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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 allows for better use of 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 you to correctly separate one single element from another at reception 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 the capacity of the working channel by allocating 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 influences the Agricultural Generator 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 Agricultural Instrument. If they do not match, a corresponding pulse signal is generated. 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 AChI 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, the following parameters are usually set: synchronization error, transmission speed B, root mean square value of edge distortion, correcting ability of the receiver µ, synchronization time t c , synchronization maintenance time t p.s. Based on the specified parameters, the following are calculated: frequency of the generator f, permissible coefficient of instability of the generator k, capacity 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 synchronization 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 a certain order between the 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. The binary code digits can be thought of 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 of the PD system with OS
PC per - direct 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 made, and then the corresponding CC.
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 - transmit 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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The concept of a discrete message is more general than the concept of a data message or a telegraph message. Accordingly, the concept of a PDS system is more general. The block diagram of the PDS system is shown in Fig. 1 8 The source and recipient of messages, together with the message-to-signal converter, are not included in the PDS system
Symbols from the IS arrive in the form of code combinations, which consist of single elements (parcels). The code combination is characterized by the code base m and the number of single elements that make up the code combination (code length) reflecting the transmitted symbol
Rice. 1.8 Block diagram of the PDS system
The code base characterizes the possible number of distinguishable significant positions of the signal coming from the IC
In PDS technology, codes with base 2 are most widely used. Such codes are often called binary, or binary. The main reasons for the widespread use of binary codes are ease of implementation, reliability of binary logic elements, low sensitivity to external interference, etc. Therefore, in the future, in all cases (unless otherwise stated), binary codes are considered. An example of a binary code is the International Telegraph Code No. 2 (MTK-2), in which each transmitted symbol corresponds to a five-element code combination
Using five-element combinations, only 32 characters can be transmitted. Let us remember that the Russian alphabet consists of 32 letters, in addition, there are numbers and it is desirable to ensure the transmission of Latin letters, punctuation marks, etc. Therefore, in the MTK-2 code, the same five-element code combination is used up to 3 times depending on the mode transmission, which is defined by a so-called register. The MTK-2 code has three registers: Russian, Latin and digital. Before transmitting specific characters, the transmitter informs the receiver, using a special service sign, of the register in which the subsequent transmission will be carried out. Then, depending on the register, each five-element code combination received from the IC, can have one of three meanings. Thus, the combination 11101 in the Russian register means the letter Y, in digital - 1, in Latin - Q. This approach allows you to significantly expand the volume of transmitted symbols with the same number of elements in the code combination (in the considered example, through the use of three registers, the number of different transmitted characters increases approximately 3 times)
The character set provided by the MTK-2 code is sufficient for writing telegrams, and in some cases even for transmitting data. As a rule, more characters are required to transmit data. In this regard, the seven-element MTK-5 code was developed, recommended by the CCITT. It was called the standard data transmission code (SDTC). The code has two registers
MTK-2 and MTK-5 codes in the PDS technique are called primary codes
The message coming from the IS in some cases contains redundancy. The latter is due to the fact that the characters that make up the message can be statistically related. This allows part of the message not to be transmitted, restoring it upon reception via a known static connection
By the way, this is what they do when transmitting telegrams, excluding conjunctions, prepositions, and punctuation marks from the text, since they are easily restored when reading a telegram based on known rules for constructing phrases and words. Of course, redundancy in the received telegram makes it easy to correct some of the distorted words (to read them correctly). However, redundancy results in fewer messages being transmitted in a given period of time and, therefore, less efficient use of the PDS channel. The task of eliminating redundancy in transmission in the PDS system is performed by the source encoder, and the restoration of the received message is performed by the source decoder. Often the source encoder and decoder are included in the IC and PS. The issues of eliminating redundancy are discussed in more detail in Chap. 5.
In order to increase transmission fidelity, redundant coding is used, which allows errors to be detected or even corrected during reception. During the encoding process carried out by the channel encoder, the original code combination is transformed and redundancy is introduced into it. At the receiving end, the channel decoder performs the inverse transformation (decoding), as a result of which we obtain a combination of the source code. Often the channel encoder and decoder are called error protection devices (ECDs).
In order to match the encoder and decoder of the channel with a continuous communication channel (the medium in which continuous signals are usually transmitted), signal conversion devices (SCDs) are used, which are switched on during transmission and reception. In a particular case, it is a modulator and demodulator. Together with the communication channel, the UPS forms a discrete channel, i.e., a channel designed to transmit only discrete signals (digital data signals).
There are synchronous and asynchronous daytime channels. In synchronous discrete channels, each unit element is introduced at strictly defined points in time. These channels are designed to transmit isochronous signals only. Any signals can be transmitted over an asynchronous channel - isochronous, anisochronous. Therefore, such channels are called transparent, or code-independent. Synchronous channels are opaque, or code-sensitive.
A discrete channel in combination with a channel encoder and decoder (CDC) is called an extended channel (EDC). If, in relation to a discrete channel, the transmission of single elements is considered, taking the value “0” or “1” and the alphabet of the “source” operating on a discrete channel can be considered equal to 2, then in relation to the DKK, the transmission of code combinations with the length of elements is considered and when using a binary code the number of possible combinations is equal to .
Therefore, the alphabet of the “source” running on the RDK can be considered equal to , hence the name “extended”. In data communication technology, a DDC is called a data transmission channel.
A discrete channel is characterized by the speed of information transmission, measured in bits per second (bps). Another characteristic of a discrete channel is the telegraph speed B, measured in baud. It is determined by the number of units transmitted per second. In PD technology, instead of the term telegraph speed, the term modulation speed is used.
Example 1 1. Let's calculate the speed of telegraphy B and information transmission R in a discrete channel. Duration of a single element: each information element carries 1 bit of information and let there be one verification bit for every seven information elements.
Telegraph speed and therefore Baud. The speed of information transfer will be determined by the number of information elements transmitted per second, i.e.
When determining the effective speed, it is taken into account that not all combinations arriving at the input of the PD channel are issued to the recipient. Some combinations may be rejected. In addition, it is taken into account that not all elements transmitted to the channel carry information (see Chapter 8).
Another characteristic of a discrete channel is the fidelity of transmission of single elements. It is determined through the error rate for elements
i.e., the ratio of the number of erroneously received elements to the total number of transmitted Lgtrans during the analysis interval.
To characterize the PD channel, the following parameters are used - the error rate for code combinations and the effective information transmission rate. The error rate for code combinations characterizes the accuracy of transmission and is determined by the ratio of the number of erroneously received code combinations to the number of transmitted ones in a given time interval.
Synchronization is a procedure for establishing and maintaining certain time relationships between two or more processes.
There are element-by-element, group and cyclic synchronization.
With element-by-element synchronization, the required phase relationships are established and maintained between the significant moments of transmitted and received unit elements of digital data signals. Element-by-element synchronization allows you to correctly separate one single element from another at reception and provide the best conditions for its registration.
Group synchronization - ensures correct division of the received sequence into code combinations.
Cycle synchronization - ensures proper separation of time-combining cycles.
Timing devices with adding and subtracting pulses
The device belongs to the class without direct influence on the generator frequency and is 3-position.
When the synchronization system is running, three cases are possible:
The generator pulses pass unchanged to the input of the frequency divider.
1 pulse is added to the pulse sequence.
1 pulse is subtracted from the pulse sequence.
The master oscillator produces a relatively high-frequency pulse sequence. This sequence passes through a divider with a given division coefficient. Clock pulses from the output of the divider ensure the operation of the transmission system blocks and also enter the phase discriminator for setting.
The phase discriminator determines the sign of the phase discrepancy between the CM and TI of the master oscillator.
If the receiving frequency is greater, the PD generates a pulse subtraction signal for the UDVI, through which the passage of one pulse is prohibited.
If the receiving frequency is lower, then the pulse is added.
As a result, the clock sequence at the output D k is shifted by.
The following figure illustrates the change in clock position as a result of adding and subtracting pulses.
TI2 - as a result of addition, TI3 - as a result of subtraction.
Role of the up/down counter:
In a real situation, the received elements have edge distortions that randomly change the position of significant moments in different directions from the ideal SM. This may cause false timing adjustments.
Under the influence of CI, shifts of the CM both towards the advance and towards the lag are equally probable.
When the CM is displaced due to the fault of the synchronization device, the phase is stably shifted in one direction.
Therefore, to reduce the influence of the CI on the synchronization error, a reverse capacitance counter S is installed. If S signals to add a pulse arrive in a row, indicating that the receiving generator is lagging, then the pulse will be added and the next TI will appear earlier.
If the S-1 signal about advance comes first, then the S-1 signal about lag, then there will be no addition or subtraction.
Introduction 3 1. Synchronization in PDS systems 4 1.1 Classification of synchronization systems 4 1.2 Element-by-element synchronization with the addition and subtraction of pulses (operation principle). 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 an encoder and decoder of a cyclic code. Formation of a cyclic code combination 22 3 PDS systems with feedback 28 3.1 Classification of systems with OS 28 3.2 Timing diagrams for systems with feedback and waiting for a non-ideal reverse channel 30 Conclusion 32 References 33
Introduction
The problem of transmitting information over significant distances in the shortest possible time and with fewer 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, as well as disadvantages. Devices for transmitting discrete messages currently play a significant role in the life of human society. Their widespread use allows for better use of computing technology through the organization of computer networks and data networks. It is no longer possible to imagine modern society without the achievements made in the field of discrete message transmission technology over a little over a hundred years of development. The PDS technique used makes it possible to create powerful computer networks and data transmission networks. The relevance of this work lies in the fact that the continuously growing need for transmitting information flows over long distances is one of the distinctive features of our time. In addition, almost no organization can function without PDS technology; without it, it is impossible to organize corporate computer networks, which can significantly reduce the time for information exchange between departments. The purpose and objectives of the course work are to consider theoretical issues of synchronization and coding in PDS systems, consideration of PDS systems with OS feedback, 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, gating methods, synchronization in PDS systems, coding, PDS systems with OS, as well as the effect of errors on the speed of information transfer were studied. All tasks were completed in accordance with the methodological instructions. 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. Under conditions of strong signal distortion, the communication channel will contain errors during registration; as the synchronization error increases, the number of errors will also increase. An increase in the number of errors leads to a decrease in transmission speed. To detect and correct errors, error-correcting coding is used, which also reduces the transmission speed. The use of efficient coding, which eliminates message redundancy, makes it possible to reduce the average number of elements per message and thereby increase the transmission speed.
References
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