RU2584495C1 - Device for calculating factor of generalised polyadic error correction - Google Patents

Abstract

FIELD: computer engineering.

SUBSTANCE: invention relates to computer engineering, in particular to modular neurocomputing tools, and is designed to calculate coefficients of generalised polyadic system (OPS), represented in Galois fields GF(2^v). Device comprises a two-layer neural network, each layer of which includes 15 neurons, memory unit 7 and corrective modulo two adders.

EFFECT: technical result is to enable error correction coefficients in OPS, which were obtained from code combination presented in polynomial residue class system (PSKV).

1 cl, 1 dwg, 4 tbl

Description

The invention relates to computing, in particular to modular neurocomputer means, and is intended to calculate the coefficients of the generalized polyadic system (OPS) presented in the Galois fields GF (2 ^ν ).

A neural network is known for calculating the coefficients of a generalized polyadic system (OPS) represented in the extended Galois fields GF (2 ^ν ) ([1] Kalmykov IA, Lobodin MV, Aleksishin EV, Schelkunova Yu.O. A neural network for calculating the coefficients of a generalized polyadic system presented in the extended Galois fields // Patent of the Russian Federation No. 2258956, G06N 3/04), containing two layers of 15 neurons each, while the first layer of 15 neurons is connected to the corresponding inputs of 15 neurons of the second layer .

The disadvantage of this device is the inability to perform the procedure for correcting errors that occur during the operation of a computing device.

The main objective is to expand the functionality that will allow the neural network to correct errors.

The technical result achieved in the implementation of the claimed invention is the expansion of functionality that allows you to correct errors in the coefficients of OPS, which were obtained from the code combination presented in the polynomial system of classes of deductions (PSCV).

The specified technical result is achieved by introducing a memory unit and 7 correcting adders modulo two, with the help of which error correction takes place.

In the polynomial system of residue classes, the minimum polynomials p _i (z), i = 1, 2, ..., n, defined in the extended Galois fields GF (2 ^ν ) are used as the base of the system. Then any polynomial A (z) satisfying the condition

- полный диапазон, можно представить в виде n-мерного вектораwhere degA (z) is the degree of the polynomial A (z);

- full range, can be represented as an n-dimensional vector

i=1, 2, …, n.Where

i = 1, 2, ..., n.

Using the PSKV codes, the operation of addition, subtraction, and multiplication of two operands represented in the polynomial form A (z) and B (z) can be reduced to performing these operations on the corresponding residues α _i (z) and β _i (z). Moreover, in PSKV these operations are performed independently for each of the modules p _i (z), which indicates the parallelism of this algebraic system. Moreover, due to the parallelism of the algebraic system, calculations can be implemented using neural networks ([2] - Kalmykov I.A., Voronkin R.A., Rezenkov D.N., Emarlukova Y.V., Falko A.A. Genetic algorithms in digital signal processing systems // Neurocomputers: development and application. - 2011. - No. 5. - P. 20-27).

расширенного поля Галуа GF(p^v) на два непересекающихся подмножества.In addition, the peculiarity of PSKV is that the independence of information processing on the basis of PSKV allows not only to increase the speed and accuracy of processing, but also to ensure the detection and correction of errors during the operation of the computing device of the residue class. If restrictions are imposed on the range of possible changes in the coded set of polynomials, that is, choose k from n bases of PSCW (k <n), then this will allow splitting the full range

the extended Galois field GF (p ^v ) into two disjoint subsets.

The first subset is called the working range and is determined by the expression

A polynomial A (z) with coefficients from the field GF (p) will be considered allowed if and only if it is an element of the zero interval of the full range P _full (z), that is, it belongs to the working range degA (z) <degP _slave ( z).

The second subset of GF (p ^v ) defined by the product r = nk of the control bases

sets the combination of prohibited combinations. If A (z) is an element of the second subset, then this combination is considered to contain an error. Thus, the location of the polynomial A (z) with respect to these two subsets allows us to unambiguously determine whether the code combination A (z) = (α ₁ (z), α ₂ (z), ..., α _{k + r} (z)) is allowed or contains erroneous symbols ([3] Kalmykov IA, Sarkisov AB, Yakovleva EM, Kalmykov MI Modular systolic processor of digital signal processing with reconfigurable structure // Bulletin of the North Caucasus Federal University. - 2013. - No. 2 (35). - S. 30-35.)

In [1], a neural network is presented for transferring from the modular code of PSCW to a generalized polyadic system in which 5 irreducible polynomials p ₁ (z) = z + 1, p ₂ (z) = z ² + z + 1, p ₃ ( z) = z ⁴ + z ³ + z ² + z + 1, p ₄ (z) = z ⁴ + z ³ +1, p ₅ (z) = z ⁴ + z + 1. If we assume that the first three bases are informational, i.e. k = 3, then the working range will be determined according to (6) and is equal to

The remaining two bases p ₄ (z) = z ⁴ + z ³ +1 and p ₅ (z) = z ⁴ + z + 1 will be considered as control modules, with the help of which the search and correction of errors that occur in the PSKV codes will be performed.

In this case, any polynomial represented in the PSKV code whose degree will be less than seven, i.e. degA (z) <7, is allowed, and its code combination does not contain errors. Otherwise, the code combination contains errors.

The coefficients of the generalized polyadic system allow searching and correcting errors in the PSKV codes. For this example, the polynomial A (z) can be represented in a generalized polyadic system as

Where

The orthogonal bases of such a system are equal to:

B ₁ (z) = z ¹⁴ + z ¹³ + z ¹² + z ¹¹ + z ¹⁰ + z ⁹ + z ⁸ + z ⁷ + z ⁶ + z ⁵ + z ⁴ + z ³ + z ² + z + 1;

B ₂ (z) = z ¹⁴ + z ¹³ + z ¹¹ + z ¹⁰ + z ⁸ + z ⁷ + z ⁵ + z ⁴ + z ² + z;

₃ B (z) = z + z ^{14 13 12} + z + z + z ^{11 9} + z ⁸ + z ⁶ + z ⁷ + z ⁴ + z ³ + z ² + z;

B ₄ (z) = z ¹⁴ + z ¹³ + z ¹² + z ¹¹ + z ⁹ + z ⁷ + z ⁶ + z ³ ;

B ₅ (z) = z ¹² + z ⁹ + z ⁸ + z ⁶ + z ⁴ + z ³ + z ² + z.

We represent orthogonal bases in the form of OPS coefficients

According to the Chinese remainder theorem, the polynomial A (z) is defined as

- полный диапазон ПСКВ.Where

- full range of PSKV.

If we take their representations in the OPS as the orthogonal bases B _i (z), then by multiplying the remainders α _i (z) by the latter, we can obtain the OPS

- коэффициенты ОПС i-го ортогонального базиса с учетом переполнения (i-l)-го основания.Where $${\gamma }_{PeR}^i$$

- OPS coefficients of the i-th orthogonal basis, taking into account the overflow of the (il) -th base.

осуществляется помодульно и поразрядно, при этом учитывается превышение модуля p_i(z) как перенос в старший коэффициент ОПС a_i+1(z).Moreover, the multiplication of residues by the corresponding coefficients $${\gamma }_{PeR}^i(z)$$

is carried out modularly and bitwise, while the excess of the module p _i (z) is taken into account as a transfer to the senior OPS coefficient a _{i + 1} (z).

From the expression (8) it is clearly seen that if the polynomial A (z) presented in the PSKV does not contain an error, then its degree will not exceed the degree of the working range. Therefore, the values of the highest OPS coefficients should be zero, i.e. a ₄ (z) = 0 and a ₅ (z) = 0.

If the polynomial A ^* (z) presented in the PSKV contains an error, then its value will be determined as

- глубина ошибки по j-му основанию ПСКВ.Where $${\alpha }_j^{*}(z)$$

- the depth of the error on the j-th basis of PSKV.

As a result of this, the result of the erroneous code A ^* (z) when transferred to the positional code will be outside the working range P _paб (z). Consequently, the values of the highest OPS coefficients will not be zero. In this case, by the value of the senior coefficients of the FSA, one can unambiguously determine the location and depth of the error.

In order to carry out error correction, two additional layers of neurons were introduced in the combination of the PSCW code. The structure of the device is shown in figure 1. The device consists of a two-layer neural network (neurons 1-15 form the first layer, neurons 16-30 create the second layer), a memory unit 31, which has eight inputs 32-39 and seven outputs 40-46, seven two-input corrective adders 47-53.

первого основания. Нейроны 2, 3 предназначены для распределения нулевого $${\alpha }_2^0(z)$$

и первого $${\alpha }_2^1(z)$$

разрядов второго основания соответственно. Нейроны 4-7 используются для приема и распределения $${\alpha }_3^0(z)$$

, $${\alpha }_3^1(z)$$

, $${\alpha }_3^2(z)$$

, $${\alpha }_3^3(z)$$

разрядов третьего основания соответственно. Для перераспределения разрядов $${\alpha }_4^0(z)$$

, $${\alpha }_4^1(z)$$

, $${\alpha }_4^2(z)$$

, $${\alpha }_4^3(z)$$

четвертого основания p₄(z) используются нейроны 8, 9, 10, 11 соответственно. Нейроны 12, 13, 14, 15 применяются для приема разрядов $${\alpha }_5^0(z)$$

, $${\alpha }_5^1(z)$$

, $${\alpha }_5^2(z)$$

, $${\alpha }_5^3(z)$$

пятого основания p₅(z) соответственно.Consider a two-layer neural network, the structure of which coincides with the prototype [1]. Each layer contains 15 neurons. The input layer consists of 15 neurons distributed in accordance with the dimension of the discharge grids of the modules -1-2-4-4-4. These neurons branch the input vector (α ₁ (z), α ₂ (z), α ₃ (z), α ₄ (z), α ₅ (z)), presented in binary form. Moreover, neuron 1 is designed to distribute the zero discharge $${\alpha }_{\mathrm{one}}^0(z)$$

first foundation. Neurons 2, 3 are designed to distribute zero $${\mathrm{<figure-callout\; id="2"\; label="\alpha "\; filenames="00000086.png"\; state="\{\{state\}\}">\alpha </figure-callout>}}_2^0(z)$$

and first $${\alpha }_{}^{}$$$${}_2^{\mathrm{one}}(z)$$

discharges of the second base, respectively. Neurons 4-7 are used for reception and distribution $${\alpha }_{}^{}$$$${}_3^0(z)$$

, $${\mathrm{<figure-callout\; id="3"\; label="\alpha "\; filenames="00000086.png"\; state="\{\{state\}\}">\alpha </figure-callout>}}_3^{\mathrm{one}}(z)$$

, $${\mathrm{<figure-callout\; id="3"\; label="\alpha "\; filenames="00000086.png"\; state="\{\{state\}\}">\alpha </figure-callout>}}_3^2(z)$$

, $${\mathrm{<figure-callout\; id="3"\; label="\alpha "\; filenames="00000086.png"\; state="\{\{state\}\}">\alpha </figure-callout>}}_3^3(z)$$

discharges of the third base, respectively. To redistribute discharges $${\alpha }_{\mathrm{four}}^0(z)$$

, $${\alpha }_{\mathrm{four}}^{\mathrm{one}}(z)$$

, $${\alpha }_{\mathrm{four}}^2(z)$$

, $${\alpha }_{\mathrm{four}}^3(z)$$

the fourth base p ₄ (z) uses neurons 8, 9, 10, 11, respectively. Neurons 12, 13, 14, 15 are used to receive discharges $${\alpha }_5^0(z)$$

, $${\mathrm{<figure-callout\; id="5"\; label="\alpha "\; filenames="00000086.png"\; state="\{\{state\}\}">\alpha </figure-callout>}}_5^{\mathrm{one}}(z)$$

, $${\mathrm{<figure-callout\; id="5"\; label="\alpha "\; filenames="00000086.png"\; state="\{\{state\}\}">\alpha </figure-callout>}}_5^2(z)$$

, $${\mathrm{<figure-callout\; id="5"\; label="\alpha "\; filenames="00000086.png"\; state="\{\{state\}\}">\alpha </figure-callout>}}_5^3(z)$$

fifth base p ₅ (z), respectively.

The second layer of the neural network also contains 15 neurons distributed in accordance with the dimension of the discharge grids of coefficients (a _i (z), i = 1, 2, 3, 4, 5) of the OPS -1-2-4-4-4. Neurons 16-30 of the second layer perform the basic operation of summing modulo two values of the discharges coming from the outputs of the corresponding neurons of the first layer. Synaptic link weights are equal to one.

Neuron 16 is designed to receive data coming from the output of neuron 1 of the input layer. The output of neuron 16 corresponds to the zero discharge of the first OPS coefficient a ₁ (z).

,

разрядов второго коэффициента ОПС соответственно. Причем вход нейрона 17 подключен к выходу нейрона 3. Вход нейрона 18 подключен к выходу нейронов 1, 2, 3.Neurons 17, 18 calculate the zero and first

,

bits of the second coefficient of OPS, respectively. Moreover, the input of neuron 17 is connected to the output of neuron 3. The input of neuron 18 is connected to the output of neurons 1, 2, 3.

,

,

,

третьего коэффициента ОПС a₃(z) соответственно. Причем нейрон 19 подключен к выходам нейронов 2, 4 и 6 первого слоя. Нейрон 20 - к выходам нейронов 1, 4, 5, 6 и 7. Вход нейрона 21 - к выходам нейронов 2, 3, 4, 5 и 7. Вход нейрона 22 - к выходам нейронов 1, 2, 5.Neurons 19, 20, 21, 22 carry out the calculation of the zero, first, second and third digits

,

,

,

the third coefficient of OPS a ₃ (z), respectively. Moreover, the neuron 19 is connected to the outputs of the neurons 2, 4 and 6 of the first layer. Neuron 20 - to the outputs of neurons 1, 4, 5, 6 and 7. The input of neuron 21 - to the outputs of neurons 2, 3, 4, 5 and 7. The input of neuron 22 - to the outputs of neurons 1, 2, 5.

,

,

,

четвертого коэффициента ОПС a₄(z) соответственно. Причем входы нейрона 23 подключены к выходам нейронов 2, 4, 7, 10 первого слоя. Вход нейрона 24 - к выходам нейронов 2, 3, 5, 8, 11. Вход нейрона 25 - к выходам нейронов 3, 4, 6, 8, 9. Вход нейрона 26 - к выходам нейронов 1, 2, 3, 4, 5, 6, 9.Neurons 23, 24, 25, 26 carry out the calculation of the zero, first, second and third digits

,

,

,

fourth coefficient of OPS a ₄ (z), respectively. Moreover, the inputs of the neuron 23 are connected to the outputs of the neurons 2, 4, 7, 10 of the first layer. The input of neuron 24 is to the outputs of neurons 2, 3, 5, 8, 11. The input of neuron 25 is to the outputs of neurons 3, 4, 6, 8, 9. The input of neuron 26 is to the outputs of neurons 1, 2, 3, 4, 5 , 6, 9.

,

,

,

пятого коэффициента ОПС a₅(z) соответственно. Причем вход нейрона 27 подключен к выходам нейронов 5, 9, 11 и 15 первого слоя. Вход нейрона 28 - к выходам нейронов 1, 3, 5, 7, 8, 9, 11, 12, 15. Вход нейрона 29 - к выходам нейронов 1, 2, 4, 5, 6, 8, 9, 10, 13.Вход нейрона 30 - к выходам нейронов 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 14 первого слоя.Neurons 27, 28, 29, 30 calculate the zero, first, second and third bits

,

,

,

the fifth OPS coefficient a ₅ (z), respectively. Moreover, the input of neuron 27 is connected to the outputs of neurons 5, 9, 11 and 15 of the first layer. The input of neuron 28 is to the outputs of neurons 1, 3, 5, 7, 8, 9, 11, 12, 15. The input of neuron 29 is to the outputs of neurons 1, 2, 4, 5, 6, 8, 9, 10, 13. The input of neuron 30 is to the outputs of neurons 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 14 of the first layer.

четвертого коэффициента a₄(z), на второй вход 33 - первый разряд

коэффициента ОПС a₄(z), на третий вход 34 - второй разряд

коэффициента ОПС a₄(z), на четвертый вход 35 - третий разряд

коэффициента ОПС a₄(z). Значения нулевого, первого, второго и третьего разрядов

,

,

,

пятого коэффициента ОПС a₅(z) поступают соответственно на пятый 36, шестой 37, седьмой 38 и восьмой 39 входы блока памяти 31.The memory unit 31 has 8 inputs. The first input 32 is connected to the output of neuron 23. The second input 33 is connected to the output of neuron 24. The third input 34 is connected to the output of neuron 25. The fourth input 35 of the memory unit 31 is connected to the output of the neuron 26. The fifth input 36 of the memory unit 31 is connected to the output of the neuron 27 The sixth input 37 of the memory unit 31 is connected to the output of the neuron 28. The seventh input 38 of the memory unit 31 is connected to the output of the neuron 29. The eighth input 39 of the memory unit 31 is connected to the output of the neuron 30. Thus, the first input 32 of the memory unit 31 receives a value of zero discharge

the fourth coefficient a ₄ (z), at the second input 33 - the first discharge

OPS coefficient a ₄ (z), to the third input 34 - the second discharge

OPS coefficient a ₄ (z), at the fourth input 35 - the third digit

OPS coefficient a ₄ (z). Zero, first, second and third digits

,

,

,

of the fifth OPS coefficient a ₅ (z) are respectively supplied to the fifth 36, sixth 37, seventh 38 and eighth 39 inputs of the memory unit 31.

первого коэффициента ОПС a₁(z), а на второй вход - корректирующее значение

. В результате этого происходит исправление ошибки по нулевому разряду первого коэффициента а₁(z).The first input of the correcting adder 47 is connected to the output of the neuron 16, and the second input is connected to the first output 40 of the memory unit 31. Thus, a zero discharge is supplied to the first input of the correcting adder 47

the first OPS coefficient a ₁ (z), and at the second input, the correction value

. As a result of this, an error is corrected for the zero bit of the first coefficient a ₁ (z).

второго коэффициента ОПС a₂(z), а на второй вход - корректирующее значение

. В результате этого происходит исправление ошибки в данном разряде.The first input of the correcting adder 48 is connected to the output of the neuron 17, and the second input is connected to the second output 41 of the memory unit 31. Thus, a discharge is received at the first input of the correcting adder 48

the second OPS coefficient a ₂ (z), and at the second input, the correction value

. As a result of this, an error is corrected in this category.

второго коэффициента ОПС a₂(z), а на второй вход - корректирующее значение

. В результате этого происходит исправление ошибки в данном разряде.The first input of the correcting adder 49 is connected to the output of the neuron 18, and the second input is connected to the second output 42 of the memory unit 31. Thus, a discharge is received at the first input of the correcting adder 49

the second OPS coefficient a ₂ (z), and at the second input, the correction value

. As a result of this, an error is corrected in this category.

третьего коэффициента ОПС a₃(z), а на второй вход - корректирующее значение

. В результате этого происходит исправление ошибки в данном разряде.The first input of the correcting adder 50 is connected to the output of the neuron 19, and the second input is connected to the second output 43 of the memory unit 31. Thus, a discharge is received at the first input of the correcting adder 50

the third OPS coefficient a ₃ (z), and at the second input, the correction value

. As a result of this, an error is corrected in this category.

третьего коэффициента ОПС a₃(z), а на второй вход - корректирующее значение

. В результате этого происходит исправление ошибки в данном разряде.The first input of the correcting adder 51 is connected to the output of the neuron 20, and the second input is connected to the second output 44 of the memory unit 31. Thus, a discharge is received at the first input of the correcting adder 51

the third OPS coefficient a ₃ (z), and at the second input, the correction value

. As a result of this, an error is corrected in this category.

третьего коэффициента ОПС a₃(z), а на второй вход - корректирующее значение

. В результате этого происходит исправление ошибки в данном разряде.The first input of the correcting adder 52 is connected to the output of the neuron 21, and the second input is connected to the second output 45 of the memory unit 31. Thus, a discharge is received at the first input of the correcting adder 52

the third OPS coefficient a ₃ (z), and at the second input, the correction value

. As a result of this, an error is corrected in this category.

третьего коэффициента ОПС a₃(z), а на второй вход - корректирующее значение

. В результате этого происходит исправление ошибки в данном разряде.The first input of the correcting adder 53 is connected to the output of the neuron 22, and the second input is connected to the second output 46 of the memory unit 31. Thus, a discharge is received at the first input of the correcting adder 53

the third OPS coefficient a ₃ (z), and at the second input, the correction value

. As a result of this, an error is corrected in this category.

From the outputs of the correcting adders 47-53, which are the outputs of the device, the corrected values of the OPS coefficients a ₁ (z), a ₂ (z), a ₃ (z) are removed.

The memory unit 31 is designed to store correction constants, the value of which depends on the calculated values of the senior coefficients of the OPS. The dependence of the values of the highest OPS coefficients a ₄ (z) and a ₅ (z) on the location and depth of error in the PSCC code are given in table 1.

The relationship between the values of the leading coefficients a ₄ (z), a ₅ (z) and the correcting values of the OPS coefficients a ₁ (z), a ₂ (z), a ₃ (z) are given in table 2.

Consider the operation of the device.

Let a polynomial A (z) = z ⁶ + z ⁵ + z ⁴ + z + 1 be given, which belongs to the working range P _paб (z). Then its code in the PSKV has the form A (z) = (1, z + 1, z ³ + z ² + z + 1, z ³ + z ² + z, z ³ + z) and this code does not contain an error . We use expression (10) and calculate the OPS coefficients. Since the polynomial A (z) belongs to the working range, when transferring from PSKV to the generalized polyadic system, according to equality (8), there should be values of the highest OPS coefficients a ₄ (z) = 0 and a ₅ (z) = 0. As a result of the calculations, the following values were obtained:

a ₁ (z) = 1, a ₂ (z) = z + 1, a ₃ (z) = z ³ + z ² + z + 1, a ₄ (z) = 0, a ₅ (z) = 0.

This indicates that this code combination, presented in the PSKV, does not contain errors.

. Так как на его вход подается 3 единицы, то результат суммирования по модулю два (суммируем по столбцам) равен единице. Аналогичным образом вычисляются значения на выходах остальных нейронов второго слоя. Коэффициенты ОПС, полученные с помощью таблицы 3, совпали с вычисленными ранее.In the prototype [1], it was shown how it is possible to calculate the OPS coefficients using a two-layer direct distribution neural network. We use table 3, with which we show the operation of the first and second layers of the neural network. Consider receiving a signal at the output of neuron 18, which corresponds to the first bit of the second OPS coefficient

. Since 3 units are fed to its input, the result of summing modulo two (we sum over columns) is equal to one. Similarly, the values at the outputs of the remaining neurons of the second layer are calculated. The OPS coefficients obtained using table 3, coincided with those calculated previously.

Since the highest OPS coefficients are equal to zero, this indicates that the code combination of PSKV does not contain an error, and it does not need to be corrected. In this case, the inputs of the memory unit 31 receive zero signals from the outputs of the neurons 23-26 and 27-30, which correspond to the binary representation of the coefficients a ₄ (z) and a ₅ (z). As a result, the outputs 40-46 are also removed the result, which is fed to the correcting adders 47-53. In accordance with this, at the outputs of these correcting adders performing the summation operation modulo, the values of the OPS coefficients are a ₁ (z) = 1, a ₂ (z) = z + 1, a ₃ (z) = z ³ + z ² + z +1, which were obtained from the outputs of neurons 16-23 of the second layer, will remain without correction.

. В результате этого на вход нейронной сети поступает код ПСКВ A^*(z)=(0, z+1, z³+z²+z+1, z³+z²+z, z³+z²). На выходах нейронов 16-30 второго слоя получатся значения коэффициентов ОПС.Let an error occur in the first remainder of the PSKV code and its depth is $${\alpha }_{\mathrm{one}}^{*}(z)=\mathrm{one}$$

. As a result of this, the PSKV code A ^* (z) = (0, z + 1, z ³ + z ² + z + 1, z ³ + z ² + z, z ³ + z ² ) arrives at the input of the neural network. At the outputs of neurons 16-30 of the second layer, the values of the OPS coefficients are obtained.

and ₁ (z) = 0;

a ₂ (z) = 1;

a ₃ (z) = z ² +1;

a ₄ (z) = z ³ ;

a ₅ (z) = z ³ + z ² + z.

Work on a direct distribution neural network can be represented in table 4.

Since the values of the highest OPS coefficients are a ₄ (z) ≠ 0 and a ₅ (z) ≠ 0, this indicates that the code combination contains an error.

In accordance with the obtained values a ₄ (z) = z ³ and a ₅ (z) = z ³ + z ² + z, a single signal will be at the output of neurons 26, 28, 29 and 30 of the second layer. This signal from the outputs of neurons 26, 28, 29, 30 is fed to the fourth 35, sixth 37, seventh 38 and eighth 39 inputs of the memory unit 31, respectively.

As a result, the correcting values Δа ₁ (z) = 1, Δа ₂ (z) = z, Δa ₃ (z) = z ³ + z will be removed from the outputs of the memory unit 31, according to the data given in table 2. This means that the signals will appear respectively on the first 40, third 42, fifth 44 and seventh 46 outputs of the memory unit 31. Therefore, these signals will go to the second inputs of the first 47, third 49, fifth 51 and seventh 53 correcting adders.

As a result, at the output of the first 47 correcting adder, we obtain

The bug was fixed. Now, the corrected value of the first OPS coefficient is a ₁ (z) = 1.

At the output of the second 48 correcting adder we get a signal

At the output of the third 49 correcting adder we get a signal

An error has been fixed. Now, the corrected value of the first OPS coefficient is a ₂ (z) = z + 1.

At the output of the fourth 50 correcting adder we get a signal

The error in the discharge is fixed.

At the output of the fifth 51 correcting adder we get a signal

The error in the discharge is fixed.

At the output of the sixth 52 correcting adder we get a signal

The error in the discharge is fixed.

At the output of the seventh 53 correcting adder we get a signal

The bug is fixed. Now, the corrected value of the third OPS coefficient is a ₃ (z) = z ³ + z ² + z + 1.

Claims (1)

1. A device for calculating the coefficients of a generalized polyadic system with error correction contains a neural network that has a first layer of fifteen neurons that receives and distributes the input vector, presented in the form of residues α _i (z), i = 1, 2, ..., n , and the second layer of fifteen neurons that sum modulo p _i (z) the product of the residues by the corresponding values of the orthogonal bases represented in the generalized polyadic system, and the input of the first neuron of the second layer is connected to the output ohm of the first neuron of the first layer, the input of the second neuron of the second layer is connected to the output of the third neuron of the first layer, the input of the third neuron of the second layer is connected to the output of the first, second, third neurons of the first layer, the input of the fourth neuron of the second layer is connected to the outputs of the second, fourth, sixth neurons the first layer, the entrance of the fifth neuron of the second layer is connected to the outputs of the first, fourth, fifth, sixth, seventh neurons of the first layer, the entrance of the sixth neuron of the second layer is connected to the outputs of the second, third, fourth fifth, seventh neurons of the first layer, the input of the seventh neuron of the second layer is connected to the outputs of the first, second, fifth neurons of the first layer, the input of the eighth neuron of the second layer is connected to the outputs of the second, fourth, seventh, tenth neurons of the first layer, the input of the ninth neuron of the second layer is connected to the outputs of the second , the third, fifth, eighth, eleventh neurons of the first layer, the input of the tenth neuron of the second layer is connected to the outputs of the third, fourth, sixth, eighth, ninth neurons of the first layer, the input of the eleventh neuron of the second the layer is connected to the outputs of the first, second, third, fourth, fifth, sixth, ninth neurons of the first layer, the input of the twelfth neuron of the second layer is connected to the outputs of the fifth, ninth, eleventh, fifteenth neurons of the first layer, the input of the thirteenth neuron of the second layer is connected to the outputs of the first , third, fifth, seventh, eighth, ninth, eleventh, twelfth, fifteenth neurons of the first layer, the input of the fourteenth neuron of the second layer is connected to the outputs of the first, second, fourth, fifth, sixth, eighth, d the ninth, tenth, thirteenth neurons of the first layer, the input of the fifteenth neuron of the second layer is connected to the outputs of the first, second, third, fourth, fifth, sixth, seventh, eighth, ninth, tenth, eleventh, fourteenth neurons of the first layer, characterized in that it in addition, a memory block and seven correcting adders were introduced, while the memory block has eight inputs and seven outputs, the first input of the memory block is connected to the output of the eighth neuron of the second layer, the second input of the memory block is connected to the output of the ninth neuron of the second layer, the third input of the memory block is connected to the output of the tenth neuron of the second layer, the fourth input of the memory block is connected to the output of the eleventh neuron of the second layer, the fifth input of the memory block is connected to the output of the twelfth neuron of the second layer, the sixth input of the memory block is connected to the output of the thirteenth neuron of the second layer, the seventh input of the memory block is connected to the output of the fourteenth neuron of the second layer, the eighth input of the memory block is connected to the output of the fifteenth neuron of the second layer, while the first output of the memory block is connected n to the second input of the first correction adder, the first input of which is connected to the output of the first neuron of the second layer, the second output of the memory block is connected to the second input of the second correction adder, the first input of which is connected to the output of the second neuron of the second layer, the third output of the memory block is connected to the second input the third correcting adder, the first input of which is connected to the output of the third neuron of the second layer, the fourth output of the memory unit is connected to the second input of the fourth correcting adder, the first input of which is connected to the output of the fourth neuron of the second layer, the fifth output of the memory block is connected to the second input of the fifth correction adder, the first input of which is connected to the output of the fifth neuron of the second layer, the sixth output of the memory block is connected to the second input of the sixth correction adder, the first input of which is connected to the output of the sixth neuron of the second layer, the seventh output of the memory unit is connected to the second input of the seventh correcting adder, the first input of which is connected to the output of the seventh neuron of the second layer.

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