In systems with OS, redundancy is introduced into the transmitted information taking into account the state of the discrete channel. As the channel condition deteriorates, 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 (IFE)

with combined feedback (COS)

Figure 21 – Scheme PDS systems with ROS.

Figure 22 – Scheme of the PDS system with IOS.

In a system with POC, the receiver, having received a code combination and analyzed it for errors, makes the final decision to issue the combination to the information consumer or to erase it and send a signal through the reverse channel to retransmit this code combination. Therefore, systems with POC are often called systems with re-questioning, or systems with automatic error request (AEO). If a code combination is received without errors, the receiver generates and sends a confirmation signal to the OS channel, having received which, the PCper transmitter transmits the next code combination. Thus, in systems with DFB, the active role belongs to the receiver, and the decision signals generated by it are transmitted via the reverse channel.

In systems with IOS, information about code combinations arriving at the receiver is transmitted via the reverse channel before their final processing and final decisions are made. A special case of IOS is the complete retransmission of CCs 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 of the characteristics of the message, then the IOS is called shortened. Thus, either the entire useful 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 transmitting the next CC or repeating previously transmitted ones. After this, the transmitter transmits service signals about the decisions made, and then the corresponding CC. The PKpr receiver either gives the accumulated code combination to the recipient, or erases it and remembers the newly transmitted one. In systems with a shortened IOS, there is less load on the reverse channel, but there is a greater likelihood of errors compared to a full IOS.

In systems with CBS, the decision to issue a 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 (QC is repeated until the receiver or transmitter decides to issue this combination to the consumer).

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

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

Research has shown that, for a given transmission fidelity, the optimal code length in systems with IOS is somewhat smaller than in systems with POS, which reduces the cost of implementing encoding and decoding devices. However, the overall complexity of implementing systems with IOS is greater than systems with DOS. Therefore, systems with POC have found wider application. Systems with IOS are used in cases where the return channel can be effectively used for transmitting receipts without prejudice to other purposes.

Simplified block diagram of the PDS equipment.

On Fig.1.6 a simplified block diagram of the equipment is presented data transmission, which is a typical representative of discrete message transmission equipment. Shown in the picture functional units equipment corresponds GOST 17657-72 and fully reflect the traditionally established content of the discipline being studied and enshrined in regulatory documents.

OOD APD APD OOD

RCD UPS Communication channel UPS RCD

Coder

UCC

DC channel

Discrete channel

Data link

Fig.1.6

On Fig.1.6 The following notations are accepted:

OUD – final data setting,

ADF – data transmission equipment,

DTE – data terminal equipment,

RCD – error protection device,

UPS - device signal conversion,

RU - recording device,

UONS – device for assessing signal reliability,

USP – element synchronization device,

UCS – frame synchronization device.

Data terminal equipment(OOD) is a collection of data input and output devices. These devices are on Fig.1.6 represented by the source and recipient of data messages. Typically this is technical means. The source generates a message for further transmission, and the receiver displays the message in a form adequate to its content for presentation to the user. Data messages, by their nature, are of the type discussed above.

In the case of analog messages, they are subject to additional processing using analog-to-code converters on the transmitting side and code-to-analog converters at the receiving side.

Typically, message input from the data source is controlled by the ADF, and output to the recipient is forced as messages arrive.

Data transmission equipment(APD)– the totality of funds indicated on Fig.1.6. Ancillary devices can be added to them, such as control and measuring devices, automatic call and answer devices, etc.

Final Data Setup(OUD)– a set of terminal data equipment and data transmission equipment united by a common control device (not shown in the figure).

Error protection device(RCD) designed to reduce the number of errors appearing in a data message under the influence of interference in the communication channel. The RCD includes devices for noise-resistant coding and decoding of messages (encoder, decoder) and a frame synchronization device (CSD). The encoder converts a simple code, in which the message arrives at the ADF from the DTE, into a noise-resistant code, and the decoder selects the source message from the code combinations of the noise-resistant code that came from the communication channel, eliminating some of the errors that appeared during the transmission of the message over the communication channel as a result of the influence interference

Framing device(UCS) establishes and maintains the required phase relationships between the processing cycles of transmitted messages in the encoder and decoder.

Signal conversion device(OOPS) is intended to bring the message signal generated in the OUD to a form that ensures its transmission over a telecommunication channel. The main composition of the UPS is presented at Fig.1.6.

Modulator – a device that performs modulation. Demodulator carries out inverse conversion. The combination of the modulator and demodulator forms modem .

Recording device(RU) determines and stores the significant position of the received signal within each unit interval, i.e. in the binary case, determines and stores the value of each received bit.

Signal reliability estimator(UONS)– a device that measures one or more parameters of a received signal and produces a special signal indicating possible errors. Here and below mistake we will understand the event that the sequence of signals reproduced by the ADF receiver does not correspond to the original one. An erroneous single element appears at the output of the switchgear as a result wrong decision RU about the value of the received single element, an erroneous code combination - at the output of the decoder as a result of the decoder’s incorrect decision about the correspondence of the received code combination to the transmitted one. The ONS is designed to reduce the number of errors at the output of the ADF receiver. This is achieved by processing - erasing a single element at the output of the RU or refusing decoding - erasing the code combination. These decisions are made, among other things, based on the results of the work of the UONS.

Element synchronization device (or element-by-element synchronization ) (USP) ensures synchronization of the transmitted and received signals, in which the required phase relationships between the significant moments of the transmitted and received are established and maintained single elements these signals.

Let us briefly describe the process of information transfer in the system under consideration.

The source produces a message. If this message is of a discrete nature (letters, numbers, etc.), then it is presented at the source output in the form of simple code combinations. Typically, five-element codes or seven-element codes, called primary codes, are used for this purpose. If the generated message is analog (change in temperature, radiation level, illumination, etc.), then using a digital-to-analog converter (“analog - code”) it is reduced to discrete form and then presented as a sequence of combinations of the primary code.

Upon command from the ADF, messages from the data source are entered into encoder. Here ℓ- elemental combination of the primary code is converted into n -element combination of redundant code, where n>ℓ. In a redundant code combination, in addition to elements carrying information from the message source (information elements), a certain rule redundant elements that provide the code with noise-resistant properties. Further bit by bit n -element combination is introduced in the form of DC signals into modulator, where direct current signals are converted to a form consistent with the channel used, and with the help of channel-forming equipment, through the propagation medium, they arrive at the input demodulator, where the modulated signal is converted back into DC signals. When an electrical signal passes through a communication channel, it is affected by various types of interference, which manifest themselves in the form of distortions in the duration of DC signals at the output demodulator.

The USP determines the expected significant moments of direct current pulses arriving at the input of the RU, and the RU restores the significant positions of the received signals at significant intervals.

From the output of the RU, the received message is sent bit by bit to decoder. With the help of the UCC, the beginning of accepted n -element combinations. The decoder, based on the connections between information and redundant elements, selects information elements, and the RCD forcibly outputs them to the data recipient in the form ℓ -element combinations. Received messages, depending on their original form, are issued to the recipient either in discrete form (primary code combinations) or using digital-to-analog converter(“code – analogue”) in continuous form.

To ensure the intended purpose of the system in question, certain requirements are imposed on it.

Since the communication system is complex system, then in order to present requirements for it, it is decomposed into its component parts.

On Fig.1.6 In the communication system under consideration, three components are distinguished:

• DC channel,
• discrete channel,
• data channel.

DC channel as seen from Fig.1.6, represents the part of the communication system from the modulator input to the demodulator output. The signals at the input and output of this channel are direct current pulses, which are subject to requirements for the amount of distortion, i.e. The direct current channel is normalized by the amount of distortion in the duration of transmitted and received signals.

Discrete channel – part of the communication system from the encoder output to the decoder input. At the input and output of this channel, the signals are in the form of sequences of code symbols; in the binary case – sequences of binary units. The output of this channel is the output of the switchgear, which is characterized by the possibility of errors resulting from exceeding the permissible value of distortion of the duration of the signals at the input of the switchgear. A discrete channel is introduced to specify the requirements, i.e. normalizing the probability of errors occurring in the code sequence at the input of the RCD decoder.

Data link - part of the communication system from the encoder input to the decoder output. At the input and output of this channel, the transmitted messages are in the form of code combinations of the primary code. This channel is used to specify requirements, i.e. normalizing the flow of primary code combinations by the probability of distortion of the primary code code combination. The implementation of these requirements makes it possible to reduce the probability of an error in the combination of the primary code arriving at the recipient to a specified value. Therefore, the data transmission channel is called an error-protected channel.

The main parameters of the PDS system are reliability , speed And reliability transmission of discrete messages.

Credibility determined by the following characteristics:

• the probability of erroneous reception of code symbols as a result of an incorrect decision by the control unit when the duration of single elements is distorted;

p ;

for existing discrete channels p=10 -4 ÷10 -2 ;

• the probability of distortion of code combinations of the primary code received at the input of the data transmission channel and issued to the recipient of messages with errors as a result of the presence of errors in the code symbols;

for this probability the notation is accepted p(≥1,ℓ), which means there is at least one error in the combination of the primary length code ℓ ;

for existing transmission channels the required values ​​are p(≥1,ℓ)≤10 -9 ÷10 -6 .

There are two approaches to determining the transmission rate of discrete messages.

First approach - informational . It requires the ability to measure the amount of information in messages at the output of a data channel relative to the input messages. In this case, the information transmission rate is defined as the amount of information about the ensemble of input messages contained in the output messages per unit of time.

The maximum speed of information transmission for given channel characteristics, when the maximum is taken over all possible probabilistic characteristics of the signal supplied to its input, is called throughput channel or communication system.

Second approach - structural . It's based on counting structural units messages arriving at the receiver at certain time intervals.

The following characteristics of the transmission speed of discrete messages are used:

• unit transmission rate(R e) is the reciprocal of the unit interval, measured in seconds.

The unit of measurement for this speed is s -1 ;

• bit rate(R b) – the number of bits transmitted per unit of time. The unit of measurement for this speed is bit/s . Determined by the formula:

R b = R e log 2 m ,

Where m – number of significant positions along the length of a unit element;

• relative data rate(R o) – the ratio of the number of data bits issued to the data recipient to the total number of transmitted bits;
• effective data transfer rate(R e) – the ratio of the number of data bits issued to the data recipient to the total transmission time:

R e =R o ·R b.

• One of the most commonly used characteristics of the reliability of discrete message transmission is reliability of timely delivery of messages , or probabilistic-time characteristics of message delivery. It is defined as follows:

P(t back ≤T back)≥P add,

which means: the probability of delivering a message within time t dov , not exceeding some specified time T back , must be no less than the acceptable probability P extra .

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Introduction

Since time immemorial, humanity 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 to transmit data have been invented. They all have their advantages and disadvantages. Therefore, this problem is still relevant today.

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

This work will discuss 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 certain time relationships between two or more processes. There are element-by-element, group and cyclic synchronization. Element-by-element synchronization allows the reception to correctly separate one single element from another and provide the best conditions for its registration. Group synchronization ensures the correct division of the received sequence into code combinations, and frame synchronization ensures the correct division of cycles and temporary combination of elements at reception.

Element-by-element synchronization can be achieved through the use of an autonomous source - the keeper of the time standard and forced synchronization methods. The first method is used only in cases where the time of the communication session, including the time of entering into communication, does not exceed the time for maintaining 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 generator or the working (information) sequence are transmitted. Using the first method requires reducing bandwidth working channel due to the allocation of an additional synchronization 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 direct action on the master clock generator and with indirect action.

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 AChI generator.

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-by-element synchronization with adding and subtracting pulses (operating principle)

The synchronization device with the addition and subtraction of pulses consists of a phase detector (PD), a master oscillator (MO) and a phase control unit for synchronizing pulses (PCU) (Fig. 1). This block contains a frequency divider (DF) for the repetition of pulses generated by the generator. At the output of the frequency divider, ACI is obtained, which is supplied to the second input of the PD and to the receiver.

The FD compares the positions in time of the pulses of the fronts (boundaries) of the received unit elements and the ACI. If they do not match, it generates the corresponding pulse signal. For example, if the ACIs 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 arrive at the inputs of the up/down counter (RS).

The control pulse from the output of the filled PC is sent to the circuit for adding and excluding pulses (SDIA) from the sequence generated by the SG. So, in the case of advance of the ACI of the boundaries of single elements for the construction of the ACI phase in the SDII, one pulse is excluded from the sequence generated by the SG. This will lead to a displacement of the ACS towards the boundary of a single element. The phase of the synchronization pulses has shifted to the right.

When the ACI lags behind the boundaries of single elements in the SDII, an impulse is added to the sequence coming from the SG. The ACI phase shifts to the left.

RS is used to eliminate the influence of random factors on the adjustment of the ACI phase, in particular, random edge distortions. The control pulse at the output of the RS will appear only when there is a predominance of cases of displacement of the boundaries of the elements relative to the Agricultural Instrument in one direction. This occurs in a situation where there is a real phase divergence, since the number of displacements of the boundaries of elements to the left and to the right relative to the AChI with random edge distortions is approximately the same.

1.3 Parameters of the synchronization system with adding and subtracting pulses

The main parameters characterizing synchronization devices with adding and subtracting pulses include:

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

m is the division factor of the divider;

k is the instability coefficient of the transmitting and receiving generators;

S - capacity RS;

RMS value of edge distortions of single elements.

The first two terms determine the static synchronization error. In this case, the first term determines the minimum possible shift of the AChI in the process of phase adjustment and is called the correction step. The second term is equal to the phase difference between the ACI and the element boundaries 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 agricultural apparatus relative to the boundaries of the received elements.

expressed as fractions of a unit interval

3. Time to maintain synchronism t p.s. - the time during which the deviation of the AChI from the boundaries of individual elements will not go beyond the permissible mismatch limit (additional) when the phase adjustment synchronization device stops operating.

4. Probability of failure of synchronism P c . c. - the probability that, due to interference, the deviation of the chemical information system from the boundaries of individual elements will exceed half of the unit interval. This phase shift disrupts the operation of synchronization devices and leads to failure. When designing and calculating synchronization devices, it is usually specified following parameters: synchronization error, transmission rate B, root mean square value of edge distortion, correcting ability of the receiver µ, synchronization time t c, time to maintain synchronization t p.s. Based on specified parameters the following are calculated: frequency of the generator f, permissible coefficient of instability of the generator k, capacitance of the RS S, division coefficient of the divider m.

1.4 Calculation of synchronization system parameters with adding and subtracting pulses (tasks)

1. Instability coefficient of the MG synchronization device and transmitter k=10 -6. Receiver correction ability µ=40%. There are no edge distortions. Plot the dependence of the time of normal operation (without errors) of the receiver on the telegraphy speed after the failure of the PD synchronization device. Will errors occur a minute after the FD failure, if the telegraphy speed is B=9600 Baud? ?

Solution:

t p.s =; => t p.s =

t p.s =

According to the condition:

=> - not true, because

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

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 of errors. And since errors appear at, we will take it equal to.

Graph of the dependence of the time of normal operation of the receiver on the telegraphy speed

Answer: After a minute, errors will occur.

2. The data transmission system uses a synchronization device without directly affecting the frequency of the master oscillator. The modulation speed is equal to V. The correction step should be no more than? Determine the frequency of the main generator and the number of frequency divider cells if the division coefficient of each cell is two. Determine the values ​​of B, ?ts for your option using the formulas: B=1000+100N*Z, ?ts =0.01+0.003N, where N is the number of the option.Z=1.

Solution:

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

?ts=0.01+0.003*13=0.049

;

Number of cells

Answer:

n=5

3. Calculate the parameters of a synchronization device without directly affecting the frequency of the main generator with the following characteristics: synchronization time no more than 1 s, time to maintain in-phase no less than 10 s, synchronization error no more than 10% of a unit interval. d cr?? - the root mean square 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 option using the formula: B=(600+100N) Baud, where N is the number of the option.

Solution:

B=600+100*13=1900 Baud

To find the parameters, we solve the system:

Answer: S=99; ; m=13

4. Determine whether a synchronization device is feasible without directly affecting the frequency of the main generator, providing a synchronization error e = 2.5% under the conditions of the previous problem.

Solution:

S > 0 => The device can be implemented

Answer: The device can be implemented

5. The data transmission system uses a synchronization device without direct impact on the frequency of the main generator with instability coefficient k=10 -5. Divider division coefficient m=10, PC capacity S=10. The displacement of significant moments is subject to the normal law with zero mathematical expectation and standard deviation equal to dcr.i.=(15+N/2)% of the duration of a unit interval (N is the number of the option). Calculate the probability of error when registering elements using 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 erroneous registration

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

where P 1 and P 2 are respectively the probabilities of shifting 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;

1) Without taking into account 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 it is equal. 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 its code combinations (CC). But this set can be considered as some algebraic system called a group with a modulo 2 () operation specified on it.

It is usually said that a group is closed under the operation “”

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

1. Associativity;

2. The existence of a neutral element;

3. Existence of an inverse element.

Using the property of closure, the group code can be specified as 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 CCs that make up the matrix are linearly dependent.

VDS systems typically use correction codes. 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.

By going through all possible pairs of allowed CCs, you can find the minimum value of d, which is called the code distance.

In order for the code to detect an error, the inequality N A must be satisfied< 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.

Error correction is also possible only if the transmitted allowed combination becomes prohibited. The conclusion that such a CC was transferred is made based on a comparison of the accepted prohibited combination with all permitted ones.

Noise-resistant codes are divided into block and continuous. Block codes include codes in which each character 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 uneven. In continuous codes, the transmitted information sequence is not divided into blocks, and check elements are placed in in a certain order between information ones. Check elements, unlike information elements 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 inseparable. In separable codes, elements are divided into informational and verification, which occupy certain places in the QC. In inseparable codes, there is no division of elements into informational and verification.

2.2 Cyclic codes

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

A common property of all cyclic codes allowed by QC (as polynomials) is their divisibility without remainder by some selected polynomial, called generating. The error syndrome in these codes is the presence of a remainder when dividing the accepted QC by this polynomial. The description of cyclic codes and their construction are usually carried out using polynomials. Numbers binary code can be considered as the coefficients of a polynomial of the variable x.

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

Cyclic codes are block, uniform and linear. Compared to conventional linear codes, an additional restriction is imposed on the allowed QCs of a cyclic code: divisibility without 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). Just as in conventional linear codes, the type of syndrome in cyclic codes depends on the location 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 CC, the number of different residues will also be equal to 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 dividing 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 verification elements in the resulting CC will be the last r elements, and the rest will be 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 CC coming from the message source 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, the QC was obtained: 0100011

Answer: 0100011

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

Solution:

Error detection in cyclic code is done by dividing by the generating polynomial.

Decoder:

4. Calculate the probability of incorrect reception of the CC (error correction mode) under 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 without taking into account the synchronization error).

Solution:

If the code is used in error correction mode and the error correction factor is equal to t i.o. , then the probability of incorrectly taking CC is calculated:

It's good here. - probability of incorrect reception of a single element;

n is the length of the code combination;

t acting - frequency of corrected errors;

Multiplicity of corrected ones. errors t i.o is defined as, where d 0 is the code distance. For code (7.4) specified in problem No. 3, d 0 = 3 and t i.o. = 1, i.e. This code is capable of correcting one-time errors.

1) Calculation without taking into account synchronization error:

2) Calculation taking into account synchronization error:

If there is a synchronization error, the likelihood of incorrectly receiving the CC increases.

Answer: 0,0073; 0,123

3. PDS systems with feedback

3.1 Classification of OS systems

Depending on the purpose of the OS, systems are distinguished: with decisive feedback (DCF), information feedback (IFE) and with combined feedback (COS).

In systems with POC, the receiver, having received the CC and analyzed it for errors, makes the final decision to issue the combination to the information consumer or to erase it and send a signal through the reverse channel to retransmit this CC.

If the CC is received without errors, the receiver generates and sends a confirmation signal to the OS channel, upon receiving which the transmitter transmits the next CC. Thus, in systems with DFB, the active role belongs to the receiver, and the decision signals generated by it are transmitted via the reverse channel.

Block diagram PD systems with OS

PC per - forward channel transmitter, PC pr - forward channel receiver, OK per - reverse channel transmitter, OK pr - reverse channel receiver, RU - decision device

In systems with IOS, information about the CCs arriving at the receiver is transmitted via the reverse channel before their final processing and final decisions are made.

A special case of IOS is the 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 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 via the direct OS channel (receipt) is equal to the amount of information in the message transmitted via the forward channel, then the IOS is called complete. If the information contained in the receipt reflects only some of the characteristics of the message, then the IOS is called shortened.

The information (receipt) received via the OS channel is analyzed by the transmitter, and based on the results of the analysis, the transmitter makes a decision to transmit the next CC or to repeat previously transmitted ones. After this, the transmitter transmits service signals about the decision taken, and then the corresponding QCs.

In systems with a shortened IOS, there is less load on the reverse channel, but there is a greater likelihood of errors compared to a full IOS.

In systems with CBS, the decision to issue a 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 are also divided 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 (transmission of the combination is repeated until the receiver or transmitter decides to issue the combination to the consumer).

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

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

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

Currently, numerous algorithms for operating OS systems are known. The most common among them are:

Systems with waiting - after transmitting a CC, they either wait for a feedback signal or transmit the same CC, but the transmission of the next CC begins only after receiving confirmation of the previously transmitted combination.

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

3.2 Timing diagrams for systems with feedback and wait for a non-ideal return channel

If there is an error in the confirmation signal, an insertion occurs; if there is an error in the re-question signal, a dropout occurs.

1) QC from the message source;

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

3) CC received by the receiver via a direct channel;

4) s, transmitted via the reverse channel;

5) signal received via the reverse channel;

6) CC transferred to the recipient.

3.3 Calculation of system parameters with OS and standby

synchronization decoder pulse cyclic

1. Construct timing diagrams for a system with ROS-OZH (errors in the channel 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 DOS-COL system. Errors in the channel are independent Posh = (N/2)*10 -3 . Draw graphs of the dependence of R(R 1,R 2,R 3) on the length of the block. Find the optimal block length. If the waiting time t cool =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 length of a block in a 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 transmission speed using 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 expectation

R 3 - speed 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:

From the table and graph it is clear that the optimal block length is n=62, because at this value the maximum information transfer rate is achieved.

Answer: optimal block length n=62

4. Determine the probability of incorrect reception in a system with DOS-COL depending on the length of the block and construct a graph. Errors in the channel are considered independent. 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 and can be ignored.

Conclusion

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

The calculation results show that the synchronization error is influenced by edge distortions, and as the synchronization error increases, the probability of error increases.

The work also considered the construction of a cyclic code encoder and decoder and a PDS system with feedback.

From the calculations it is clear that in the presence of a synchronization error, the probability of incorrect reception of the CC increases.

One of the methods of dealing with errors may be the use of noise-resistant codes. For example, the cyclic code considered in this work.

References

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

2. Timchenko S.V., Shevnina I.E. Study of an element-by-element synchronization device with the addition and exclusion of data transmission system pulses: Workshop / State Educational Institution of Higher Professional Education "SibGUTI". - Novosibirsk, 2009. - 24 p.

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2.1. Course structure. Basic terms and definitions. Structure of the Unified Telecommunication Network (UTN) of the Russian Federation. Switching methods in data networks. Types of signals. Parameters of digital data signals.

2.2. Block diagram of a discrete message transmission system. Continuous channel and CBT. Edge distortion and fragmentation. Registration methods. Discrete channel. Channels with memory. Extended discrete channel and its parameters. Characteristics of SPDS.

2.3. Principles of effective coding. Huffman method. Dictionary methods ZLW.

2.4. Noise-resistant coding. Linear codes. Generating and checking matrices of a linear Hamming code. Coder. Decoder. Cyclic codes. Construction of the encoder and its operation. Decoder with error detection.

Algorithm for determining an erroneous discharge. Decoders with error correction. Reed-Solomon codec. Iterative and cascade codes. Convolutional codes. Construction of the encoder and its operation. State diagram and trellis diagram. Decoding using the Viterbi algorithm.

2.5. Adaptive systems. Systems with iOS. Systems with ROS-OZH. Calculation of reliability and speed of information transfer.

2.6. Methods for pairing a source of discrete messages with a discrete channel. DTE/DCE, RS-232, etc.

2.7. Synchronization. Types of element-by-element synchronization. Technical implementation. Calculation of synchronization parameters. Group, cyclic synchronization.

2.8. OOPS. Classification. Recoding. AM, FM, FM. Modulators and demodulators. Relative phase modulation. Multi-position phase and amplitude-phase modulation. DMT, Trellis modulation. Review of xDSL technology. OFDM. Radio modems, satellite modems.

2.9. Computer networks PD. Principles of construction. Classification. Purpose of LAN. LAN types. Network topologies. Basic transmission media in a LAN. Data transmission network technologies in operator networks. Corporate networks PD, VPN. Model of interaction of open systems. OSI and IEEE network models. Interactions between levels. Examples of protocols different levels. Protocol stacks. Methods of access to the transmission medium. Network architectures: Ethernet, Token Ring. LAN expansion devices. Repeater, bridge, switch, router, IP addressing.

Routing methods. Interaction of application processes via the TCP protocol. Gateways.

BASICS OF DISCRETE MESSAGES

Lecture No. 1.

Course structure. Basic terms and definitions.

Lectures 34 hours;

Practical classes 17 hours;

Laboratory work 17 hours.

Lecture topics:

1. Course structure. Basic terms and definitions;

2. Block diagram of the PDS system;

3. The principle of effective coding;

4. Noise-resistant coding;

5. Methods for pairing a source of discrete messages with a discrete channel;

6. Synchronization;

7. Signal conversion devices (SCD);

8. Adaptive systems;

9. Switching methods in the PDS network;

10. Computer data networks.

Documentary telecommunications– this is a type of telecommunication where a message can be displayed on any medium (paper, monitor screen).

Services:

Telegraph TGSOP;

Telephone;

Telex AT/Telex;

Facsimile SFS:

Fax server; networks

Datafax;

Transfer of newspaper strips to PGP;

Video text (email).

Telematic.

Methods for distributing information in PDS networks:

1. Channel switching;

2. Switching with accumulation:

Message switching;

Packet switching.

Circuit switching (CS) - establishing a connection, transmitting a message in both directions, destruction.

Channel switching:

Switching with accumulation. TFSOP:

УУ – Control device;

NU - Storage device;

OSD – External storage device.

The message is transmitted across sections of the network and stored in the management system. Consists of header and data. There is no establishment and release phase.

The title reads: The address of the management company is located. Recipient.

Message switching (MS) TSTN.

The header consists of seven levels. At each level, the message is processed and stored in external memory.

The main disadvantage of CS is that it is necessary to have a large memory, since messages of different lengths are transmitted.

Note: TsKS on a computer (TsKS - central com. message).

IN computer networks, telematic services (mail messages).

Packet switching:

The message is divided into packets. There is no NU. Message latency is reduced. High processing speed.

Applicable in:

Computer networks;

Ethernet: at layers 1 and 2 the header is saved, and then not;

TFSOP; SSPO

They use packet switching protocols.

NGN – Next Generation Network (packet network);

IP telephony.

The following protocols are used at the transport layer:

TCP (with the establishment of a virtual connection (virtual channel));

UDP – (connectionless (datagram mode)).

VVK – Temporary virtual switch (installed by the user).

PVC – Permanent temporary channel (set by the administrator).

In datagram mode, each packet is transmitted independently of each other. Used to transmit short messages.

The TCP protocol is more reliable.

Mixing bags– packets travel along different paths and appear at different times.

Lecture No. 2.

Block diagram of the PDS system.

Basically, the data transmission system uses packet switching.

All systems use discrete messages. For transmission of which discrete signals (two-level) are used.

e.e – single element.

Such a signal enters the communication channel; depending on the channel, conversion must be done. In the communication channel, the signal is affected by interference - external and internal. Therefore, noise-resistant coding is used.

Source DS (0:1) Communication channel (0:1) DS Receiver

In telegraph communications, noise-resistant coding is rarely used.

For telematic services and SPD – mandatory.

To transmit messages, in addition to noise-resistant coding, information compression methods are often used.

Block diagram of the diesel power station system:

IS – source of message, act. disc. communication, also called source encoder or data processing equipment.

RCD is an error protection device that adds check “r” bits to the “k” information bits, also called a channel encoder.

SCD - signal conversion device - converts the signal into a form suitable for transmission to the communication channel.

RCD and UPS are combined into APD - data transmission equipment.

PS – message receiver.

DC – discrete channel.

Efficiency – data transmission channel.

MKT-2 is used as the primary code (n=5, ).

On long-distance communication – MKT-5 (SKPD) =128.

Primary codes cannot detect and correct errors.

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

Figure 1.3. Block diagram of the PDS system

Legend:

IPS – source-receiver of messages;

OU – terminal device;

UVV – input/output device;

US – matching device;

RCD – error protection device;

UPS – signal conversion device;

DKD – data channel termination equipment;

DTE – data terminal equipment;

ADF – data transmission equipment;

AP – subscriber point.

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

As source-receiver of the message The IPS can be any input/output device, for example, a terminal, display, telegraph apparatus, or PC. Typically, the IPS converts the characters of the primary alphabet into code combinations of the secondary alphabet. Coordination (pairing) device The control system ensures the coordination of the IPS with subsequent equipment, for example, the conversion of parallel code into serial code and vice versa. The constructive combination of IPS and US is called terminal equipment data OOD. The RCD error protection device is designed to increase the fidelity of the transmission of discrete messages, in most cases, using noise-resistant coding methods. Sometimes the RCD is included in the DTE, especially when implementing noise-immune coding in software. According to ITU-T recommendation X.92, the DTE is called DTE (Data Terminal Equipment) and is conventionally designated

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

The purpose of the DCE is to facilitate the transmission of messages between two or a large number DTE over a specific channel type. To do this, the DCE must provide, on the one hand, an interface with the DTE, and on the other hand, an interface with the transmission channel. In particular, the DCE performs the functions of a modulator and demodulator (modem) if a continuous (analog) communication channel is used. When using an E1/T1 or ISDN digital circuit, a channel/data service unit (CSU/DSU – Channel Service Unit/Data Service Unit) is used as the DCE.

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

The UPS together with the communication channel form discrete channel DK, i.e. a channel designed to transmit only discrete signals (digital data signals). There are 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 only isochronous signals. Synchronous channels include, in particular, channels formed by methods of time division of VRC 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 methods of frequency division of FDM channels.

The discrete channel in combination with the RCD is called data channel Efficiency In /1/ it is proposed to call this channel extended discrete channel RDK.

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