Shannon-Hartley theorem

Considering all possible multi-level and multi-phase encryption methods, the Shannon-Hartley theorem states that the channel capacity C, which means the theoretical upper limit of the information transfer rate that can be transmitted with a given average signal power S through one analog communication channel subjected to additive white Gaussian noise of power N is equal to:

C- channel capacity in bits per second; B- channel bandwidth in hertz; S is the total power of the signal over the bandwidth, measured in watts or volts squared; N is the total noise power over the bandwidth, measured in watts or volts squared; S/N is the signal-to-noise ratio (SNR) of signal to Gaussian noise, expressed as a power ratio.

Units

Bits per second

For more high levels network models, as a rule, a larger unit is used - bytes per second(B/c or bps, from English. b ytes p er s econd ) equal to 8 bit/s.

Often, erroneously, it is believed that baud is the number of bits transmitted per second. In reality, this is true only for binary encoding, which is not always used. For example, modern modems use quadrature amplitude modulation (QAM - QAM), and several (up to 16) bits of information can be encoded by one change in the signal level. For example, at a symbol rate of 2400 baud, the transmission rate can be 9600 bps due to the fact that 4 bits are transmitted in each time interval.

In addition, bauds express complete channel capacity, including service characters (bits), if any. The effective channel speed is expressed in other units, such as bits per second (bps, bps).

Methods for increasing the speed of information transfer

see also

Notes

Literature

• Information transfer rate//In the book. Zyuko AG Noise immunity and efficiency of communication systems. M .: "Communication", 1972, 360 pp., pp. 33-35

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See what "Information transfer rate" is in other dictionaries:

information transfer rate- the amount of information transmitted per time unit The amount of information about the ensemble of input signals (input messages) contained in the ensemble of output signals (output messages) related to the unit of time. [Compilation of recommended ... ...

information transfer rate- informacijos perdavimo sparta statusas T sritis automatika atitikmenys: angl. information transmission rate vok. Informationsgeschwindigkeit, f rus. information transfer rate, fpranc. vitesse de transmission d information, f … Automatikos terminų žodynas

information transfer rate- The amount of information transmitted over the channel per unit of time ... Polytechnic terminological explanatory dictionary

user information transfer rate- The rate of transmission of user information to be transmitted over the radio channel. For example, the output rate of a speech codec. (ITU T Q.1741). Telecommunication topics, main ... ... Technical Translator's Handbook

maximum information transfer rate- - [L.G. Sumenko. English Russian Dictionary of Information Technologies. M.: GP TsNIIS, 2003.] Topics information Technology in general EN maximal information rateMIR … Technical Translator's Handbook

speed of information creation- epsilon message entropy per unit time source performance Per unit time the smallest amount of information about a given ensemble of messages contained in another ensemble representing the given one with the specified fidelity.… … Technical Translator's Handbook

information transfer rate- information exchange rate transmission rate - [L.G.Sumenko. English Russian Dictionary of Information Technologies. M .: GP TsNIIS, 2003.] Topics information technology in general Synonyms information exchange rate EN transfer rate ... ... Technical Translator's Handbook

AE information processing speed- 2.46 AE information processing speed: The speed of processing and recording a set of parameters of AE signals by the system in real time without interrupting data transmission, expressed in pulses / s.

Open lesson in informatics

Topic: “Transfer of information. Information transfer rate"

Goals:

Educational:

introduce the concepts of source, receiver and information transmission channel.

information transfer rate and channel capacity;

solving problems on the speed of information transfer

Developing:

develop curiosity,

development of group work skills,

Nurturing:

education of accuracy, discipline, perseverance.

1. Repetition of previously studied material

The concept of information

Information - in the general case, a set of information about any events, phenomena, objects obtained as a result of interaction with the external environment. The form of information presentation is a message.

Types and properties of information

The main types of information in its form of presentation, methods of its encoding and storage, which has highest value for computer science, this is:

graphic;

sound;

text;

numerical;

Units for measuring the amount of information

- 1 byte = 8 bits,
- 1 kilobyte = 1024 bytes,
- 1 megabyte = 1024 KB,
- 1 gigabyte = 1024 MB,
- 1 terabyte = 1024 GB,
- 1 petabyte = 1024 TB.

2. Introduction of new material

All types of information are encoded in a sequence of electrical impulses: there is an impulse (1), there is no impulse (0), that is, in a sequence of zeros and ones. This encoding of information in a computer is called binary encoding. Accordingly, if it is possible to store and process these pulses using computer devices, then they can be transmitted.

To transfer information, you need:

A source of information- the system from which information is transmitted.

Information transmission channel- the way in which information is transmitted.

Information receiver- a system that provides necessary information.

The conversion of information into signals suitable for passing through the communication line is carried out by the transmitter.

In the process of converting information into a signal, it is encoded. In a broad sense, coding is the transformation of information into a signal. In a narrow sense, coding is the transformation of information into a combination of certain symbols. In our case, in the sequence of 1 and 0.

On the receiving side, the reverse decoding operation is performed, i.e. recovery from the received signal of the transmitted information.

The decoding device (decoder) converts the received signal to a form convenient for perception by the recipient.

One of the most important properties of information transfer is the speed of information transfer and channel capacity.

Transfer rate- the rate at which information is transmitted or received in binary form. Typically, the data rate is measured by the number of bits transmitted per second.

Minimum unit of measure for speed information transfer - 1 bit per second (1 bps)

Communication channel capacity- the maximum data transfer rate from the source to the recipient.

Both values ​​are measured in bits / sec, which is often confused with Bytes / sec and is addressed to communication service providers (providers) in connection with the deterioration of the speed or inconsistency in the speed of information transfer.

1. Problem solving

Solving problems on the speed of information transfer almost completely coincides with solving problems on speed, time and distance.

S - the size of the transmitted information

V - information transfer rate

T - information transfer time

Therefore, the formulas: are valid when solving problems for the speed of information transfer. However, it should be remembered that all measurement values ​​must match. (if the speed is in KB/sec, then the time is in seconds, and the size is in Kilobytes)

Consider an example task:

How many seconds will it take for a modem transmitting a message at a speed of 28800 bps to transmit a color image of 640 * 480 pixels, provided that the color of each pixel is encoded in 3 bytes.

Solution:

Let's determine the number of pixels in the image:

640*480= 307200 pixels

Because each pixel is encoded by 3 bytes, we define the information volume of the image:

307200 * 3 = 921600 bytes

Note that the information transfer rate is measured in bits / sec, and the information weight of the image is in bytes. Let's translate the speed into bytes / sec, for the convenience of calculation:

28800: 8 = 3600 bytes/sec

Determine the message transmission time if the speed is 3600 bytes/sec:

921600: 3600 = 256 sec

Answer: 256 seconds will be required

Tasks:

The data transfer rate over an ADSL connection is 64,000 bps. A 375 KB file is transmitted through this connection. Specify the file transfer time in seconds.

How many seconds does it take a modem transmitting a message at 28800 bps to transmit 100 pages of text in 30 rows of 60 characters each, provided that each character is encoded in one byte.

The data transfer rate via a modem connection is 56 Kbps. Broadcast text file through this connection took 12 seconds. Determine how many characters the passed text contained, if it is known to be UNICODE encoded.

The modem transmits data at a rate of 56 Kbps. Transferring the text file took 4.5 minutes. Determine how many pages the transmitted text contained if it is known to be in Unicode, and there are 3072 characters on one page.

The average data transfer rate using a modem is 36 Kbps. How many seconds does it take a modem to transmit 4 pages of KOI8 text, assuming that each page has an average of 2,304 characters?

Scout Belov must transmit a message: “The meeting place cannot be changed. Eustace." the direction finder determines the location of the transmission if it lasts at least 2 minutes. At what speed (bps) should the intelligence officer transmit a radiogram?

Tasks:

It is known that the duration of a continuous connection to the Internet using a modem for some PBXs does not exceed 10 minutes. Determine the maximum file size (KB) that can be transferred during such a connection if the modem transmits information at an average rate of 32 Kbps.

Determine the connection time in seconds:

10 min * 60 = 600 sec.

Determine the file size transmitted by the modem in 600 seconds:

600 sec * 32 Kbps = 19200 Kbps

We translate into Kbytes, as required by the condition of the problem:

19200 kb/8 = 2400 kb.

Answer: 2400 KB

7. Data transfer rate through ADSL connection is 64000 bps. A 375 KB file is transmitted through this connection. Specify the file transfer time in seconds.

Convert file size to bits:

375 KB * 8 * 1024 = 3072000 bits

Determine the file transfer time in seconds:

3072000 bps / 64000 bps = 48 sec.

Answer: 48 sec

8. How many seconds does it take a modem transmitting a message at 28800 bps to transmit 100 pages of text in 30 rows of 60 characters each, provided that each character is encoded in one byte.

Determine the number of characters on one page of text:

30 lines * 60 characters = 1800 characters.

We determine the information volume of the entire text, provided that one character = 1 byte.

1800 characters * 100 lines = 180000 bytes = 1440000 bits

Determine the message transmission time:

1440000 bps / 28800 bps = 50 sec.

Answer: 50 sec

9. Data transfer rate via modem connection is 56 Kbps. Transferring a text file over this connection took 12 seconds. Determine how many characters the passed text contained, if it is known to be UNICODE encoded.

We determine the information volume of the transferred text:

56 kbps * 12 sec = 672 kbps

Converting to bytes:

672 kb * 1024/8 = 86016 bytes

Since when using the Unicode encoding, one character is encoded in 2 bytes, we find the number of characters:

86016 bytes/2 = 43008 characters

Answer: 43008 characters

10. The modem transmits data at a rate of 56 Kbps. Transferring the text file took 4.5 minutes. Determine how many pages the transmitted text contained if it is known to be in Unicode, and there are 3072 characters on one page.

Convert minutes to seconds:

4.5 min = 4*60+30=270 sec.

Determine the size of the transferred file:

270 sec * 56 Kbps = 15120 Kbps = 1935360 bytes

One page of text contains 3072 characters * 2 bytes = 6144 bytes of information.

Determine the number of pages in the text:

1935360 bytes / 6144 bytes = 315 pages

Answer: 315 pages

11. The average data transfer rate using a modem is

36 Kbps How many seconds does it take a modem to transmit 4 pages of KOI8 text, assuming that each page has an average of 2,304 characters?

In KOI-8 encoding, each character is encoded with one byte.

Determine the size of the message:

4 lines * 2304 characters = 9216 characters = 9216 bytes = 9216 * 8/1024 = 72 Kbits.

Determine the transfer time:

72 kbps/36 kbps = 2 sec

Answer: 2 sec

12. Scout Belov must send a message: “The meeting place cannot be changed. Eustace." the direction finder determines the location of the transmission if it lasts at least 2 minutes. At what speed (bps) should the intelligence officer transmit a radio message?

We determine the information content of the message: “The meeting place cannot be changed. Eustace." - contains 37 characters, that is, it is equal to 37 bytes = 296 bits.

The transmission time must be less than 2 minutes or 120 seconds.

In this case, the transmission rate must be greater than 296 bits / 120 sec = 2.5 bits / sec. Round up and get

3 bps

Answer: 3 bps

Serious interest in the subject internet connection speed usually occurs after or blogging in the process of them. This is due to the need to learn and, as a rule, increase the speed of loading a site, which depends, among other factors, to a large extent on internet speed. In this article, we will briefly consider what is incoming speed, outgoing speed, and most importantly, let's deal with units of data transfer rate, the concept of which is very vague for many novice users. In addition, we present simple Internet connection speed measurement methods through the most common online services.

What is it internet connection speed? The speed of an Internet connection is understood as the amount of information transmitted per unit of time. Distinguish incoming speed (receiving speed)- the speed of data transfer from the Internet to our computer; outgoing speed (transmission speed)- the speed of data transfer from our computer to the Internet.

Basic units for measuring internet speed

The basic unit for measuring the amount of transmitted information is bit(bit). Taken as the unit of time second. So the transmission speed will be measured bps Usually operate in units "kilobits per second" (Kbps), "megabits per second" (Mbps), "gigabits per second" (Gbps).

1 Gbps = 1000 Mbps = 1,000,000 Kbps = 1,000,000,000 bps.

On English language basic unit for measuring the rate of information transfer, used in computer science- bits per second or bps will be bits per second or bps.

Kilobits per second and, in most cases, Megabits per second (Kbit / s; Kb / s; Kb / s; Kbps, Mbps; Mb / s; Mb / s; Mbps - the letter "b" is small) are used in technical specifications and contracts for the provision of services by Internet providers. It is in these units that the speed of an Internet connection is determined in our rate plan. Usually, this speed promised by the provider is called the declared speed.

So, quantity transmitted information is measured in bits. The size of a file being transferred or located on a computer's hard drive is measured in bytes(kilobytes, megabytes, gigabytes). Byte (byte) is also a unit of quantity of information. One byte is equal to eight bits (1 Byte = 8 bits).

To make it easier to understand difference between bit and byte, can be said in other words. Information on the network is transmitted bit by bit. Therefore, the transfer rate is measured in bits per second. Volume the same stored data is measured in bytes. That's why download speed of a certain volume measured in bytes per second.

File transfer speed used by many user programs(downloaders, Internet browsers, file hosting) is measured in Kilobytes, Megabytes Gigabytes per second.

In other words, when connected to the Internet, tariff plans The data transfer rate is in Megabits per second. And downloading files from the Internet shows the speed in megabytes per second.

1 GB = 1024 MB = 1,048,576 KB = 1,073,741,824 Bytes;

1 MB = 1024 KB;

1 KB = 1024 Bytes.

In English, the basic unit for measuring the speed of information transfer - Byte per second or Byte / s will be byte per second or Bytes/s.

Kilobytes per second are referred to as KBytes/s, KB/s, KB/s, or KBps.

Megabytes per second - MB/s, MB/s, MB/s or MBps.

Kilobytes and Megabytes per second are always written with capital "B" both in Latin transcription and in Russian spelling: MB / s, MB / s, MB / s, MBps.

How to determine how many megabits are in megabytes and vice versa ?!

1 MB/s = 8 Mbit/s.

For example, if the data transfer rate displayed by the browser is 2 MB/s (2 megabytes per second), then in megabits it will be eight times more - 16 Mbps (16 megabits per second).

16 Megabits per second = 16 / 8 = 2.0 Megabytes per second.

That is, to get the speed value in "Megabytes per second", you need to divide the value in "Megabits per second" by eight and vice versa.

In addition to the data transfer rate, an important measured parameter is reaction time of our computer, denoted ping. In other words, ping is the time it takes our computer to respond to a sent request. The lower the ping, the lower, for example, the waiting time required to open a web page. It is clear that the lower the ping, the better. When measuring ping, the time it takes for a packet to pass from the measuring server is determined. online service to our computer and back.

Determination of Internet connection speed

For speed detection Internet connection, there are several methods. Some are more accurate, others are less accurate. In our case, for practical needs, I think it is enough to use some of the most common and well-proven online services. Almost all of them, in addition to checking the speed of the Internet, contain many other functions, including our location, provider, the reaction time of our computer (ping), etc.

If you wish, you can experiment a lot by comparing the measurement results various services and choosing the ones you like. For example, I am satisfied with such services as the well-known Yandex internetometer, as well as two more SPEED.IO andSPEEDTEST.NET.

The Internet speed measurement page in Yandex Internetometer opens at ipinf.ru/speedtest.php(picture 1). To increase the measurement accuracy, select your location with a marker on the map and press the left mouse button. The measurement process starts. Results of the measured incoming (download) And outgoing (upload ) speeds are reflected in the pop-up table and on the left in the panel.

Figure 1. Internet speed measurement page in Yandex internetometer

The SPEED.IO and SPEEDTEST.NET services, in which the measurement process is animated in a dashboard similar to a car one (Figures 2, 3), are simply pleasant to use.

Figure 2. Internet connection speed measurement in the SPEED.IO service

Figure 3. Internet connection speed measurement in the SPEEDTEST.NET service

The use of these services is intuitive and usually does not cause any difficulties. Again, incoming (download), outgoing (upload) speeds are determined, ping . Speed.io measures the current speed of the Internet to the company's server closest to us.

In addition, in the SPEEDTEST.NET service, you can test the quality of the network, compare your previous measurement results with real ones, find out the results of other users, compare your results with the speed promised by the provider.

Along with the above, the following services are widely used:CY- PR. com, SPEED. YOIP

The data transfer rate over a communication channel is measured by the number of bits of information transmitted per unit of time - a second.

The unit of data transfer rate is bits per second.

Note. The unit of measure used for speed is baud. Baud is the number of media state changes per second. Since each state change can correspond to several bits of data, the actual bits per second may exceed the baud rate.

The data transfer rate depends on the type and quality of the communication channel, the type of modems used and the method of synchronization adopted.

So, for asynchronous modems and a telephone communication channel, the speed range is 300-9600 bps, and for synchronous - 1200-19200 bps.

For users computer networks what matters is not abstract bits per second, but information, the unit of which is bytes or characters. Therefore, a more convenient characteristic of a channel is its capacity, which is estimated by the number of characters transmitted over the channel per unit of time - a second. In this case, all service characters are included in the message. The theoretical throughput is determined by the data rate. The actual throughput depends on a number of factors, including the transmission method, the quality of the communication channel, its operating conditions, and the message structure.

Unit bandwidth communication channel - sign per second.

An essential characteristic of the communication system of any network is the reliability of the transmitted information. Since decisions are made about one or another course of the process based on the processing of information about the state of the control object, the fate of the object may ultimately depend on the reliability of information. The reliability of information transmission is evaluated as the ratio of the number of erroneously transmitted characters to the total number of transmitted characters. The required level of reliability must be provided by both the equipment and the communication channel. It is inexpedient to use expensive equipment if the communication channel does not provide the necessary requirements regarding the level of reliability.

Reliability measurement unit: number of errors per sign - errors/sign.

For computer networks, this indicator should lie within 10-6 -10-7 errors/sign, i.e. one error per million characters transmitted, or ten million characters transmitted.

Finally, the reliability of a communication system is determined either by the share of uptime in the total operating time, or by the average time uptime. The second characteristic makes it possible to more effectively assess the reliability of the system.

Reliability measurement unit: mean time of non-failure operation - hour.

For computer networks, the mean time to failure should be large enough and be at least several thousand hours.

The amount of information transmitted over the channel per unit of time is called information transfer rate.

The speed of information transfer over communication channels is estimated by the number of bits of information transmitted to its recipient within one second ( bps).

Note that in the early stages of the development of telecommunications, each change in the information parameter of the carrier signal gave the recipient one bit of information and the transmission rate was estimated at bauds(for example, it was used to estimate the transmission rate of telegraph data, in which each "elementary" signal carried one bit of information). Today, the transfer rate is estimated at bps, since each change in the information parameter of the signal modern means data transmission can carry information in several bits.

If from the source IN transmitted over a communication channel s characters per unit of time, and the average amount of information per character is H(B), then the information transfer rate: С = s H(B).

When digital signals(assuming their equiprobability and independence) maximum entropy for the source IN with the number of alphabetic characters m is determined by the formula H(B) max = log 2 m .

The maximum possible information transfer rate is called throughput communication channel. It is determined by the value

G= C max = s log 2 m .

Variable throughput formulas depend on a number of physical characteristics of the communication line, the power of the message source and the noise in the communication channel.

The bandwidth is determined not only by the physical characteristics of the conductive medium (symmetric, coaxial or fiber optic cables, twisted pair, etc.), but also by the spectrum of transmitted signals. The most important physical characteristics of communication lines include attenuation and bandwidth.

The parameters of the communication lines are usually estimated in relation to the signals of a sinusoidal form. If we apply a sinusoidal signal of a fixed frequency and amplitude to one end of the communication line (which does not have amplifiers), then at the other end we will get a weakened signal, i.e. having a smaller amplitude.

attenuation characterizes a decrease in the amplitude or power of a signal when a signal of a certain frequency or frequency range passes through the communication line. For wired cables, it is measured in decibels per meter and is calculated by the formula:

A \u003d 10 lg 10 P out / P in,

where P out and P in are the signal power at the input and output of the line in 1 m, respectively.

The attenuation depends on the frequency of the signal. On fig. 1.13 shows a typical shape of the amplitude-frequency characteristic, which characterizes the attenuation of signals of different frequencies. The lower the attenuation modulus, the higher the quality of the communication line (the logarithm of a number less than 1 is always a negative number).

Attenuation is the most important parameter for communication lines in computer networks, and standards establish standard attenuation values ​​for various types cables used in laying computer networks. Thus, Category 5 twisted-pair cable for indoor wiring should have an attenuation of at least -23.6 dB, and Category 6 - at least 20.6 at a frequency of 100 MHz with a line length of 100 m. Typical attenuation values ​​for cables based on fiber optics : 0.15 to 3 dB at 1000 m.

Bandwidth– a continuous range of frequencies, for each of which the ratio of the amplitude of the output signal to the amplitude of the input signal is not less than a certain value. Often this ratio is taken equal to 0.5 (see Fig. 1.13). It is measured in hertz (Hz). The difference between the values ​​of the extreme frequencies of the range is called bandwidth.

Actually, bandwidth- this is the frequency interval used by this communication channel for signaling. For various calculations, it is important to know the maximum value of the frequency from a given band (n m), since it is this band that determines the possible information transfer rate over the channel.

Signal transmitters that send signals to the communication line (for example, an adapter or a modem) are characterized by power. The signal power level is determined in decibels per 1 mW according to the formula (such a unit of power is denoted by dBm):

p=10 lgP (dBm), where P is the power in mW.

An important characteristic wire lines communications (for example, coaxial cable) is wave resistance. This is the total (complex) resistance that an electromagnetic wave of a certain frequency propagating along the cable meets. Measured in ohms. To reduce attenuation, it is necessary that the output impedance of the transmitter be approximately equal to the impedance of the communication line.

Fig.1.13. Amplitude-frequency response of the communication channel

It is known that a signal of any shape can be obtained by summing several sinusoidal signals with different frequencies and amplitudes. The set of frequencies that must be summed to obtain a given signal is called the signal spectrum. If some frequencies from the spectrum are strongly attenuated, then this is reflected in the waveform. Obviously, the quality of signal transmission significantly depends on the bandwidth. So, according to the standards for high-quality transmission telephone conversations the communication line must have a bandwidth of at least 3400 Hz.

There is a relationship between bandwidth and the maximum bandwidth that K. Shannon established:

G \u003d F log 2 (1 + P c / P w) bps, where

G is the maximum bandwidth, F is the bandwidth in Hz, P c is the signal power, P w is the noise power.

Determining the signal strength and noise is quite a difficult task. However, there is another formula obtained by Nyquist for the case discrete signals, which can be applied when the number of states of the information parameter is known:

G =2 F log 2 M (bps),

where F is the bandwidth in Hz, M is the number of possible states of the information parameter. It follows from this formula that when M=2 (i.e., when each change in the signal parameter carries one bit of information), the throughput is equal to twice the bandwidth.

When interference (noise) affects the transmitted symbols, some of them may be distorted. Then, taking into account the previously given formulas for entropy, the amount of information received and, accordingly, the throughput of the communication channel will decrease.

For the case of transmission of equally probable digital symbols and the same probabilities of replacement when transmitting values ​​1(0) to false 0(1), the maximum throughput is C max = s×=s×, where P osh is the error probability.

A graph illustrating the form of the dependence of the relationship C max / s (ie, the amount of transmitted information per symbol) on P osh is shown in Fig. 1.14.

Fig.1.14. Dependence of throughput on errors in the communication channel