond our control, so that it would be inefficient to keep it when we transmit the signal over the channel.

Example: The noise and distortion introduced by the channel can cause errors in the bits we send over it. Consider the following abstraction for a channel: we can send a string of bits (zeros or ones) over it, and the channel randomly flips each bit with probability 0.01 (i.e., the channel has a 1% error rate). If we cannot tolerate this error rate, we could repeat each bit that we wish to send three times, and use a majority rule to decide on its value. Now, we only make an error if two or more of the three bits are flipped by the channel. It is left as an exercise to calculate that an error now happens with probability approximately 0.0003 (i.e., the error rate has gone down to 0.03%). That is, we have improved performance by introducing redundancy. Of course, there are far more sophisticated and efficient techniques for introducing redundancy than the simple repetition strategy just described.

Modulator 

The modulator maps the coded bits at the output of the channel encoder to a transmitted signal to be sent over the channel. For example, we may insist that the transmitted signal fit within a given frequency band and adhere to stringent power constraints in a wireless system, where interference between users and between co-existing systems is a major concern. Unlicensed WiFi transmissions typically occupy 20-40 MHz of bandwidth in the 2.4 or 5 GHz bands. Transmissions in fourth generation cellular systems may often occupy bandwidths ranging from 1-20 MHz at frequencies ranging from 700 MHz to 3 GHz. While these signal bandwidths are being increased in an effort to increase data rates (e.g., up to 160 GHz for emerging WiFi standards, and up to 100 MHz for emerging cellular standards), and new frequency bands are being actively explored (see the epilogue for more discussion), the transmitted signal still needs to be shaped to fit within certain spectral constraints.

Example: Suppose that we send bit value 0 by transmitting the signal s(t), and bit value 1 by transmitting −s(t). Even for this simple example, we must design the signal s(t) so it fits within spectral constraints (e.g., two different users may use two different segments of spectrum to avoid interfering with each other), and we must figure out how to prevent successive bits of the same user from interfering with each other. For wireless communication, these signals are voltages generated by circuits coupled to antennas, and are ultimately emitted as electromagnetic waves from the antennas.

The channel encoder and modulator are typically jointly designed, keeping in mind the anticipated channel conditions, and the result is termed a coded modulator.

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