What are the channels for transmitting information? Understanding Data Transfer

A communication channel is a collection technical means to transmit messages from one point in space to another. From the point of view of information theory, the physical structure of the channel is unimportant. The message source (IS) has an output alphabet of characters A={A i },i=1.. n- the amount of information on average per source character:

Where p i, - probability of symbol appearance a i,at the source output, the source symbols are considered independent. The communication channel has the alphabet of characters B = ( b j },j=1.. m, average amount of information in one channel symbol

Where q j - probability of symbol appearance b i , in the channel.

Technical characteristics of the communication channel are:

technical performance of the source  A - the average number of symbols issued by the source per unit of time;

technical bandwidth of the communication channel  B - the average number of symbols transmitted over a channel per unit of time.

An information characteristic of a source is information productivity. By definition, information productivity is the average amount of information produced by a source per unit of time.

In a channel without interference, the information characteristics are:

1) speed of information transmission over the channel

2) channel capacity

Where ( P) - the set of all possible probability distributions of alphabet symbols IN channel. Taking into account the properties of entropy

C K = B . log 2 m.

In a noisy channel general case the input and output alphabets do not match. Let

B ВХ =X=(x 1,x 2,…,x n);

B OUT =Y=(y 1 ,y 2 ,…,y m ).

If the symbol sent at the channel input X To recognized in the receiver as y i And i K, then an error occurred during transmission. The channel properties are described by a matrix of transition probabilities (the probability of receiving a symbol at i , provided that it is sent X k):

|| P(yi|xk) ||, k=1..n, i=1..m.

Fair ratio:

Average amount of information per channel input symbol:

p i =p(x i ) .

Average amount of information per channel output symbol:

Information carried by the channel output about the input:

I(Y,X)=H(X)-H Y (X)=H(Y)-H X (Y).

Here Well(X) - conditional entropy of the input symbol of the channel when observing the output symbol (unreliability of the channel), N X (Y) - the conditional entropy of the output symbol of the channel when observing the input symbols (noise entropy).

Information transmission rate over a channel with interference:

dI(B)/dt= B I(X,Y).

Channel capacity with interference:

Where (p) - the set of all possible probability distributions of the input alphabet of channel symbols.

Let's look at an example

N Find the capacity of a binary symmetric channel (a channel with two-symbol input and output alphabets) and equal error probabilities (Fig. 1), if the prior probabilities of the appearance of input symbols are: P(x 1 )=P 1 =P, P(x 2 )=P 2 =1-P.

Solution. According to the channel model, the conditional probabilities

P(y 1 | x 2 ) = P(y 2 | x 1 ) = P i ,

P(y 1 | x 1 ) = P(y 2 | x 2 ) = 1-P i .

Channel capacity - C K =  B . max(H(Y)-H(X|Y)). Let's find the entropy of noise:

According to the multiplication theorem: P(y j x i)=P(x i)P(y j |x i), hence,

P(x 1 y 1 )=P(1-P i), P(x 2 y 1 )=(1- P)P i ,P(x 1 y 2 )=PP i ,P(x 2 y 2 )=(1-P)(1-P i).

Substituting into the formula, we get:

Thus, H( Y| X ) does not depend on the distribution of the input alphabet, therefore:

Let's determine the entropy of the output:

Probabilities P(y 1 ) And P(y 2 ) we get as follows:

P(y 1 )=P(y 1 x 1 )+P(y 1 x 2 )=P(1-P i)+(1-P i)P i , P(y2)=P(y 2 x 1 )+P(y 2 x 2 )=PP i +(1-P)(1-P i).

By varying P, we make sure that the maximum value H(Y), equal to 1, is obtained with equally probable input symbols P(y 1 ) And P(y 2 ). Hence,

Task. Find the channel capacity with three-character input and output alphabets ( x 1 ,x 2 ,x 3 And y 1 ,y 2 ,y 3 accordingly). The intensity of the appearance of symbols at the channel input k = V. 10 characters/s.

Probabilities of symbols appearing:

,
, .

Probabilities of transmitting symbols through a communication channel:

,
,,

,
,,

,
,.

4. INFORMATION CODING

4.1. General information The code is called:

A rule describing the mapping of one set of characters to another set of characters or to a set of words without signs;

There are many images resulting from such a display.

In technical codes, letters, numbers, and other characters are almost always encoded in binary sequences called binary codewords. Many codes have words of the same length (uniform codes).

The choice of codes for encoding specific types of messages is determined by many factors:

Convenience of receiving original messages from the source;

Speed ​​of message transmission through the communication channel;

The amount of memory required for storing messages per day;

Ease of data processing;

Convenient decoding of messages by the receiver.

Encoded messages are transmitted over communication channels, stored in memory, and processed by the processor. The volumes of encoded data are large, And Therefore, in many cases it is important to ensure data encoding: ", which is characterized by the minimum length of the resulting messages. This is a data compression problem. There are two approaches to data compression:

Compression based on the analysis of statistical properties of encoded messages.

Compression based on the statistical properties of data is also called the theory of economical or efficient coding. Parsimonious coding is based on the use of codes with variable codeword length, for example, Shannon-Fano code, Huffman code /31. The idea of ​​using variable length codes for data compression is to assign messages with a higher probability of occurrence to code combinations of shorter length and, conversely, messages with a low probability of occurrence are encoded in words of longer length. The average length of a code word is determined by:

where /, is the length of the code word for encoding the i-th message; p t - probability of occurrence of the i -th message.

4.2. Quests

4.2.1. From Table 4, select the day of subsequent encoding the original alphabet containing 10 characters, starting with N-ro(N- serial number of the student in the group journal). Normalize symbol probabilities.

4.2.2. Normalize the one selected in paragraph 4.2.1. the original alphabet is uniform binary code, Shannon-Fano code, Huffman code. For each encoding option, calculate the minimum, maximum, average value of the codeword length. Analyze the results.

4.2.3. Complete task 4.2.2. for ternary code.

Table 4

4.3. Instructions for completing individual tasks For task 4.2.1. Probabilities are normalized using the formula:

/W-HO / *Rk " JC=AT

Where Pi- the probabilities of the appearance of symbols are given in Table 4.

For task 4.2.2. The rules for constructing binary codes are set out in /4.6/.

For task 4.2.3. When constructing a ternary code, words written in the ternary number system are taken as code words. An optimal ternary code is constructed using the Huffman procedure (a suboptimal code is constructed using the Shannon-Fano procedure). In this case, the alphabet is divided into three groups, the first group is assigned “O”, the second - “1”, the third - “2”.

In general, the information transmission channel is understood as the entire set of technical means that ensure the transmission of electrical signals from the source of messages to the consumer. When considering channels, the communication line is most often assumed to be given (it is believed that all the necessary characteristics of the communication line are known) and all tasks of analysis and synthesis of information transmission channels are reduced to the analysis and synthesis of signal conversion operators in the transmitter, receiver and other devices.

Information transmission channels are classified according to various criteria: by purpose, by the nature of communication lines, by frequency range, by the nature of signals at the input and output of channels, etc. By purpose, channels are divided into telephone,

telegraph, television, phototelegraph, sound broadcasting, telemetry, data transmission, etc. Depending on whether the signals are distributed in free space or along guide lines, distinguish between radio communication channels and channels wired communication: overhead, cable, waveguide, light-guide, etc. Overhead wire communication lines transmit signals in the range of 0-160 kHz. For more high frequencies ah, the influence of interference increases, the attenuation of signals increases sharply, and the influence of long-wave radio broadcasting stations is affected. Significant disadvantage overhead wire communication lines - their characteristics are highly dependent on atmospheric conditions. Significantly best characteristics and have greater stability in work cable lines communications. They are the basis of backbone networks long distance communication, they transmit signals in the frequency range from 600 kHz to 60 MHz. With a further increase in frequency, the attenuation of signals increases sharply.

Currently, intensive theoretical and experimental work on the study of metal waveguides. The results obtained allow us to hope that these communication lines will be widely used to transmit signals in the range of 35-80 GHz (wavelength 8.6-3.75 mm). A circular waveguide with an internal diameter of 6 cm is promising, through which it is possible to organize more than 200,000 standard telephone channels (voice frequency channels with an effectively used frequency band from 300 to 3400 Hz) or about 200 television channels. Economic calculations show that when organizing telephone channels up to 30,000, it is still advisable to use a coaxial cable, and over 30,000 channels - a waveguide. More larger number standard channels can be organized using optical systems communications in which signals are used in the frequency band 600-900 THz (0.5-0.3 µm). Using closed guide systems, which are called light guides, it is possible to achieve stable communication on long distances. Dielectric flexible fiber light guides are of great practical interest.

Along with wired communication lines, radio lines of various ranges are widely used. In many cases, these lines are more economical and allow you to quickly organize ultra-long-distance (global) communications without intermediate stations. In addition, and this is very important, these lines are the only means of communication with moving objects (aircraft, spacecraft, by sea vessels, including submarines, cars, etc.).

The most widely used for transmitting multichannel messages are terrestrial radio relay lines operating in the meter, decimeter and centimeter wavelength ranges at frequencies from 60 MHz to 15 GHz. At these frequencies, a wide bandwidth of the transmission path is provided, necessary for multi-channel telephone and television communications; the level of

atmospheric and industrial interference. All this ensures high noise immunity of information transmission.

Variety radio relay lines are tropospheric lines in which signals reflected from inhomogeneities in the troposphere are received. The use of long-distance tropospheric propagation of radio waves makes it possible to create long-distance radio communication lines with distances between relay stations of several hundred kilometers. These lines operate most often in the frequency range from 0.5 to 6 GHz.

Satellite communication lines are promising. According to the principle of operation, they represent a type of radio relay lines, the repeaters of which are located on artificial satellites Earth. A significant advantage of satellite lines is the long communication range, which with one satellite (repeater) is about 10,000 km. When using a satellite system, you can organize global connectivity- between any points on Earth. Satellite lines communications operate in the frequency range 4-6 GHz. Currently, six new frequency ranges have been allocated from 11 to 250 GHz, the development of which will significantly improve quality indicators satellite communications. Satellite systems connections, especially with digital methods signal transmission are also promising in civil aviation, especially with access to air routes of supersonic passenger ships.

As we see, for modern methods and the means of information transmission are characterized by a transition to ever higher frequencies. This is due to the following main reasons: the use of high frequencies makes it possible to obtain highly directional radiation with small antenna sizes; in high-frequency ranges, atmospheric and industrial interference have less influence; the higher the carrier frequency, the greater the number of channels that can be organized without mutual interference; only in high-frequency ranges, starting from meter, can it be organized large number broadband channels, such as video telephone channels and television channels.

One of the main tasks of analyzing information transmission channels is to analyze the distortions of the signals transmitted through them. Most of all, the quality of information transmission is affected by signal shape distortions, determined by the real amplitude and frequency characteristics channels, as well as multipath propagation of radio waves. Mathematical models for a complete analysis of distortions in real channels are quite complex.

For a general approximate analysis of distortions, the channel is considered as an equivalent four-port network, the operation of which is described by a certain operator If the input signal, then the signal at the output of the channel For more detailed analysis distortion, the communication channel is represented as a serial connection of a linear, generally inertial, and nonlinear non-inertial four-terminal network, in

where linear and nonlinear signal distortions occur. If the channel includes a modulator and a demodulator or signal fading is taken into account, then a quadripole with variable parameters. If you need to analyze your work individual devices channel, the number of series-connected quadripoles is increased. For example, to analyze a radio transmission channel discrete messages often use the block diagram presented in Fig. 1.1.

Rice. 1.1. Block diagram information transmission channel

The channel is considered as a serial connection of the encoder, the first and second modulator, the communication line, the first and second demodulator and the decoder. Using a channel model in the form of an equivalent four-port network (or serial connection quadripoles) allows you to solve a number of problems of analysis and synthesis of channels using theoretical methods radio circuits and statistical radio engineering.

Based on the nature of the signals at the input and output of channels, discrete, continuous, discrete-continuous and continuous-discrete channels are distinguished. Discrete channel, for example in the diagram in Fig. 1.1 is the channel considered from the encoder input to the decoder output or from the first modulator input to the second demodulator output. If we consider the set of technical means from the output of the first or second modulator to the input of the first or second demodulator, then in any information transmission system this set forms a continuous channel. An example of a discrete-continuous channel is a set of technical means from the input of the first modulator to the input of the first or second demodulator. A continuous-discrete channel is formed if analyzed in the circuit of Fig. 1.1 the passage of signals from the output of the first or second modulator to the output of the second demodulator or, in general, to the output of the decoder. Thus, based on a continuous channel (in Fig. 1.1 it is shown as dashed

line) channels of all other types are formed. Therefore, much attention is paid to the study of continuous channels.

Mathematical models for studying channels are built taking into account the classification considered. Essentially, the development of the model comes down to determining the structure and parameters of the equivalent signal transformation operator in the channel. Depending on the type of this operator, channels are distinguished: linear, nonlinear, inertial, inertial-free, stationary, non-stationary, deterministic, probabilistic, etc. Linear inertial channels with constant parameters are the most studied.

If the transmitted signal is considered as a random process, which significantly brings the signal models closer to real ones, then when analyzing the passage of the signal through the channel it is necessary to analyze the passage random processes through quadripoles described various operators. Such problems are solved in statistical radio engineering; the results of solving these problems find direct application in the analysis of information transmission channels.

As with signals, it is convenient to use the following for channels: physical characteristics, as channel busy time, channel bandwidth (transparency), range permissible levels signals when transmitted over a channel, channel base channel capacity

Today, information spreads so quickly that there is not always enough time to comprehend it. Most people rarely think about how and by what means it is transmitted, much less imagine a scheme for transmitting information.

Basic Concepts

The transfer of information is considered to be physical process movement of data (signs and symbols) in space. From the point of view of data transfer, this is a pre-planned, technically equipped event for moving information units over set time from the so-called source to the receiver via an information channel, or data transmission channel.

Data transmission channel is a set of means or medium for data distribution. In other words, this is that part of the information transmission circuit that ensures the movement of information from the source to the recipient, and under certain conditions, and back.

There are many classifications of data transmission channels. If we highlight the main ones, we can list the following: radio channels, optical, acoustic or wireless, wired.

Technical channels for transmitting information

Directly to technical channels Data transmission includes radio channels, fiber optic channels and cable. The cable can be coaxial or twisted pairs. The first are an electrical cable with a copper wire inside, and the second are twisted pairs of copper wires, insulated in pairs, located in a dielectric sheath. These cables are quite flexible and easy to use. Optical fiber consists of optical fiber strands that transmit light signals through reflection.

The main characteristics are throughput and noise immunity. Bandwidth is usually understood as the amount of information that can be transmitted over a channel in certain time. And noise immunity is the parameter of the channel’s resistance to influence external interference(noise).

Understanding Data Transfer

If you do not specify the scope of application, the general scheme for transmitting information looks simple; it includes three components: “source”, “receiver” and “transmission channel”.

Shannon scheme

Claude Shannon, an American mathematician and engineer, was at the origins of information theory. They proposed a scheme for transmitting information through technical communication channels.

This diagram is not difficult to understand. Especially if you imagine its elements in the form of familiar objects and phenomena. For example, the source of information is a person talking on the phone. The handset will be an encoder that converts speech or sound waves into electrical signals. The data transmission channel in this case is the communication nodes, in general, the entire telephone network leading from one telephone set to another. The decoding device is the subscriber's handset. It converts the electrical signal back into sound, that is, into speech.

In this diagram of the information transfer process, data is represented as a continuous electrical signal. This type of communication is called analog.

Coding concept

Coding is considered to be the transformation of information sent by a source into a form suitable for transmission over the communication channel being used. Most clear example coding is Morse code. In it, information is converted into a sequence of dots and dashes, that is, short and long signals. The receiving side must decode this sequence.

IN modern technologies used digital communication. In it, information is converted (encoded) into binary data, that is, 0 and 1. There is even a binary alphabet. Such a connection is called discrete.

Interference in information channels

There is also noise in the data transmission circuitry. The concept of "noise" in in this case means interference due to which the signal is distorted and, as a result, its loss. The reasons for the interference may be various. For example, information channels may not be well protected from each other. To prevent interference, various technical methods protections, filters, shielding, etc.

K. Shannon developed and proposed for use a coding theory to combat noise. The idea is that since information loss occurs under the influence of noise, it means that the transmitted data should be redundant, but at the same time not so much that it reduces the transmission speed.

IN digital channels communication information is divided into parts - packets, for each of which a checksum is calculated. This amount is transferred along with each package. The information receiver recalculates this sum and accepts the packet only if it matches the original one. Otherwise, the packet is sent again. And so on until sent and received checksums will not match.

Using Internet resources, find answers to the questions:

Task 1

1. What is the process of transmitting information?

Transfer of information- the physical process by which information is transferred in space. We recorded the information on a disk and moved it to another room. This process characterized by the presence of the following components:

Based on the type of distribution medium, communication channels are divided into:

Telecommunications(Greek tele - into the distance, far away and lat. communicatio - communication) is the transmission and reception of any information (sound, image, data, text) over a distance via various electromagnetic systems (cable and fiber optic channels, radio channels and other wired and wireless channels communications).

Telecommunications network is a system of technical means through which telecommunications are carried out.

Telecommunication networks include:
1. Computer networks(for data transfer)
2. Telephone networks(transmission of voice information)
3. Radio networks (transmission of voice information - broadcast services)
4. Television networks (voice and image transmission - broadcast services)

Computer telecommunications are telecommunications whose terminal devices are computers.

The transfer of information from computer to computer is called synchronous communication, and through an intermediate computer, which allows messages to be accumulated and transmitted to personal computers as requested by the user - asynchronous.

Computer telecommunications are beginning to be introduced into education. In higher education they are used to coordinate scientific research, prompt exchange of information between project participants, distance learning, and consultations. In the school education system - to increase the effectiveness of students’ independent activities associated with various types of creative work, including educational activities, based on widespread use research methods, free access to databases, exchange of information with partners both within the country and abroad.

The speed of information transfer depends largely on the speed of its creation (source performance), encoding and decoding methods. The highest possible information transmission speed in a given channel is called its throughput. Channel capacity, by definition, is the speed of information transmission when using the “best” (optimal) source, encoder and decoder for a given channel, so it characterizes only the channel.

Communication channels (CC) serve for signal transmission and are a common link in any information transmission system.

According to their physical nature, communication channels are divided into mechanical, used for the transfer of tangible media, acoustic, optical And electric, transmitting sound, light and electrical signals, respectively.

Electrical and optical communication channels, depending on the method of signal transmission, can be divided into wired ones, which use physical conductors to transmit signals ( electrical wires, cables, light guides), and wireless, using for signal transmission electromagnetic waves(radio channels, infrared channels).

According to the form of presentation of the transmitted information, communication channels are divided into analog, through which information is transmitted in continuous form, i.e. in the form of a continuous series of values ​​of any physical quantity, And digital, transmitting information presented in the form of digital (discrete, pulsed) signals of various physical natures.

Depending on the possible directions of information transfer, communication channels are divided into simplex, allowing information to be transmitted in only one direction; half duplex, providing alternating transmission of information in both forward and reverse directions; duplex, allowing information to be transmitted simultaneously in the forward and reverse directions.

There are communication channels switched, which are created from separate sections (segments) only for the duration of the transmission of information through them, and upon completion of the transmission such a channel is eliminated (disconnected), and non-switched(selected) created on long time and having constant characteristics in length, throughput, noise immunity.

Widely used in automated systems information processing and control electrical wired communication channels vary in capacity:

low speed, information transmission speed in which is from 50 to 200 bit/s. These are telegraph communication channels, both switched (subscriber telegraph) and non-switched;

medium speed, using analog (telephone) communication channels; the transmission speed in them is from 300 to 9600 bps, and in the new standards V.32 - V.34 of the International Telegraph and Telephony Consultative Committee (ICITT) and from 14400 to 56,000 bps;

high speed(broadband), providing information transmission speeds of over 56,000 bps.

To transfer information to low-speed and medium-speed compressor stations physical environment are usually wired lines: groups of either parallel or twisted wires called twisted pair It consists of insulated conductors twisted together in pairs to reduce both electromagnetic crosstalk and signal attenuation during transmission at high frequencies.

To organize high-speed (broadband) CS are used various cables:

Shielded with twisted pairs of copper wires;

Unshielded with twisted pairs of copper wires;

Coaxial;

Fiber optic.

STP cables(shielded with twisted pairs of copper wires) have good technical characteristics, but are inconvenient to operate and expensive.

UTP cables(unshielded with twisted pairs of copper wires) are quite widely used in data transmission systems, in particular in computer networks.

There are five categories of twisted pairs: the first and second categories are used for low-speed data transmission; the third, fourth and fifth - at transmission speeds of up to 16.25 and 155 Mbit/s, respectively. These cables have good technical characteristics, relatively inexpensive, easy to use, and do not require grounding.

Coaxial cable It is a copper conductor coated with a dielectric and surrounded by a revolute of thin copper conductors with a shielding protective sheath. Data transfer speed coaxial cable quite high (up to 300 Mbit/s), but it is not convenient enough to use and has a high cost.

Fiber optic cable(Fig. 8.2) consists of glass or plastic fibers with a diameter of several micrometers (light-leading core) with a high refractive index ps, surrounded by low refractive index insulation n 0 and placed in a protective polyethylene shell. In Fig. 8.2, A shows the distribution of the refractive index over the cross section of the fiber optic cable, and in Fig. 8.2, b- ray propagation diagram. The source of radiation propagated over fiber optic cable, is an LED or semiconductor laser, the radiation receiver is a photodiode, which converts light signals into electrical signals. Transmission of a light beam through a fiber is based on the principle of total internal reflection of the beam from the walls of the light guide core, which ensures minimal signal attenuation.

Rice. 8.2. Beam propagation along a fiber optic cable:

A- distribution of the refractive index over the cross-section of the fiber-optic cable;

b - ray propagation diagram

In addition, fiber optic cables provide protection for transmitted information from external electromagnetic fields and high speed transfers up to 1000 Mbit/s. Information encoding is carried out using analog, digital or pulse modulation light beam. Fiber optic cable is quite expensive and is usually used only for laying important backbone communication channels, for example, a cable laid along the bottom of the Atlantic Ocean connects Europe with America. In computer networks, fiber optic cable is used in the most critical areas, in particular on the Internet. One thick backbone fiber optic cable can simultaneously organize several hundred thousand telephone, several thousand video telephone and about a thousand television communication channels.

High-speed compressor stations are organized on the basis of wireless radio channels.

Radio channel - This is a wireless communication channel laid over the air. To form a radio channel, a radio transmitter and a radio receiver are used. Data transmission rates over a radio channel are practically limited by the bandwidth of the transceiver equipment. The radio wave range is determined by the frequency band of the electromagnetic spectrum used for data transmission. In table 8.1 shows the radio wave ranges and their corresponding frequency bands.

Most commonly used for commercial telecommunications systems frequency ranges 902 - 928 MHz and 2.40 - 2.48 GHz.

Wireless channels communications have poor noise immunity, but provide the user with maximum mobility and speed of response.

Telephone lines most branched and widespread. They transmit audio (tone) and fax messages. Information and reference systems, systems email And computer networks. Analogue and digital information transmission channels can be created on the basis of telephone lines.

IN analog telephone lines telephone microphone converts sound vibrations into an analog electrical signal, which is transmitted via subscriber line in the automatic telephone exchange. The required bandwidth for human voice transmission is approximately 3 kHz (range 300 Hz -3.3 kHz). Call signals are transmitted over the same channel as voice transmission.

IN digital communication channels The analog signal is sampled before input - converted into digital form: every 125 µs (sampling frequency is 8 kHz) current value analog signal displayed in 8-bit binary code.

Table 8.1

Radio wave ranges and corresponding frequency bands