RU2301442C2 - Neuron network for finding, localizing and correcting errors in residual classes system - Google Patents

Abstract

FIELD: computer engineering, possible use in modular neuro-computer systems.

SUBSTANCE: in accordance to invention, neuron network contains input layer, neuron nets of finite ring for determining errors syndrome, memory block for storing constants, neuron nets for computing correct result and OR element for determining whether an error is present.

EFFECT: increased error correction speed, decreased amount of equipment, expanded functional capabilities.

1 dwg, 3 tbl

Description

The invention relates to computer technology and can be used in modular neurocomputer systems.

A device is known for monitoring and correcting errors in redundant modular code (patent No. 2022472, class Н03М 13/00, RU, 1999), consisting of an input code converter, an output converter, a block of a group of comparison elements, a block of a group of elements OR, a block of elements AND .

However, this device has the following disadvantages:

low speed, high hardware costs and low functionality, since the device uses one redundant module, error correction is carried out by a large module equal to the range of control numbers.

The closest in technical essence to the claimed device is a device for detecting and correcting errors in the system of residual classes (AS No. 714399, G06F 11/08, 1980), containing two units of modular convolution, and the first output of the register is connected to the input of the first and the second blocks of modular convolution and with the first input of the third adder, the outputs of the first and second blocks of modular convolution are connected respectively to the first inputs of the first and second adders, the second and third outputs of the register are connected respectively to the second input said first and second adders and the second and third inputs of the third adder, the output of the storage unit is coupled to a fourth input of the third adder whose output is an output device.

A disadvantage of the known device is the complexity, which is explained by the presence of two blocks of modular convolution, low speed, which is proportional to the number of modules of the system of residual classes and small functionality.

The aim of the present invention is to simplify the device, improve performance and expand the functionality.

This goal is achieved in that the device contains a neural network 8, consisting of neural networks of the final ring 4, 5 and 6 and neural networks of the final ring 27, 28, which form the residuals of the control modules of the system of residual classes, the outputs 9 of which are connected to the first inputs of the neural networks of the final ring 10, 11 computing the error syndrome, the second inputs of which are connected to the outputs of the neurons 23 of the redundant modules α _{n + 1} and α _{n + 2} , the outputs of the neural networks of the final ring 10, 11, buses 12 and 13 are connected to the inputs of the memory unit 14 for choosing from n its error constants, outputs 15, which are received on the buses 16, 17 and 18, which determine the number of the faulty module (channel), and on the input of the OR element 19, the output 20 of which determines the presence of an error, in addition, the outputs of the memory unit 14 are fed to the first inputs neural networks of the final ring 21, and the second inputs of which receive the remains of the wrong number α ₁ , α ₂ , ..., α _n . The corrected number from the outputs of the neural networks of the final ring 21 goes to the outputs 22 of the device.

Consider the error correction method.

Let a controlled number A = (α ₁ , α ₂ , ..., α _n , α _{n + 1} , α _{n + 2} ) be given, where

α _i = Amodp _i ∀i = 1, 2, ..., n + 2, p ₁ , p ₂ , ..., p _n , p _{n + 1} , p _{n + 2} are the bases of RNS with two excess bases p _{n + 1} , p _{n + 2} .

The principle of detecting, localizing and correcting errors is based on the functional integration of all three operations into one operation. This method is based on the determination of figures on excess grounds on the basis of figures on working grounds and comparing them with the originally known figures on excess bases. If the calculated digits α ' _{n + 1} and α' _{n + 2} in the control digits are equal to the initial digits α _{n + 1} and α _{n + 2 of} these digits, then there is no error; if they are not equal, then it is necessary to determine the error syndrome equal to the difference between these digits δ ₁ = (α _{n + 1} -α ' _{n + 1} ) mod p _{n + 1} and δ ₂ = (α _{n + 2} -α' _{n + 2} ) mod p _{n + 2} , the values of which determine the error constant. Next, summing the error constant with the wrong number, which is selected in such a way that the implicit place of the error in the number is eliminated. To localize the error, it is necessary to compare bitwise the corrected number with the erroneous one, and if α _i -α _i '≠ 0, an erroneous discharge is determined. The stated method allows you to detect, localize and correct the error through one of the information channels.

We calculate α ' _{n + 1} and α' _{n + 2} based on the base system extension method, which is based on the use of the Chinese remainder theorem and a generalized positional number system. We first consider an extension to one base, and then generalize the extension to two bases.

Расширим систему оснований, добавляя основание р_n+1, тогда диапазон системы станет P_n+1=p_n+1·P, ортогональные базисы системы

их веса

причем

Задача состоит в определении цифры α_n+1 числа А по основанию р_n+1.Let a base system p ₁ , p ₂ , ..., p _{n be given} with a range P = p ₁ · p ₂ · ... · p _n , orthogonal bases B ₁ , B ₂ , ..., B _n , whose weights m ₁ , m ₂ , ..., m _n and are determined from comparison

We expand the base system by adding the base p _{n + 1} , then the range of the system becomes P _{n + 1} = p _{n + 1} · P, orthogonal bases of the system

their weight

moreover

The task is to determine the numbers α _{n + 1 of the} number A on the basis of p _{n + 1} .

Then the number A in the base system p ₁ , p ₂ , ..., p _n , p _{n + 1} will have the form

- диапазон расширенной системы оснований;Where

- range of extended base systems;

- ортогональные базисы расширенной системы оснований.

- orthogonal bases of the extended base system.

в обобщенной позиционной системе счисления, тогдаWe represent orthogonal bases

in a generalized positional number system, then

- коэффициенты ОПСС;Where

- OPSS coefficients;

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

Based on (2), we write expression (1) in the form

From the expression (3), we can determine the coefficients α _{i of the} number A, then

where α _i are the residues of the number A with respect to mod p _i ;

- ортогональные базисы, представленные в ОПСС.

- orthogonal bases presented in the OPSS.

и переносом, генерируемым при формировании α_i-1. Перенос генерируется как число раз, когда сумма цифр в ОПСС переполняется по модулю p_i. Этот перенос используется для формирования цифр α_i+1. Последний перенос, генерируемый при получении последней цифры числа в ОПСС, отбрасывается. Предлагаемый метод выполняется в параллельном режиме. Выигрыш в быстродействии данного метода с итеративным методом очевиден, поскольку он уменьшает время преобразования с 2(n+1) циклов синхронизации до трех циклов.The numbers α _i in the OPSS representation are obtained by summing modulo p _i all the products

and the transfer generated by the formation of α _i-1 . The transfer is generated as the number of times when the sum of the digits in the OPSS is overflow modulo p _i . This transfer is used to form the numbers α _{i + 1} . The last transfer generated when the last digit of the number is received in the OPSS is discarded. The proposed method is executed in parallel. The speed gain of this method with the iterative method is obvious, since it reduces the conversion time from 2 (n + 1) synchronization cycles to three cycles.

принимают значения от 0 до p_i-1, причем

являются константами, поэтому произведение α_i

можно поместить в ПЗУ или в весовые коэффициенты связей между нейронами. Адресами произведений α_i

являются вычеты α_i числа А по модулю p_i.The numbers α _i ,

take values from 0 to p _i-1 , and

are constants; therefore, the product α _i

can be placed in ROM or in weights of connections between neurons. The addresses of the works α _i

are the residues α _{i of the} number A modulo p _i .

Example 1. Let p ₁ = 2, p ₂ = 3, p ₃ = 5, p ₄ = 7, P _{n + 1} = 2 · 3 · 5 · 7 = 210, B ₁ = 105, B ₂ = 70, B ₃ = 126, B ₄ = 120.

:Then, on the basis of (2), we define

:

Consider converting a number from JUICE to OPSS.

:Let A = 11 = (1, 2, 1, 4). Then in the ROM we put the values α _i ,

:

The conversion of the number A from RNS to OPSS has the form

When adding the numbers for each module, taking into account the transfer, we get the number A, presented in the OPS as A = [1,2,1,0].

Добавим к числу оснований СОК новое основание p_n+1. Объем диапазона этой системы

Тогда любое число А из диапазона [0, Р_n+1] в обобщенной позиционной системе счисления можно представить в видеConsider the method of determining the deduction on an extended basis. Let the RNS consists of the bases p ₁ , p ₂ , ..., p _n. The range of this system will be

Add to the number of SOK bases a new base p _{n + 1} . Range of this system

Then any number A from the range [0, P _{n + 1} ] in the generalized positional number system can be represented as

If the number A will lie in the original range [0; P], then in OPSS the figure is α _{n + 1} = 0. If α _{n + 1} ≠ 0, then the value of the number A goes beyond the dynamic range. The fact that α _{n + 1} = 0 is used to obtain the remainder (deduction) from dividing the number A by a new base SOCr _{n + 1} .

в системе оснований p₁, р₂,..., р_n, p_n+1, где

- остаток от деления числа А на р_n+1, т.е. искомая цифра по новому основанию.Let the number A have a representation (α ₁ , α ₂ , ..., α _n ) on the bases p ₁ , p ₂ , ..., p _n. Add a new base p _{n + 1} , then the number

in the base system p ₁ , p ₂ , ..., p _n , p _{n + 1} , where

- the remainder of dividing the number A by p _{n + 1} , i.e. the desired number on a new basis.

в проводимые операции. При этом мы параллельно получим цифры ОПСС α₁, α₂,...,α_n и выражение для цифры α_n+1. Но так как по условию число А∈[0;P], то цифра α_n+1=0.To determine this figure, we use the method of converting a number from RNS to OPSS, including an unknown figure

in ongoing operations. At the same time, we obtain in parallel the numbers OPSS α ₁ , α ₂ , ..., α _n and the expression for the number α _{n + 1} . But since, by hypothesis, the number is A∈ [0; P], the digit α _{n + 1} = 0.

From the obtained ratio and determine the desired figure

Example 2. Let a system of modules p ₁ = 2, p ₂ = 3, p ₃ = 5 be given, then P = 2 · 3 · 5 = 30. And let the number A = 11 = (1, 2, 1) be given. We expand the base system by adding p ₄ = 7. Then A = 11 = (1, 2, 1, | A | ₇ ) in the base system p ₁ = 2, p ₂ = 3, p ₃ = 5, p ₄ = 7.

The set of constants b _{ij is} given in (5) and is given by the matrix

The process of solving the problem is shown in table 1.

Table 1 The deductions of the number A modulo p _i Modules p ₁ = 2 p ₂ = 3 p ₃ = 5 p ₄ = 7 one one one 2 3 2 0 four 2 four one 0 0 one four | A | ₇ 0 0 0 4 · | x | ₇ OPSS coefficients of the number A one 2 one 5 + 4 · | x | ₇

. Мультипликативная обратная величина

, и так как число 5 отрицательное, возьмем его дополнение по модулю 7. Итак, вычет числа А по модулю 7 определяется выражением |А|₇=2·(7-5)=4.After adding the numbers modulo p _i we get A = [1, 2, 1, 5 + 4 | A | ₇ ], but since α ₄ = | 5 + 4 · | A | ₇ | ₇ , but by hypothesis α ₄ = 0, i.e. 4 · | A | ₇ = -5 or

. Multiplicative Inverse

, and since the number 5 is negative, we take its complement modulo 7. So, the residue of the number A modulo 7 is determined by the expression | A | ₇ = 2 · (7-5) = 4.

Then the extended representation of the number will be A = 11 = (1, 2, 1, 4). Since the result of the formation of a digit in the RNS on a new basis, p _{n + 1,} depends only on information bits, the operation to expand the residues can be carried out immediately on several additionally entered bases.

Example 3. Let a system of bases (modules) of RNS be given p ₁ = 2, p ₂ = 3, p ₃ = 5. We expand the base system by adding p ₄ = 7, p ₅ = 11. Then another column and one row are added to expression (5), namely

Let the number A = 17 = (l, 2,2, | A | ₇ , | A | ₁₁ ) be given, it is necessary to find the residues from the bases p ₄ = 7, p ₅ = 11.

The decision process is shown in table 2.

table 2 The deductions of the number A modulo p _i Modules p ₁ = 2 p ₂ = 3 p ₃ = 5 p ₄ = 7 p ₅ = 11 one one one 2 3 5 2 0 four 2 four fourteen 3 0 0 2 8 four

0 0 0 4 | A | ₇ -

0 0 0 - 7 | A | _eleven OPSS coefficients of the number A α ₁ = 1 α ₂ = 2 α ₃ = 2 α ₄ = 2 + 4 | A | ₇ α ₅ = 2 + 7 | A | _eleven

After adding the numbers modulo p _i we get

A = [1,2,2,2 + 4 | A | ₇ , 2 + 7 | A | ₁₁ ]

but since α ₄ = 2 + 4 | A | ₇ , and α ₅ = 2 + 7 | A | ₁₁ , and by hypothesis α ₄ = 0 and α ₅ = 0, then

Multiplicative Values

Since | A | ₇ = -4, and | A | ₁₁ = -5 take their complement, i.e. | A | ₇ = 7-4 = 3, and | A | ₁₁ = 11-5 = 6.

Then the expanded representation of the number will be equal to the information number, i.e. A = (1,2,2,3,6) ₁₁ , and this suggests that the number A is faultless.

The advantages of the proposed method of expanding the system of deductions is that:

- all calculations are performed in parallel channels on separate modules, and each module is identified with a separate channel;

и мультипликативных величин по расширенным основаниям;- calculation of a large number of additional quantities is not required, only the presence of constants is necessary

and multiplicative values on extended grounds;

- it is possible to obtain an extended representation of the deductions of the number at once for several additional reasons, which does not affect the performance of the entire expansion operation.

We apply this method to detect, localize, and correct errors.

Error correction in RNS is based on the representation of numbers in an extended system. As the extended bases we take excessive (control) bases. Suppose, in the process of processing and storing data in a computer system, the residual numbers on redundant bases, on the one hand, are absolutely correct, and on the other hand, they are calculated on the basis of balances on non-redundant (informational) bases, immediately before data control. If the calculated excess residuals are equal to the initial ones, then an error in the information bases did not occur; otherwise, an error occurred in the information grounds. Based on this information, the error is eliminated and the faulty module is determined.

The introduced restriction on the absolute fidelity of the redundant bases is ensured by the absolute reliability of the channels with respect to the redundant modules, which can be provided by known structural technologies (for example, using conventional correcting codes or a majority scheme).

Example 4. The initial data are the same as in example 3.

будет иметь вид

=(1,2,3,3,6).Suppose an error occurred on a third information basis, then an erroneous number

will have the form

= (1,2,3,3,6).

Excessive digits on the fourth and fifth bases are 3 and 6, respectively, and they are absolutely true.

Based on the information residuals, we define the error syndrome δ.

The method for detecting, correcting and localizing errors in the RNC is as follows.

The controlled number α ₁ , α ₂ , ..., α _n , α _{n + 1} , α _{n + 2} is divided into two parts: information, which includes balances on information grounds α ₁ , α ₂ , ..., α _n , and the control part, which includes the residues on the excess (control) bases α _{n + 1} , α _{n + 2} .

Further, according to the remnants of information channels, we determine the residuals on excessive grounds. We use table 2, then the third row will have the form not [0, 0, 2, 8, 4], but [0, 0, 3, 12, 6].

When performing the operation according to table 2 we get

From here

Using the residuals found, we determine the error syndrome:

By the values of δ ₁ , δ ₂ , error constants are formed in such a way that when they are added to the information bits of the controlled number A, the error in the number that is eliminated is eliminated. Note that if the controlled number does not contain errors, then the values of δ ₁ and δ ₂ are equal to zero.

To localize the error, it is necessary to compare the digits of the initial number with the corrected number, and by the category where the comparison is not performed, an erroneous digit is determined.

Define the error constants for this example and summarize them in table 3.

Table 3
Error constants for RNS with bases p ₁ = 2, p ₂ = 3, p ₃ = 5, p ₄ = 7, p ₅ = 11 Error on the base p ₁ δ ₁ , δ ₂ Error on the base p ₂ δ ₁ , δ ₂ Base error p ₃ δ ₁ , δ ₂ 0,0,0 0,0 0,0,0 0,0 0,0,0 0,0 1,0,0 6.7
1.4 0,1,0 1,2
3.10 0,0,1 4.9
6.6 0,0,2 3.4
5.1 0.2.0 4.1
6.9 0,0,3 4.7
2.10 0,0,4 1,5
3.2

In accordance with δ ₁ = 1, δ ₂ = 5 of Table 2, the error value (0,0,4) is determined, which is added to the controlled number

By the magnitude of the error (0,0,4) the erroneous discharge is localized, it will be the discharge according to modp ₃ . Using the error syndrome allows you to combine all the procedures for detecting, localizing and correcting errors in one procedure, which allows to reduce the time of error correction and increase efficiency.

The drawing shows a neural network for detecting, localizing and correcting errors in the system of residual classes. The neural network consists of an input layer of neurons 2, 23, an input layer 24, designed to store the remainder of the number on the working and control grounds during the time the error is detected, the input of which is connected to inputs 1 (α ₁ , α ₂ , ..., α _n ) and the inputs of 25 (α _{n + 1} , α _{n + 2} ) neural networks; neural network 8, designed to calculate the remains of numbers on control bases, the inputs of which are connected to the outputs of neurons 2, which store the remains on working bases; neural networks of the final ring 10, 11, designed to calculate the syndromes of error on the control bases, the first inputs of which are connected respectively to the outputs of the neural network calculate residues on the control bases, and the second, respectively, with the outputs of neurons 23, which store the remains on the control bases, the inputs of which are connected to the bus 25; a memory unit 14 for storing constants, the input of which is connected to the outputs of the neural networks of the final ring 10, 11; neural networks of the final ring 21, designed to receive the corrected number by summing the wrong number with the error constant, the first inputs of which are connected respectively to the outputs of the memory unit, bus 15, which are the output buses 16, 17 and 18, forming the numbers of the faulty modules and the input of the OR element 19, the output 20 of which generates a signal "there is an error", and the second with the outputs of neurons 2, and the output signals 22 of the neural networks of the final ring 21 are outputs of the neural network of error correction.

The operation of a neural network to detect, localize and correct errors in the system of residual classes is as follows.

и w_jk=1. Нейронные сети конечного кольца 4, 5 и 6 реализуют вычислительную модель, представленную в таблице 2.To the inputs 1, 25 of neurons 2 and 23 of the neural network to detect, localize and correct errors in the system of residual classes, a controlled number A = (α ₁ , α ₂ , ..., α _n , α _{n + 1} , α _{n + 2} ) From the outputs of neurons 2 residuals on working grounds with weight coefficients w _ij 3 are fed to the input of neural network 8 calculating the residuals of the control modules. Neural network 8 consists of a set of neural networks of a finite ring 4, 5, 6. Weighting factors w _ij 3 and w _jk 7 of neurons of neural networks of a finite ring, which play the role of distributed memory, are determined respectively

and w _jk = 1. Neural networks of the final ring 4, 5 and 6 implement the computational model presented in table 2.

где l - количество расширяемых модулей и принимает значение 1,2,....The output signals of NSCC 5 and 6 of the last line are fed to the input of NSCC 27 and 26, with weights w _kl 29 equal to

where l is the number of expandable modules and takes the value 1.2, ....

The output signals 9 NSCC 27 and 28 will be negative values: -α ' _{n + 1} and -α' _{n + 2} , which are respectively fed to the inputs 9 of the NSCC 10 and 11, and the values α _{n + 1} and α _{n +} are received at the second inputs ₂ on tires 30 and 31, respectively. NSCC 10 and 11 implement a computational model:

δ ₁ = α _{n + 1} - (- α ' _{n + 1} );

δ ₂ = α _{n + 2} - (- α ' _{n + 2} ).

The output values of NSCC 10 and 11 on buses 12 and 13, corresponding to the error syndromes, are fed to the inputs of memory block 14 and the corresponding constant is selected from there according to table 3. These constants from the output of memory block 14 via buses 15 are sent to the corresponding bus 16, 17 and 18 , which show the number of the faulty module, as well as the input of the OR element 19, the output 20 of which indicates the presence of an error. The signals from the output of the memory block are fed to the inputs of the NSCC 21, and the output signals of the working channels, neurons 3, and the output bus 26, respectively, are received at the second inputs, where they are summed with error constants chosen in such a way that when it is added to the controlled number A, an error occurs in the number is eliminated. At the output of the NSCC 21, the output bus 22 forms a corrected number.

Claims (1)

A neural network for detecting, localizing and correcting errors in a system of residual classes (RNS), containing an input layer of neurons, the inputs of which are supplied with a controlled number A = (α ₁ , α ₂ , ..., α _n , α _{n + 1} , α _{n + 2} ), where α _i = Amod p _i i = 1, 2, ..., n + 2, p ₁ , ... p _n are the working bases of RNS, p _{n + 1} , p _{n + 2} are control SOK bases, memory block, OR element, n output neural networks of the final ring, characterized in that, the outputs of the input layer neurons along the working bases are branched respectively to the first inputs of the output neural networks of the final ring, The values for the corrected number by summing an incorrect number with the constant errors and to the inputs of the neural network for calculating the residual α _{'n + 1} and α' _{n + 2} to the control bases outputs of which are connected to the inputs of the neural networks forming the negative residual values of control bases, the outputs of which are connected respectively to the first inputs of the neural networks of the final ring of the definition of the error syndrome δ ₁ = | α _{n + 1} - (- α ' _{n + 1} ) | _{p + 1} and δ ₂ = | α _{n + 2} - (- α ' _{n + 2} ) | _{p + 2} , the outputs of the input layer neurons on the control bases are connected respectively to the second inputs of the neural networks of the final ring of the definition of the error syndrome, the outputs of which are connected to the address inputs of the memory block, which stores the constants determined by the error syndromes δ ₁ and δ ₂ , the outputs of the memory block connected to the buses for determining the basis on which the error occurred and to the OR element generating the signal “there is an error”, as well as to the second inputs of the n output neural networks of the final ring, the outputs of which are They are outputs of the neural network for detecting, localizing, and correcting errors in the RNS.