Modern Communication Principle 9.1: General Model of Digital System

  The digital communication system model is shown in Figure 1. We explain each module one by one according to the signal flow.

Figure 1 Digital communication system model

• Source

[Baidu Encyclopedia] The so-called information source is the source of information, which can be people, machines, objects in nature, and so on. When a source sends information, it is usually expressed in a certain way of information, which can be symbols, such as text, language, etc., or signals, such as images, sounds, and so on.

  The first module in Figure 1 is the source, the waveform or data stream output by the source will enter the second module, the source code. Generally speaking, the source may be analog or digital. If the source is analog, it is considered that it will output a certain signal waveform. For example, a microphone generates an analog voice signal, or an analog video recorder generates an analog video signal, which means that the number of waveforms generated by the source is infinite. If the source is digital, it is generally considered to output "0" and "1" data streams.

• Source coding

[Baidu Encyclopedia] Source coding is a conversion of source symbols for the purpose of improving the effectiveness of communication, or to reduce or eliminate source redundancy.

  Generally speaking, there are two different types of source coding. If the source is digital, the main function of source coding is to compress by reducing redundancy. Such source coding is called digital source coding, which encodes the input data stream and outputs a new bit stream. We only use the following examples to make a brief explanation. You will learn more in the "Information Theory and Coding" course.

  For example, for a static image of a human face, the brightness and color of the background, human face, hair, etc. all change smoothly. Adjacent pixels and chrominance signal values ​​are relatively close, and have a strong correlation. If the brightness and chromaticity information of each pixel are directly saved, there is more spatial redundancy in the data. If the redundant data is removed before encoding, it means that the number of bits required for each pixel will decrease. This is commonly referred to as intra-frame encoding of an image, and data can be compressed by reducing spatial redundancy.
  For another example, a video is a sequence of frame images in the time axis direction, and the correlation between adjacent frame images is also very strong. Usually, the method of reducing the time between frames is used to reduce time redundancy. For example, for a bird on the grass, if the bird does not move for a few seconds, then tens or hundreds of frames of images may be unchanged. Obviously, it is not necessary to save and transmit every pixel of every frame of image. . Therefore, it is possible to perform inter-frame compression, and use motion estimation and motion compensation techniques to meet the decoding quality requirements during reconstruction.

  If the source is analog, the main function of source coding is to transform the analog signal generated by the analog source into a digital signal so that it can be transmitted on a digital system. Such source coding is called analog source coding. It encodes the input analog waveform and outputs it as a data stream. In lectures 14 and 15, we will learn about analog speech coding, that is, how to turn a speech signal into a data stream.

• Channel coding

[Baidu Encyclopedia] Due to interference and fading in mobile communications, errors will occur during signal transmission. Therefore, digital signals must be corrected with error detection technology, that is, error detection and coding technology, to enhance data transmission in the channel. Various interference capabilities improve the reliability of the system. The error and error detection coding performed on the digital signal to be transmitted in the channel is the channel coding. The reason why channel coding can detect and correct errors in the received bit stream is because some redundant bits are added to spread the information carried in a few bits to more bits. The price paid for this is that more bits must be transmitted than required for the information.

  Obviously, the role of channel coding and source coding is exactly the opposite. Source coding is to minimize redundancy, while channel coding is to increase redundancy. Again, here we only give a simple example, and you will learn more in the "Information Theory and Coding" course.

The first example is the parity check that everyone has encountered in courses such as microcomputer principles and single-chip microcomputers. In fact, parity is one of the simplest error detection codes. We combine several binary data bits to be transmitted into a frame, and add a redundant bit for each frame, that is, a parity bit. If there are an even number of "1"s in the entire frame, we set the parity check to "0"; if there are an odd number of "1"s, then set it to "1". Obviously, if the frame has an odd number of errors during transmission, it can be detected by the parity bit. (Think about it, why can only an odd number of errors be detected?)
Parity can only detect part of the errors in the transmission, but cannot correct the errors. Let's take another simple example of error correction code, repeating code. For example, we are going to send the binary data stream "10010". If the repetitive code is used, each bit is sent three times, that is, the binary data "111000000111000" is sent. Obviously, here we have introduced redundant bits. On the receiving end, if the three-digit code output "111" corresponding to the first bit is wrongly changed to "101" due to the influence of noise, using the voting principle, we can get the correct output if two of the three are the same." 1".

  From the above example, the so-called error detection code introduces redundant bits, such as parity bits, to detect errors. The error correction code introduces redundant bits, such as repeated transmission bits in the repetitive code, to correct errors. Of course, the number of errors that can be detected or corrected is related to the increased number of redundant codes. Generally speaking, the more redundancy introduced, the stronger the error correction capability.
  Obviously, the output of the channel encoder is still a bit sequence, we use {bn} \{b_n\}{ bn​} To indicate. Next, we will enter the content we will discuss in Lecture 9, pulse modulation.

• Pulse modulation The
    so-called pulse modulation, sometimes we also call baseband modulation, is the bit sequence {bn} \{b_n\}{ bn​} The waveform expression, more specifically, in this part, is the baseband waveform expression. In layman's terms, it is necessary to express each bit as a specific waveform before it can be sent to the channel.
    For example, for the bit sequence "11101001", we can represent it with the waveform on the left in the figure below, that is, "1" has a duration of$T_s$Of $+A$ level to indicate [$g_1\left(t\right)$】, "0" uses the duration as$T_s$The -A level to represent [ $g_2\left(t\right)$ ], in this way, the waveform of the bit sequence "11101001" can be obtained. In fact, we can choose any two waveforms to represent "0" and "1". For example, use the two waveforms on the right side of the figure below, where$g_1\left(t\right)$ is at$T_s$A certain waveform in the time interval, $g_2\left(t\right)$ is the duration of$T_s$A segment of zero level, the waveform of the bit sequence "11101001" can also be obtained.

  Moreover, we can also use four waveforms to represent the bit sequence "11101001". As shown in the figure below, we use four baseband waveforms to represent the four two-digit binary bit combinations, namely
$$"00"\to g_1(t),"01"\to g_2\left(t\right),"10"\to g_3\left(t\right),"11"\to g_4\left(t\right).\; In\; the$$ figure on the left, we use four baseband rectangular pulse signals with different amplitudes as the waveform, and in the figure on the right we use four tone signals with different frequencies as the waveform (of course, if the frequency of the single tone signal is very high) At that time, it is no longer a baseband signal. We put this example here, or want to illustrate that the choice of waveform can be arbitrary).

  Extending the above example, we can see that, in fact, we can choose any waveform to represent the binary bit sequence we want to send. So how to choose the waveform? In other words, what kind of waveform can bring better communication performance. This is the key content we are going to learn below. Let's see what constraints limit the design of the waveform, what kind of waveform design can bring what kind of better performance? These are all issues we will discuss. Here, the first thing we need to understand is that pulse modulation uses a suitable baseband signal waveform to represent the bit stream that we want to send. Of course, at the receiving end, you need to extract the bit stream from the received waveform. This is the function implemented by the "detection" module.

• Band-pass modulation
    is as marked in the figure. The band-pass modulation here transforms the baseband waveform into a frequency band waveform, similar to what we discussed in the analog modulation part, which is an up-conversion process. We will discuss in detail in the frequency band digital transmission section. Note that if it is digital baseband transmission, this module is not included in the system.
• Channel
    Although the actual channel will be very complicated, especially in wireless communication, our course only discusses the AWGN channel, that is, before entering the receiver, the useful signal and the additive white Gaussian noise are superimposed. We will discuss two kinds of AWGN channels, one is with unlimited frequency band, and the second is with limited frequency band.
• The
    effect of band-pass demodulation is just the opposite of band-pass modulation, which performs down-conversion. Therefore, its input signal is a bandpass waveform, and its output is a baseband waveform. Similarly, if it is digital baseband transmission, there is no such module in the system.
• The detection
    function is just the opposite of pulse modulation, extracting the bit sequence in the waveform. Due to the influence of noise interference, its output {b ^ n} \{\hat b_n\}{ b^n​} Often with the original sent{bn} \{ b_n\}{ bn​} Not exactly the same, that is, a transmission error occurs.
• Channel decoding
     Channel decoding removes redundant bits to achieve error detection or correction.
• Source Decoding
     If the transmitting end is encoding a digital source, the source decoding here restores the original information; if it is an analog source encoding, then the analog signal is restored.