In the previous article we introduced the amount of information and the average amount of information, in this article we will introduce the main performance indicators of communication systems
Previous: Principles of Communication (2): Information Volume and Average Information
1. Performance indicators of general communication system
Validity: The amount of information content transmitted in a given channel, or the "speed" of transmission, requires the communication system to transmit messages efficiently, that is, to transmit the maximum number of messages in the most reasonable and economical way
Reliability: Requires the communication system to reliably transmit messages, and the accuracy of receiving information is the "quality" problem of transmission
The two issues of effectiveness and reliability are contradictory and relatively unified, and in general, to increase the effectiveness of the system, it is necessary to reduce the reliability, and vice versa.
The rest are adaptability, confidentiality, standardization, maintenance, craftsmanship and so on
1.2 Analog communication systems
Validity: A measure of the effective transmission frequency that can be used
Reliability: Can be measured by the final output signal-to-noise ratio of the receiver
1.3 Digital Communication Systems
Effectiveness: Can be measured by the transfer rate
Reliability: Can be measured by error rate
2. Effectiveness and reliability indicators of digital communication system
Above we talked about the effectiveness of digital systems can be measured by transmission rates, there are the following three:
- The transmission rate of the code elements
- Information transfer rate
- Frequency band utilization
The reliability of a digital system can be measured by error rates in two ways:
- Code element error rate
- Information error rate
Let's first understand what is a code element?
2.1 Code Elements
Code element: A digital pulse is a code element, or it can be said that a code element is a fixed-duration waveform signal, which is used to represent a K-base number.
The following figure is a symbol, this symbol has two forms, high means 1, low means 0 (and vice versa), it represents a binary number
The relationship between the symbol and the bit: How much bit information the symbol carries, is related to the base of the symbol
For example, a quaternary coding element, he has four different forms, representing 0, 1, 2, 3; the corresponding binary is 00, 01, 10, 11; it is visible that two binary digits are required to represent it, so it carries 2 bits of information (here is a prerequisite, each symbol and other probability transmissions)
Similarly, an octal code element carries 3 bits of information
M-base code, which carries log2(M) bit information
2.2 Element transmission rate and information transmission rate
The element transfer rate RB represents how many symbols are transmitted in a second, also known as baud rate or symbol rate, in Baud
Note: Baud rate and code element are several degrees have no relationship!
The information transmission rate Rb refers to the number of bits transmitted per second, also known as the bit rate, the unit is bits / second, can be recorded as bit / s , or b / s , or bps
If the M-base symbol is transmitted with probabilities such as the source entropy, the maximum value log2M, the relationship between the baud rate and the bit rate is:
More generally, when each symbol is not necessarily transmitted with equal probability, the relationship between baud rate and bit rate is:
where H is the average amount of information contained in each symbol in the source (entropy)
2.3 Frequency band utilization
When comparing the effectiveness of different communication systems, it is not enough to look at the transmission rate; it should also look at the bandwidth of the channel occupied at the transmission rate
Therefore, the transmission efficiency of digital communication systems is measured by the transmission rate of symbols in the unit frequency band:
The digital signal transmission bandwidth B depends on the symbol rate, while RB is related to the information rate Rb. To compare the transmission efficiency of different systems, you can define the frequency band utilization as:
2.4 Error Rate
Metrics to measure the reliability of communication systems are commonly expressed as bit error rates and false error rates
Bit error rate (code element error rate): refers to the proportion of the number of code elements that have been wrong in the transmission of the total number of code elements, more precisely, the bit error rate is the probability that the code element will be transmitted incorrectly in the transmission system, that is:
False trust rate (information error rate): refers to the proportion of the number of bits that have been wrong in the total number of bits transmitted, that is:
In binary, the bit error rate Pe = the false confidence rate Pb
2.5 Example Questions
Example: It is known that a binary digital signal transmits a total of 72,000 symbols in 2 minutes, and the calculation is tried
- What is the element rate and the information rate?
- If the symbol width is unchanged (that is, the symbol rate is unchanged), but it is changed to an octal digital signal, what is its symbol rate? What is the information rate?
untie:
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