Introduction 3 1. Synchronization in PDS systems 4 1.1 Classification of synchronization systems 4 1.2 Element synchronization with addition and subtraction of pulses (principle of operation). 5 1.3 Parameters of the synchronization system with the addition and subtraction of pulses 8 1.4 Calculation of the parameters of the synchronization system with the addition and subtraction of pulses 13 2. Coding in PDS systems 19 2.1 Classification of codes 19 2.2 Cyclic codes 20 2.3 Construction of the encoder and decoder of the cyclic code. Formation of a code combination of a cyclic code 22 3 PDS systems with feedback 28 3.1 Classification of systems with feedback 28 3.2 Timing diagrams for systems with feedback and waiting for non-ideal return channel 30 Conclusion 32 References 33

Introduction

The problem of transmitting information over long distances in the shortest possible time and with less errors remains relevant to this day, although in the process of development of telecommunication technologies, many methods of data transmission have been invented and successfully applied. Each of them has its own special advantages and disadvantages. Discrete messaging devices currently play a significant role in the life of human society. Their widespread use makes it possible to provide best use computer technology through the organization of computer networks and data transmission networks. Modern society can no longer be imagined without the achievements made in the industry of technology for transmitting discrete messages, for a little more than a hundred years of development. The used PDS technique makes it possible to create powerful computer networks and data transmission networks. The relevance of this work lies in the fact that the constantly growing need for the transmission of information flows over long distances is one of the distinctive features of our time. In addition, practically no organization can function without PDS technology, without it it is impossible to organize corporate computer networks, which can significantly reduce the time of information exchange between departments. The purpose and objectives of the course work are to consider the theoretical issues of synchronization and coding in PDS systems, consideration of PDS systems with feedback OS, as well as solving problems according to the option. The work consists of an introduction, three sections, a conclusion and a list of references. The total volume of work is 33 pages.

Conclusion

During the course work, the methods of strobing, synchronization in PDS systems, coding, PDS systems with OS were studied, as well as the effect of errors on the information transfer rate. All tasks were completed in accordance with the guidelines. Based on the results of the work done, the following conclusions can be drawn: Errors can occur at different stages of signal reception: during registration, when synchronization is established. In conditions of strong signal distortion, errors will be present in the communication channel during registration, with an increase in the synchronization error, the number of errors will also increase. An increase in the number of errors leads to a decrease in the transmission speed. To detect and correct errors, error-correcting coding is used, which also reduces the transmission rate. The use of efficient coding, which eliminates the redundancy of the message, makes it possible to reduce the average number of elements per message and thereby increase the transmission rate.

Bibliography

1. Emelyanov G.A., Shvartsman V.O. Transfer of discrete information. Textbook for universities. - M .: Radio and communication, 1982 .-- 240 p. 2. Kunegin S.V. Information transmission systems. Lecture course. - M., 1997 - 317 p. 3.Kruk B. Telecommunication systems and networks. T. 1. Textbook. allowance. - Novosibirsk .: SP "Nauka" RAS, 1998. - 536 p. 4. Olifer V.G., Olifer N.A. Fundamentals of data transmission networks. - M .: INTUIT. RU "Internet - University information technologies”, 2003. - 248 p. 5. Bases of transmission of discrete messages. Textbook for universities / Ed. V.M. Pushkin. - M .: Radio and communication, 1992 .-- 288 p. 6. Peskova S.A., Kuzin A.V., Volkov A.N. Networks and telecommunications. - M.: Asadema, 2006. 7. Computer networks and telecommunications. Lecture notes. SibSUTI, Novosibirsk, 2016 8. Timchenko S.V., Shevnina I.E. Study of the device of element-by-element synchronization with the addition and elimination of pulses of the data transmission system: Workshop / GOU VPO "SibGUTI". - Novosibirsk, 2009 .-- 24p. 9. Telecommunication systems and networks. Volume 3. Modern technologies. Ed. 3. Hot line- Telecom, 2005. 10. Shuvalov V.P., Zakharchenko N.V., Shvaruman V.O. Transfer of discrete messages / Ed. Shuvalova V.P. - M .: Radio and communication - 1990

In systems with OS, redundancy is entered into the transmitted information taking into account the state of the discrete channel. With the deterioration of the channel condition, the introduced redundancy increases, and vice versa, as the channel condition improves, it decreases.

Depending on the purpose of the OS, systems are distinguished:

with decisive feedback (ROS)

information feedback (IOS)

with combined feedback (KOS)

Figure 21 - Diagram of the PDS system with ROS.

Figure 22 - Diagram of the PDS system with IOS.

In the system with POC, the receiver, having received the codeword and analyzing it for errors, makes the final decision to issue the combination to the consumer of information or to erase it and send a signal on the retransmission of this codeword via the reverse channel. Therefore, systems with POC are often called systems with over-demand, or systems with automatic error request (ADR). If the code combination is received without errors, the receiver generates and sends an acknowledgment signal to the OS channel, upon receipt of which, the PKper transmitter transmits the next code combination. Thus, in systems with POC, an active role belongs to the receiver, and the decision signals generated by it are transmitted via the return channel.

In systems with ITS, information about the code combinations arriving at the receiver is transmitted via the reverse channel before their final processing and making final decisions. A special case of the ITS is the complete retransmission of the QCs or their elements arriving at the receiving line. These systems are called relay systems. If the amount of information transmitted over the OS channel is equal to the amount of information in the message transmitted over the forward channel, then the IOS is called complete. If the information contained in the receipt reflects only some signs of the message, then the IOS is called shortened. Thus, either the entire helpful information, or information about its distinctive features, therefore such an OS is called informational.

The information received via the OS channel is analyzed by the transmitter, and based on the results of the analysis, the transmitter makes a decision on the transmission of the next CC or on the repetition of previously transmitted ones. After that, the transmitter transmits service signals about the decisions made, and then the corresponding CC. The PCpr receiver either issues the accumulated code combination to the recipient, or erases it and stores the newly transmitted one. In systems with a shortened ITS, the load of the return channel is less, but the probability of errors is higher than in a full ITS.

In systems with CBS, the decision to issue the CC to the recipient of information or to retransmit it can be made both in the receiver and in the transmitter of the PDS system, and the OS channel is used to transmit both receipts and decisions.

OS systems:

with a limited number of repetitions (CC is repeated no more than L times)

with an unlimited number of repetitions (CC is repeated until the receiver or transmitter decides to issue this combination to the consumer).

Systems with OS can discard or use the information contained in rejected QCs in order to make a more correct decision. A system of the first type is called a system without memory, and the second, with a memory.

Systems with OS are adaptive: the rate of information transmission through communication channels is automatically adjusted to the specific conditions of signal transmission.

Studies have shown that for a given transmission fidelity, the optimal code length in systems with ITS is somewhat less than in systems with DFs, which makes the implementation of coding and decoding devices cheaper. However, the overall complexity of the implementation of systems with ITS is greater than that of systems with ROS. Therefore, POC systems have found wider application. Systems with ITS are used in cases where the back channel can be effectively used for transmitting receipts without prejudice to other purposes.

Discrete messages arriving from a source and intended for transmission to a remote recipient are subjected to various transformations in PDS systems. These transformations can be either specially provided and aimed at achieving certain results, or undesirable, leading to distortions and errors.

The sequence of basic transformations in PDS systems can be represented by the diagram shown in Figure 1.2 and displaying three groups of transformations:

conversion in the transmitter,

transformations in the receiver,

conversion in a continuous communication channel (NCS).

The purpose of processing in the transmitter is to convert the transmitted message α (t) into an electrical signal S (t), which is most suitable for transmission over the NCC. The signal S (t) is subjected to the action of noise and distortion in the NCS, and therefore the signal S * (t), which differs from S (t), arrives at the input of the receiver. The task of the receiver is to transform the signal S * (t), ensuring the receipt of the message α * (t) with minimal errors regarding the transmitted message α (t).

Figure 1.2. The structure of transformations in the PDS system

Symbols:

IS - a source of discrete messages;

KI - source coder;

M - modulator;

KK - channel encoder;

PRD - transmitter;

NCS - continuous communication channel;

DM - demodulator;

DCT - receiver's decoder;

DCC - channel decoder;

PS - the recipient of messages;

PRM - receiver.

The message coming from the source of the IS, in some cases, contains redundancy due to the statistical relationship of symbols. In some cases, the redundancy of the source plays a positive role, for example, in telegraphy when correcting a part of distorted words in a telegram. However, due to the presence of redundancy, the information transfer rate decreases; therefore, one of the ways to increase the information transfer rate is associated with eliminating the redundancy of the source. The task of eliminating redundancy in transmission in the PDS system is performed by source encoder CI, and restoration of the received message - receiver decoder DCT. Often, CI and DCP are included in IS and PS. One way to eliminate redundancy is to use efficient (economical) coding, the basics of which are discussed in 3.1.

To improve the transmission fidelity, error-correcting coding is used, which implies the introduction of redundancy into the transmitted code combinations. For this purpose, the transmission uses channel encoder CC, and on the receiving side there is a DCC channel decoder that performs the inverse transformation.

To match the encoder and decoder of the channel with the continuous communication channel, a modulator M is used in transmission, and a demodulator in reception.

The considered conversions are focused on the simplex mode of operation, but can easily be generalized to half-duplex and full-duplex modes. For this purpose, each of the interacting parties must be provided with receiving and transmitting equipment.

1.4. Block diagram of the VPS system

In modern communication equipment, the main stages of message transformations are performed by appropriate hardware or software. In most cases, these tools run as stand-alone units. The interaction of these blocks is illustrated by the block diagram of the PDS system, which is shown in Fig. 1.3.

Fig 1.3. Block diagram of the PDS system

Legend:

ISS - source-receiver of messages;

ОУ - terminal device;

UVV - input / output device;

US - matching device;

RCD - error protection device;

UPS - signal conversion device;

AKD - data channel termination equipment;

OOD - data terminal equipment;

APD - data transmission equipment;

AP - subscriber station.

Consider the purpose of the main blocks that allow for two-way transmission (half-duplex and full-duplex modes).

As source-recipient of the message IPS can be any input-output device, for example, terminal, display, telegraph, PC. Typically, the ISS converts the characters of the primary alphabet into codewords of the secondary alphabet. Matching device (interface) The US provides the coordination of the ISP with the subsequent equipment, for example, the conversion of a parallel code into a serial one and vice versa. The constructive combination of ISS and RS is called data terminal equipment OOD. The RCD error protection device is designed to increase the fidelity of the transmission of discrete messages, in most cases, by means of error-correcting coding. Sometimes the RCD is included in the DTE, especially with the software implementation of error-correcting coding. According to the ITU-T recommendation X.92, the DTE is called DTE (Data Terminal Equipment) and is conventionally designated

Along with the function of noise-immune encoding / decoding, the RCD provides the setting of the message format and operating modes with or without feedback. Signal conversion device UPS provides coordination of discrete signals with a communication channel. In some cases, a constructive combination of UPS and RCDs is used, which is called data transmission equipment ADF. According to ITU-T X.92 recommendation, ATD is called DCE (Data Circuit Terminating Equipment) and is conventionally designated

The purpose of the DCE is to facilitate the transfer of messages between two or more DTEs over a certain type of channel. To do this, the DCE must provide, on the one hand, the interface with the DTE, and on the other hand, the interface with the transmission channel. In particular, the DCE acts as a modulator and demodulator (modem) if a continuous (analog) communication channel is used. When using a digital E1 / T1 or ISDN channel, a Channel Service Unit / Data Service Unit (CSU / DSU) is used as the DCE.

In modern PDS systems, error protection is assigned to the DTE, and the UTP is designed to interface the DTE with a communication channel, which in ITU-T terms is called the DCE data channel termination equipment. Communication equipment located at the user and intended for organizing the PDS system is called subscriber station AP. The PDS system is understood as a set of hardware and software tools that ensure the transmission of discrete messages from source to recipient in compliance with the specified requirements for delivery time, fidelity and reliability.

UPS together with the communication channel form discrete channel DK, i.e. a channel designed to transmit only discrete signals (digital data signals). Distinguish between synchronous and asynchronous discrete channels. IN synchronous discrete channels single elements are introduced at strictly defined points in time. These channels are called code-dependent or opaque and are designed to transmit isochronous signals only. Synchronous channels include, in particular, channels formed by the methods of time division of the TDM channels. Any signals can be transmitted via asynchronous discrete channels: isochronous and anisochronous. Therefore, such channels are called transparent or code-independent... These include channels formed by frequency division multiplexing methods.

A discrete channel in conjunction with an RCD is called data link Efficiency. B / 1 / it is proposed to call this channel extended discrete channel RDK.

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Introduction

Since time immemorial, mankind has tried to solve the problem of transmitting information over a distance in the shortest possible time and with fewer errors. In the process of the development of science, many ways of transmitting data have been invented. They all have their own advantages and disadvantages. Therefore, this problem is relevant now.

Currently, the technology of transmitting discrete messages plays an important role in the life of human society. The use of this technique makes it possible to ensure a better use of expensive high-performance equipment by creating computer networks and data transmission networks.

This paper will consider the main aspects of the PDS technique.

1. Synchronization in PDS systems

1.1 Classification of synchronization systems

Synchronization is the process of establishing and maintaining a specific timing relationship between two or more processes. Distinguish between element-wise, group and frame synchronization. Element synchronization allows at the reception to correctly separate one single element from another and provide the best conditions for its registration. Group synchronization ensures correct division of the received sequence into code combinations, and frame synchronization ensures correct division of cycles and time combination of elements at the reception.

Item-by-item synchronization can be ensured through the use of an autonomous source - the keeper of the time standard and methods of forced synchronization. The first method is used only in cases when the time of the communication session, including the time of getting into communication, does not exceed the time of keeping the synchronization. A local generator with high stability can be used as an autonomous source.

Forced synchronization methods can be based on the use of a separate channel, through which the pulses necessary to adjust the local oscillator are transmitted, or an operating (information) sequence. The use of the first method requires a reduction bandwidth working channel due to the allocation of an additional sync channel. Therefore, in practice, the second method is most often used.

According to the method of generating clock pulses, synchronization devices with forced synchronization are divided into open (without feedback) and closed (with feedback).

Closed synchronization devices are divided into two subclasses: with a direct effect on the master clock generator and with an indirect effect.

Synchronization devices with a direct effect on the frequency of generators are divided into two groups according to the control method: devices with discrete control, in which the control device discretely changes the control signal from time to time, and devices with continuous control, in which the control device continuously acts on the generator of the SCI.

Synchronization devices without direct action are divided into two types: devices in which the intermediate device is a frequency divider with a variable frequency division ratio, and devices in which, in the process of phase correction, pulses are added or subtracted at the input of the frequency divider.

1.2 Element synchronization with addition and subtraction of pulses (principle of operation)

The synchronization device with addition and subtraction of pulses consists of a phase detector (PD), a master oscillator (MO), and a sync pulse phase control unit (SCI) (Fig. 1). This block contains a frequency divider (DF) of the pulse repetition generated by the MO. At the output of the frequency divider, SCI is obtained, arriving at the second input of the PD and to the receiver.

The PD compares the position in time of the impulses of the fronts (boundaries) of the received unit elements and the SCI. If they do not coincide, the corresponding pulse signal... For example, if SCI are ahead of the boundaries of single elements, then the pulse appears at the left output of the PD, if they lag behind - at the right. These pulses are fed to the inputs of the upward counter (PC).

The control pulse from the output of the filled RS is fed to the circuit for adding and excluding pulses (SDII) from the sequence generated by the MO. So in the case of advancing the SCI of the boundaries of single elements for the construction of the SCI phase in the SDII, one impulse is excluded from the sequence generated by the MG. This will cause the ARU to move towards the border of the unit element. The phase of the sync pulses has shifted to the right.

When the SCI lags behind the boundaries of the unit elements in the SDII, an impulse is added to the sequence coming from the MG. The SHI phase is shifted to the left.

RS is used to eliminate the influence of random factors, in particular, random edge distortions, on the SHI phase adjustment. The control pulse at the output of the PC will appear only when the prevalence of cases of displacement of the boundaries of elements relative to the SCI in one direction. This takes place in a situation where a real phase divergence is observed, since the number of displacements of the boundaries of elements to the left and to the right relative to SCI with random edge distortions is approximately the same.

1.3 Parameters of the synchronization system with addition and subtraction of pulses

The main parameters characterizing synchronization devices with addition and subtraction of pulses include:

1. Synchronization error - a value expressed in fractions of a unit interval and equal to the greatest deviation of the sync signals from their optimal position, which with a given probability can occur during synchronization.

m is the division factor of the divider;

k - coefficient of instability of transmit and receive generators;

S is the PC capacity;

RMS value of edge distortion of single elements.

The first two terms define the static synchronization error. In this case, the first term determines the minimum possible shift of the SCI in the process of phase adjustment and is called the correction step. The second term is equal to the phase difference between the SCI and the boundaries of the elements due to the instability of the transmit and receive generators between the two phase adjustments.

The last term determines the dynamic synchronization error.

2. Synchronization time t s - the time required to correct the initial deviation of the SCI relative to the boundaries of the received elements.

expressed in fractions of a unit interval

3. Time of maintaining synchronism t p.s. - the time during which the deviation of the SCI from the boundaries of the single elements will not go beyond the permissible mismatch limit (add) when the synchronization device stops working on the phase adjustment.

4. Probability of failure of synchronism P c. c. - the probability that, due to the action of interference, the deviation of the SCI from the boundaries of the unit elements will exceed half of the unit interval. This phase shift disrupts the synchronization devices and results in a malfunction. When designing and calculating synchronization devices, the following parameters are usually set: synchronization error, bit rate B, root-mean-square value of edge distortion, receiver's correcting ability µ, synchronization time t c, synchronization time t p.s. Based on the specified parameters, the following are calculated: the frequency of the ZG f zg, the permissible coefficient of instability of the generator k, the capacitance of the PC S, the division factor of the divider m.

1.4 Calculation of the parameters of the synchronization system with the addition and subtraction of pulses (tasks)

1. Coefficient of instability of the MO of the synchronization device and the transmitter k = 10 -6. The correcting ability of the receiver µ = 40%. No edge distortion. Plot the dependence of the time of normal operation (without errors) of the receiver on the telegraphy speed after the failure of the PD of the synchronization device. Will errors occur a minute after PD failure if the telegraphing speed B = 9600 Baud ?

Solution:

t p.c =; => t p.c =

t p.s. =

By condition:

=> - not true, because

Consequently, the time to maintain synchronism in this case is less than a minute. Errors will occur after a minute.

Since we need to determine the time of normal operation of the receiver after the failure of the phase detector of the synchronization device, we need to determine the time of normal operation of the receiver with the appearance and appearance of errors. And since errors appear at, we will take it equal.

The graph of the dependence of the time of normal operation of the receiver on the speed of telegraphy

Answer: Errors will occur after a minute.

2. The data transmission system uses a synchronization device without directly affecting the frequency of the master oscillator. The modulation rate is B. The correction step should be no more than? C. Determine the frequency of the ZG and the number of cells of the frequency divider if the division factor of each cell is two. Determine the values of B,? Q for your version by the formulas: B = 1000 + 100N * Z,? Q = 0.01 + 0.003N, where N is the number of the option. Z = 1.

Solution:

B = 1000 + 100 * 13 * 1 = 2300 Baud

? q = 0.01 + 0.003 * 13 = 0.049

;

Number of cells

Answer:

n = 5

3. Calculate the parameters of the synchronization device without directly affecting the MO frequency with the following characteristics: synchronization time no more than 1 s, in-phase maintenance time not less than 10 s, synchronization error no more than 10% of a unit interval. d cr ?? - rms value of edge distortion is 10% f 0? , the correcting ability of the receiver is 45%, the instability coefficient of the generators is k = 10 -6. Calculate the modulation rate for your variant using the formula: B = (600 + 100N) Baud, where N is the variant number.

Solution:

B = 600 + 100 * 13 = 1900 Baud

To find the parameters, we solve the system:

Answer: S = 99; ; m = 13

4. Determine whether the synchronization device is feasible without direct impact on the MO frequency, providing the synchronization error e = 2.5% under the conditions of the previous problem.

Solution:

S> 0 => The device can be realized

Answer: The device can be realized

5. In the data transmission system, a synchronization device is used without direct impact on the MO frequency with an instability coefficient k = 10 -5. The division factor of the divider is m = 10, the capacitance of the PC is S = 10. The displacement of significant moments is subject to the normal law with zero mathematical expectation and standard deviation equal to d cr.i = (15 + N / 2)% of the duration of a unit interval (N is the number of the variant). Calculate the probability of error when registering elements by the gating method without taking into account and taking into account the synchronization error. The correcting ability of the receiver is considered equal to 50%.

Solution:

d cr.i. = (15 + N / 2)% = (15 + 13/2)% = 21.5%

Possibility of wrong registration

P osh = P 1 + P 2 -P 1 * P 2,

where P 1 and P 2, respectively, are the probabilities of displacement of the left and right boundaries by an amount greater than µ.

If the probability density is described by the normal law, then the probabilities P 1 and P 2 can be expressed through the Crump function

, where;

1) Without taking into account the synchronization error (

2) Taking into account the synchronization error (

Answer: P osh without taking into account the synchronization error is equal to 3, taking into account the synchronization error is equal to. Thus, timing error causes an increase in the probability of error.

2.Coding in PDS systems

2.1 Classification of codes

Linear and group codes are most widely used in PDS systems.

In the simplest case, the code is specified by listing all of its code combinations (CC). But this set can be considered as a certain algebraic system, called a group with an operation given on it modulo 2 ().

It is usually said that a group is closed with respect to the operation ""

A set G with a group operation defined on it is a group if the following conditions are satisfied:

1. Associativity;

2. The existence of a neutral element;

3. The existence of an inverse element.

Using the property of being closed, the group code can be specified by a matrix.

All other elements of the group (except LLC) can be obtained by adding modulo 2 different combinations of matrix rows. This matrix is called the generating matrix. The QCs that make up the matrix are linearly dependent.

In PDS systems, as a rule, correction codes are used. Sequences of n - element code used for transmission are called allowed. If all possible sequences of an n - element code are allowed, then the code is called simple, i.e. unable to detect errors.

After going through all possible pairs of allowed QCs, one can find minimum value d, which is called the code distance.

In order for the code to detect an error, the inequality N A< N 0 (N A - число разрешенных комбинаций n - элементного кода, N 0 =2 n). При этом неиспользуемые n - элементные КК называются запрещенными. Они определяют избыточность кода. В качестве N A разрешенных КК надо выбирать такие, которые максимально отличаются друг от друга.

Correction of errors is also possible only if the transmitted allowed combination turns into a prohibited one. The conclusion that such a CC was transmitted is made on the basis of a comparison of the received forbidden combination with all allowed ones.

Noise-immune codes are divided into block and continuous. Block codes include codes in which each letter of the message alphabet corresponds to a block of n (i) elements, where i is the message number.

If the block length is constant and does not depend on the message number, then the code is called uniform. If the block length depends on the message number, then the block code is called non-uniform. In continuous codes, the transmitted information sequence is not divided into blocks, but the check elements are placed in a certain order between the information ones. Checking elements, in contrast to informational ones related to the original sequence, serve to detect and correct errors and are formed according to certain rules.

Uniform block codes are divided into separable and non-separable. In separable codes, elements are divided into informational and verification ones, which occupy certain places in the QC. In inseparable codes, there is no division of elements into informational and verification ones.

2.2 Cyclic codes

The class of linear codes, which are called cyclic, has become widespread. The name of these codes comes from their main property: if CC a 1, a 2, ..., an -1, an belongs to a cyclic code, then the combinations an, a1, a 2, ..., an -1 obtained by cyclic permutation of elements also belong this code.

A common property of all allowed KK cyclic codes (as polynomials) is their divisibility without remainder by some chosen polynomial, called the generating one. The error syndrome in these codes is the presence of the remainder of the division of the received CC by this polynomial. Cyclic codes are usually described and constructed using polynomials. The numbers in the binary code can be viewed as the coefficients of the polynomial of the variable x.

In cyclic codes, allowed CCs are those that have zero residue modulo P r (x), i.e. are divided by the generator polynomial without remainder.

Cyclic codes are block, uniform and linear. In comparison with ordinary linear codes, an additional restriction is imposed on the allowed CCs of a cyclic code: divisibility without a remainder by the generating polynomial. This property greatly simplifies the hardware implementation of the code.

The possibility of correcting a single error is associated with the choice of the generating polynomial P r (x). In the same way as in ordinary linear codes, the kind of syndrome in cyclic codes depends on the place where the error occurred. Among the set of polynomials P r (x), there are so-called primitive polynomials for which there is a dependence n = 2 r -1. This means that if an error occurs in one of the n bits of the QC, the number of different residuals will also be n.

To obtain a separable cyclic code from a given CC G (x), you need:

1. Multiply G (x) by x r, where r is the number of check elements.

2. Find the remainder of the division of the resulting polynomial by the generating polynomial: R (x) = G (x) x r / P (x).

3.Add G (x) x r with the resulting remainder. G (x) x r + R (x).

The last r elements will be the check elements in the received QC, and the rest are informational.

2.3 Construction of a cyclic code encoder and decoder

1. Draw a cyclic code encoder for which the generating polynomial is given by the number (4N + 1).

Solution:

(4N + 1) = 4 * 13 + 1 = 53

57 10 -> 110101 2

P (x) = x 5 + x 4 + x 2 +1

2. Write down the CC of the cyclic code for the case when the generating polynomial has the form P (x) = x 3 + x 2 +1. The QC coming from the source of messages has k = 4 elements and is written in binary form as a number corresponding to (N-9).

Solution:

4 10 -> 0100 2

a) G (x) * x r = x 2 * x 3 = x 5

b) Division by P (x):

x 5 + x 4 + x 2 x 2 + x + 1

R (x) = x + 1 - remainder

c) Code combination:

G (x) * x r + R (x) = x 5 + x + 1

Thus obtained QC: 0100011

Answer: 0100011

3. Draw an encoder and decoder with error detection and “run” through the encoder the original QC in order to form check elements.

Solution:

Errors in cyclic code are detected by dividing by the generating polynomial.

Decoder:

4. Calculate the probability of incorrect reception of the QC (error correction mode) on the assumption that the errors are independent, and the probability of incorrect reception corresponds to that calculated in Chapter 2 (taking into account the synchronization error and excluding the synchronization error).

Solution:

If the code is used in the error correction mode and the error correction rate is equal to t and.o. , then the probability of incorrect reception of the QC is calculated:

Here r osh. - the probability of incorrect reception of a single element;

n is the length of the codeword;

t and.about. - multiplicity of corrected errors;

The multiplicity of the corrected. errors t and.o is defined as, where d 0 - code distance. For the code (7,4) specified in the problem №3, d 0 = 3 and t and.o. = 1, i.e. given code able to correct one-time errors.

1) Calculation without taking into account the synchronization error:

2) Calculation taking into account the synchronization error:

If there is a synchronization error, the probability of incorrect CC reception increases.

Answer: 0,0073; 0,123

3. PDS systems with feedback

3.1 Classification of systems with OS

Depending on the purpose of the OS, systems are distinguished: with decisive feedback (ROS), informational feedback (IOS) and with combined feedback (COS).

In systems with POC, the receiver, having received the CC and analyzing it for errors, makes the final decision to issue a combination of information to the consumer or to erase it and send a signal on the retransmission of this CC via the reverse channel.

If the CC is received without errors, the receiver generates and sends an acknowledgment signal to the OS channel, having received it, the transmitter transmits the next CC. Thus, in systems with POC, an active role belongs to the receiver, and the decision signals generated by it are transmitted via the return channel.

Structural scheme PD systems with OS

PK trans - forward channel transmitter, PK pr - forward channel receiver, OK trans - reverse channel transmitter, OK pr - reverse channel receiver, RU - deciding device

In systems with ITS, information about the QCs arriving at the receiver is transmitted via the reverse channel before their final processing and making final decisions.

A special case of an ITS is a complete retransmission of CCs or their elements arriving at the receiving side. The corresponding systems are called relay systems. In a more general case, the receiver generates special signals that have a smaller volume than the useful information, but characterize the quality of its reception, which are sent to the transmitter via the OS channel. If the amount of information transmitted over the forward channel of the OS (receipts) is equal to the amount of information in the message transmitted over the forward channel, then the IOS is called complete. If the information contained in the receipt reflects only some signs of the message, then the IOS is called shortened.

The information received via the OS channel (receipt) is analyzed by the transmitter, and based on the results of the analysis, the transmitter makes a decision on the transmission of the next CC or on the repetition of the previously transmitted ones. After that, the transmitter transmits signaling signals about the adopted decision, and then the corresponding CCs.

In systems with a shortened ITS, the load of the return channel is less, but the probability of errors is higher than in a full ITS.

Systems with OS are also subdivided into systems with a limited number of repetitions (each combination can be repeated no more than l times) and with an unlimited number of repetitions (the transmission of the combination is repeated until the receiver or transmitter decides to issue the combination to the consumer).

Systems with OS can discard or use the information contained in rejected QCs in order to accept more correct decision... Systems of the first type are called systems without memory, and the second - systems with memory.

Feedback can cover various parts of the system: communication channel, discrete channel, data transmission channel.

Systems with OS are adaptive: the rate of information transmission through communication channels is automatically adjusted to the specific conditions of signal transmission.

Numerous algorithms for operating systems with an OS are currently known. The most common among them are:

Waiting systems - after the transmission of the CC, they either wait for a feedback signal, or transmit the same CC, but the transmission of the next CC is started only after receiving an acknowledgment for the previously transmitted combination.

Systems with blocking - carry out transmission of a continuous sequence of QCs in the absence of feedback signals for the previous S combinations. After detecting errors (S + 1) - th combination, the system output is blocked for the time of receiving S combinations. The transmitter repeats the transmission of the S last transmitted CC.

3.2 Timing diagrams for feedback and standby systems for a non-ideal return link

If there is an error in the confirmation signal, an insert occurs, if an error occurs in the re-request signal, a dropout is formed.

1) QC from the source of messages;

2) code messages sent by the transmitter on the forward channel;

3) QC received by the receiver via the forward channel;

4) s, transmitted over the reverse channel;

5) the signal received via the return channel;

6) QC, transmitted to the recipient.

3.3 Calculation of system parameters with OS and waiting

clock decoder pulse cyclic

1. Build timing diagrams for the system with POC-OZH (channel errors are independent). Code combinations 1,2,3,4,5,6 are transmitted to the channel. Code combination 2 is distorted. On the 3rd code combination Yes -> No (distortion of the confirmation signal).

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2. Calculate the information transfer rate for the ROS-OZh system. Channel errors are independent Psh = (N / 2) * 10 -3. Build graphs of the dependence of R (R 1, R 2, R 3) on the block length. Find the optimal block length. If the waiting time t standby = 0.6 * t bl (at k = 8). The block transmitted to the channel has the following values: k = 8,16,24,32,40,48,56. Number of check elements: r = 6. The block length in the channel is determined by the formula

n = k i + r.

Solution:

Posh = (N / 2) * 10 -3 = (13/2) * 10 -3 = 0.0065

Let's find the information transfer rate according to the formula: R = R 1 * R 2 * R 3

R 1 - speed due to the introduction of redundancy (check elements)

R 2 - speed due to waiting

R 3 - rate due to retransmissions

Let's calculate the values of R 1, R 2, R 3, R, n for different values of k and write the result in the table:

It can be seen from the table and the graph that the optimal block length is n = 62, since at this value the maximum information transfer rate is reached.

Answer: optimal block length n = 62

4. Determine the probability of incorrect reception in the system with ROS-OZH, depending on the block length and build a graph. Consider errors in the channel as independent. The probability of error per element P osh = (N / 2) * 10 -3.

Solution:

P osh = (N / 2) * 10 -3 = (13/2) * 10 -3 = 0.0065

Because the values of P n (t) at t> 5 are too small, they can be ignored.

Conclusion

In this term paper methods of synchronization in PDS systems were considered, in particular, element-by-element synchronization with addition and subtraction of pulses and the calculation of its parameters.

The calculation results show that the edge distortions affect the synchronization error, and with an increase in the synchronization error, the error probability increases.

Also in the work was considered the construction of the encoder and decoder of the cyclic code and the system of PDS with feedback.

It can be seen from the calculations that in the presence of a synchronization error, the probability of incorrect CC reception increases.

One of the methods of dealing with errors can be the use of error-correcting codes. For example, the cyclic code considered in this work.

Bibliography

1. Shuvalov V.P., Zakharchenko N.V., Shvaruman V.O. Transfer of discrete messages / Ed. Shuvalova V.P. - M .: Radio and communication - 1990

2. Timchenko S.V., Shevnina I.E. Study of the device of element-by-element synchronization with the addition and elimination of pulses of the data transmission system: Workshop / GOU VPO "SibGUTI". - Novosibirsk, 2009 .-- 24p.

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Synchronization methods in VPS systems. Discrete Messaging Basics

1.4. Block diagram of the VPS system

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Introduction

Currently, the technology of transmitting discrete messages plays an important role in the life of human society. The use of this technique makes it possible to ensure a better use of expensive high-performance equipment by creating computer networks and data transmission networks.

This paper will consider the main aspects of the PDS technique.

1. Synchronization in PDS systems

1.1 Classification of synchronization systems

According to the method of generating clock pulses, synchronization devices with forced synchronization are divided into open (without feedback) and closed (with feedback).

Closed synchronization devices are divided into two subclasses: with a direct effect on the master clock generator and with an indirect effect.

1.2 Element synchronization with addition and subtraction of pulses (principle of operation)

When the SCI lags behind the boundaries of the unit elements in the SDII, an impulse is added to the sequence coming from the MG. The SHI phase is shifted to the left.

1.3 Parameters of the synchronization system with addition and subtraction of pulses

The main parameters characterizing synchronization devices with addition and subtraction of pulses include:

1.4 Calculation of the parameters of the synchronization system with the addition and subtraction of pulses (tasks)

Solution:

t p.c =; => t p.c =

t p.s. =

By condition:

=> - not true, because

Consequently, the time to maintain synchronism in this case is less than a minute. Errors will occur after a minute.

The graph of the dependence of the time of normal operation of the receiver on the speed of telegraphy

Answer: Errors will occur after a minute.

Solution:

B = 1000 + 100 * 13 * 1 = 2300 Baud

? q = 0.01 + 0.003 * 13 = 0.049

;

Number of cells

Answer:

n = 5

Solution:

B = 600 + 100 * 13 = 1900 Baud

To find the parameters, we solve the system:

Answer: S = 99; ; m = 13

4. Determine whether the synchronization device is feasible without direct impact on the MO frequency, providing the synchronization error e = 2.5% under the conditions of the previous problem.

Solution:

S> 0 => The device can be realized

Answer: The device can be realized

Solution:

d cr.i. = (15 + N / 2)% = (15 + 13/2)% = 21.5%

Possibility of wrong registration

P osh = P 1 + P 2 -P 1 * P 2,

where P 1 and P 2, respectively, are the probabilities of displacement of the left and right boundaries by an amount greater than µ.

If the probability density is described by the normal law, then the probabilities P 1 and P 2 can be expressed through the Crump function

, where;

, where;

2.Coding in PDS systems

2.1 Classification of codes

Linear and group codes are most widely used in PDS systems.

In the simplest case, the code is specified by listing all of its code combinations (CC). But this set can be considered as a certain algebraic system, called a group with an operation given on it modulo 2 ().

It is usually said that a group is closed with respect to the operation ""

A set G with a group operation defined on it is a group if the following conditions are satisfied:

2.2 Cyclic codes

The class of linear codes, which are called cyclic, has become widespread. The name of these codes comes from their main property: if CC a 1, a 2, ..., an -1, an belongs to a cyclic code, then the combinations an, a1, a 2, ..., an -1 obtained by cyclic permutation of elements also belong this code.

In cyclic codes, allowed CCs are those that have zero residue modulo P r (x), i.e. are divided by the generator polynomial without remainder.

Cyclic codes are block, uniform and linear. In comparison with ordinary linear codes, an additional restriction is imposed on the allowed CCs of a cyclic code: divisibility without a remainder by the generating polynomial. This property greatly simplifies the hardware implementation of the code.

To obtain a separable cyclic code from a given CC G (x), you need:

1. Multiply G (x) by x r, where r is the number of check elements.

2. Find the remainder of the division of the resulting polynomial by the generating polynomial: R (x) = G (x) x r / P (x).

3.Add G (x) x r with the resulting remainder. G (x) x r + R (x).

The last r elements will be the check elements in the received QC, and the rest are informational.

2.3 Construction of a cyclic code encoder and decoder

3. PDS systems with feedback

3.1 Classification of systems with OS

Depending on the purpose of the OS, systems are distinguished: with decisive feedback (ROS), informational feedback (IOS) and with combined feedback (COS).

In systems with POC, the receiver, having received the CC and analyzing it for errors, makes the final decision to issue a combination of information to the consumer or to erase it and send a signal on the retransmission of this CC via the reverse channel.

3.2 Timing diagrams for feedback and standby systems for a non-ideal return link

3.3 Calculation of system parameters with OS and waiting

clock decoder pulse cyclic

1. Build timing diagrams for the system with POC-OZH (channel errors are independent). Code combinations 1,2,3,4,5,6 are transmitted to the channel. Code combination 2 is distorted. On the 3rd code combination Yes -> No (distortion of the confirmation signal).

n = k i + r.

Solution:

Posh = (N / 2) * 10 -3 = (13/2) * 10 -3 = 0.0065

Let's find the information transfer rate according to the formula: R = R 1 * R 2 * R 3

R 1 - speed due to the introduction of redundancy (check elements)

R 2 - speed due to waiting

R 3 - rate due to retransmissions

Let's calculate the values ​​of R 1, R 2, R 3, R, n for different values ​​of k and write the result in the table:

It can be seen from the table and the graph that the optimal block length is n = 62, since at this value the maximum information transfer rate is reached.

Answer: optimal block length n = 62

Let's calculate the values of R 1, R 2, R 3, R, n for different values of k and write the result in the table: