Neuron network for finding, localizing and correcting errors in residual classes system

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

 

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

A device for monitoring and correcting errors in a redundant modular code (patent No. 2022472, CL NM 13/00, EN, 1999), which consists of the input of the code Converter, the output of the Converter unit controls comparison block group item OR block of items I.

However, this device has the following disadvantages:

low speed, large hardware cost and low functionality, because the device uses a single redundant module, the error correction is carried out on a large modulus equal to the range of control numbers.

The closest to the technical nature of the claimed device is a device for detecting and correcting errors in the system of residual classes (A.S. No. 714399, G06F 11/08, 1980), contains two modular block convolution, and the first output register connected to the input of the first and second blocks modular convolution and to the first input of the third adder, the outputs of the first and second blocks modular convolution respectively connected with the first inputs of the first and second adders, the second and third outputs of the register are connected respectively with the second inputs of the first and second adders and with the second and third inputs of the third adder, the output of the memory block is connected to the fourth input of the third adder, the output of which is the output device.

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

The aim of the present invention is the simplification of the device, improve performance and increase functionality.

This objective is achieved in that the device comprises a neural network 8, consisting of neural networks, the end rings 4, 5 and 6 and neural networks end rings 27, 28, which form rests for the control modules of the system of residual classes, outputs 9 are connected with the first inputs of the neural networks of the end rings 10, 11 calculate the syndrome of the error, the second inputs of which are connected to the outputs of neurons 23 redundant modules αn+1and αn+2the outputs of the neural networks of the end rings 10, 11, bus 12 and 13 are connected with the inputs of the memory unit 14 for selecting the constants of the error exits 15, which are received on bus 16, 17 and 18 defining the number of the faulty module (channel), and to the input of the OR element 19, the output 20 which detects the presence of errors, in addition, the outputs of the memory block 14 is received on the first choice of the inputs of the neural networks of the end rings 21, but on the second inputs of which receive the remains of the wrong number α1that α2,...,αn. Fixed number of outputs of the neural networks of the end ring 21 is fed to the outputs 22 of the device.

Consider the error correction method.

Given a controlled number A=(α1that α2,...,αnthat αn+1that αn+2), where

αi=Amodpi∀i=1, 2,..., n+2, R1,R2,...,Rn,Rn+1,Rn+2- base JUICE with two redundant bases of pn+1, Rn+2.

The principle of detection, localization and error correction based on the functional integration of all three operations into a single operation. This method is based on the determination of digits in redundant bases on the basis of figures on the working grounds and comparing them with the known initial digits in redundant bases. If the calculated figures α'n+1and α'n+2by means of the control bits is equal to the original numbers αn+1and αn+2these discharges, there is no error, if they are not equal, it is necessary to define the syndrome of the error, equal to the difference of these numbers δ1=(αn+1-α'n+1)mod pn+1and δ2=(αn+2-α'n+2)mod pn+2, whose values are determined by the error constant. Further summarizing the constant errors with the wrong number, which the traveler is chosen so that implicit error in the number of eliminated. To localize the error, you need to bitwise compare the adjusted number is wrong, and if αii'≠0, is determined by the erroneous discharge. The proposed method allows to detect, isolate, and correct an error in one of the information channels.

Computation α'n+1and α'n+2will carry out based on the method of system expansion bases, which is based on the use of Chinese theorems about residues and generalized positional notation. Let us first consider the extension to one basis, and then generalize the extension on two grounds.

Let set system bases p1, R2,..., Rnwith range R=R1·p2·...·pnorthogonal bases In1In2,...,Inn, weight of which m1, m2,..., mnand are determined from comparisonExtend system grounds, adding base Rn+1then the range of the system will become Pn+1=pn+1·P, orthogonal bases systemtheir weightandThe problem consists in determining the numbers αn+1the number And on the basis of pn+1.

Then the number in system is IU grounds R 1, R2,..., Rn, Rn+1will be

wherethe range of the extended basis;

orthogonal bases of the extended grounds.

Imagine orthogonal basesin the generalized positional number system, then

wherethe coefficients of the CSO;

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

On the basis of (2) let us write the expression (1) in the form

From the expression (3), we can determine the coefficients αinumber, then

where αi- deductions numbers And mod pi;

orthogonal bases presented in the round.

Figures αiin view of the round is the sum modulo piall worksand transfer generated during the formation of the αi-1. The transfer is generated as the number of times when the sum of the digits in the CSO overflows modulo pi. This transfer is used to form numbers αi+1. The last transfer generated when receiving the last digit of the number in the round, is discarded. The proposed method is performed in parallel regimens in the performance of this method with the iterative method is obvious, because it reduces the conversion time 2(n+1) cycles sync up to three cycles.

Figures αi,take values from 0 to pi-1andare constants, so the work αican be placed in ROM or in the weights of connections between neurons. Addresses works αiare deductions αinumbers And modulo pi.

Example 1. Let R1=2, p2=3, p3=5, p4=7, Pn+1=2·3·5·7=210, B1=105, B2=70, B3=126, In4=120.

Then on the basis of (2) we define:

Consider the translation of a number of JUICE in the round.

Let And=11=(1, 2, 1, 4). Then in ROM, place value αi,:

The conversion of A number of JUICE in the CSO has the form

Adding the numbers for each module taking into account migration will get the number As presented in the OPS as A=[1,2,1,0].

Consider the method of determining the deduction on an extended basis. Let the JUICE consists of grounds R1, R2,...,pn.The volume range of this system isAdd to the Isla grounds JUICE new Foundation p n+1. The volume range of this systemThen any number from range [0, Rn+1] generalized positional number system can be represented in the form

If the number And will lie in the original range [0; P], the round dial αn+1=0. If αn+1≠0, then the value of number is outside the dynamic range. Fact αn+1=0 is used to obtain the remainder (deduction) from dividing the number of And on the new basis)n+1.

Let the number And had an idea (α1that α2,..., αn) on the grounds of p1p2,..., Rn.Added a new Foundation pn+1then the number ofthe system bases p1, R2,..., Rnpn+1where- the remainder from dividing the number of And Rn+1, i.e. the required number by the new base.

To determine this number we use the method of transfer number of JUICE in the round, including an unknown numberin the ongoing operation. However, we simultaneously get the numbers SVR α1that α2,...,αnand the expression for the numbers αn+1. But as the condition number of A∈[0;P], the figure αn+1=0.

From the obtained ratio and determine the required digit

Example 2. Let set module system R1=2, p2=3, p3=5, then P=2·3·5=30. And may specify the number And=11=(1, 2, 1). Extend system grounds, adding p4=7. And then=11=(1, 2, 1, |A|7in the system bases p1=2, p2=3, p3=5, p4=7.

The set of constants bijgiven in (5) and is given by the matrix

The problem-solving process are shown in table 1.

Table 1
Deductions numbers And modulo piModules
p1=2p2=3p3=5p4=7
11123
20424
10014
|A|70004·|x|7
The coefficients of the round numbers A1215+4·|x|7

After adding the digits modulo piget And=[1, 2, 1, 5+4|A|7], but as α4=|5+4·|A|7|7but on condition α47=-5 or. Multiplicative inverse value ofand since the number 5 is negative, take it to addition modulo 7. So, the less number modulo 7 is determined by the expression |A|7=2·(7-5)=4.

Then an enlarged representation of a number is A=11=(1, 2, 1, 4). As a result of the formation of the figures in the JUICE on the new basis pn+1depends only on the information bits, the expansion operation of deductions can be performed on several added reasons.

Example 3. Let set a system reason (s) JUICE p1=2, p2=3, p3=5. Extend system grounds, adding p4=7, p5=11. Then in the expression (5) is added to another column and one row, namely

Let the number is set to A=17=(l,2,2,|A|7, |A|11), it is necessary to find the remains of the bases of p4=7, p5=11.

The solution process is given in table 2.

Table 2
Deductions numbers And modulo piModules
p1=2p2=3p3=5p4=7p5=11
11 1235
2042414
300284
0004|A|7-
000-7|A|11
The coefficients of the round numbers Aα1=1α2=2α3=2α4=2+4|A|7α5=2+7|A|11

After adding the digits modulo piget

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

but as α4=2+4|A|7and α5=2+7|A|11and on condition α4=0 and α5=0, then

Multiplicative

Since |A|7=-4, and |A|11=-5 take their supplements, ie, |A|7=7-4=3 and |A|11=11-5=6.

Then an enlarged representation of a number is equal to the information, i.e. A=(1,2,2,3,6)11and this suggests that the number And unmistakable.

The advantages of the proposed method is extended the I residue system is that:

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

- does not require calculation of a large number of additional variables, you need only constantsand multiplicative values for the advanced bases;

- you may receive an expanded representation of deductions numbers on several additional grounds, which does not affect the performance of the whole operation of the extension.

We apply this method for the detection, location and correction of errors.

Correction of errors in JUICE-based representation of a number in the extended system. As extended basis take excess (control). For example, in processing and storing data in a computer system rests on a redundant basis, on the one hand, is absolutely true, but on the other hand, they are calculated based on the balances of non-redundant (information) the grounds immediately before the control data. If the calculated excess remains equal to the original, errors in the information bases has not occurred, otherwise an error has occurred on informational grounds. Based on this information eliminates the error and determined a faulty module.

Widen the e limitation on the absolute loyalty of excess bases ensures absolute reliability channels redundant modules, you can provide a known structural technologies (for example, using conventional error correcting codes, or a majority of the schema).

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

For example, an error occurred on the third information base, then a wrong numberwill be=(1,2,3,3,6).

Excess digits in the fourth and fifth bases, respectively, 3 and 6, and they are absolutely correct.

On the basis of information residues define the syndrome error δ.

Method of detection, correction and localization errors in the JUICE is as follows.

Controlled number α1that α2,...,αnthat αn+1that αn+2divided into two parts: information, which includes balances on information and belief α1that α2,..., αn, and a control part, which includes balances excess (control) grounds αn+1that αn+2.

Further information on the remaining channels defined balances excess grounds. Use table 2, then the third line would be not[0, 0, 2, 8, 4], and[0, 0, 3, 12, 6].

When the operation is performed according to table 2 will receive

Here

Using the found remains defined the syndrome of the error:

The values δ1that δ2formed constants of errors in such a way that, when added together with the information bits of a controlled number And occurred error number is eliminated. Note that if the controlled number will not contain errors, then the value of δ1and δ2zero.

To localize the error, you need to compare the digits of the original number with a fixed number and the discharge, where the comparison is carried out, is determined by the erroneous discharge.

Define constants errors for this example, and bring them in table 3.

Table 3

Constant errors for the JUICE with the bases of p1=2, p2=3, p3=5, p4=7, p5=11
The error on the basis of p1δ1that δ2The error on the basis of p2δ1that δ2The error on the basis of p3δ1that δ2
0,0,00,00,0,00,00,0,00,0
1,0,06,7

1,4
0,1,01,2

3,10
0,0,14,9

6,6
0,0,23,4

5,1
0,2,04,1

6,9
0,0,34,7

2,10
0,0,41,5

3,2

According to δ1=1, δ2=5 table 2 determines the magnitude of the error (0,0,4), which is controlled by the number of

Largest errors (0,0,4) is localized erroneous discharge, the discharge on modp3. The use of the syndrome of the error allows all procedures for the detection, localization and correction of errors be combined into a single procedure that can reduce the time error correction and improve efficiency.

The drawing shows a neural network for detecting, locating and correcting errors in the system of residual classes. A neural network consists of input layer neurons 2, 23, the input layer 24, intended for storage of the remaining number of working and reference grounds during the time of error detection, the input of which is connected to the inputs 1(α1that α2,..., αnand inputs 25(αn+1that αn+2) neural network; neural the network 8, designed to calculate the residue numbers for control reasons, the inputs of which are connected to the outputs of neurons 2 holding rests on the working grounds; neural networks end rings 10, 11, designed for calculating syndromes of the error on the test grounds, the first inputs of which are connected respectively to the outputs of the neural network calculation rests on the test grounds, and the latter respectively to the outputs of neurons 23 storing the remains in control reasons, the inputs of which are connected to the bus 25; a memory unit 14 for storing constants, an input connected to the outputs of the neural networks of the end rings 10, 11; neural networks end rings 21, designed to obtain the corrected number by summing the wrong number with constant error, the first inputs of which are connected respectively to the outputs of the memory block, bus 15, which are output tires 16, 17 and 18 forming the non-faulty modules and the input element OR 19, the output 20 which generates a signal "there is an error", and the second - with the outputs of the neurons 2, and the output signals 22 neural networks end rings 21 are the outputs of the neural network bug fixes.

The operation of the neural network for detecting, locating and correcting errors in the system of residual classes is following the way.

The inputs 1, 25 neurons 2 and 23 of the neural network for the detection, location and correction of errors in the system of residual classes served controlled number A=(α1that α2,...,αnthat αn+1that αn+2). From the outputs of the neurons 2 remains on the working grounds with weights wij3 is fed to the input of the neural network 8 calculation rests on the control modules. The neural network 8 consists of a set of neural networks end rings 4, 5, 6. The weighting coefficients wij3 and wjk7 neurons in the neural networks of the end rings, the role of distributed memory, are defined respectivelyand wjk=1. Neural network end rings 4, 5 and 6 implement the computational model presented in table 2.

The output signals of the NJC 5 and 6 of the last line is fed to the input of the NJC 27 and 26, with weights wkl29 equalwhere l is the number of extensible modules and takes the value 1,2,....

Output signals 9 of the NJC 27 and 28 will be negative values: -α'n+1and -α'n+2that come respectively to the inputs 9 NJC 10 and 11, and the second input values arrive αn+1and αn+2on tires, respectively 30 and 31. The NJC 10 and 11 implement a computational model:

δ1 n+1-(-α'n+1);

δ2n+2-(-α'n+2).

The output values of the NJC 10 and 11 of the tire 12 and 13 corresponding to the syndromes of the error, proceed to the inputs of the memory block 14 and pick out the appropriate constant according to table 3. These constants from the output of the memory block 14 to 15 tires come on the appropriate bus 16, 17 and 18, which show the number of the faulty module, and also to the input of the OR element 19, the output 20 which indicates the presence of errors. The inputs of the NJC 21 receives the signal from the output of the memory block, and the second input receives respectively the output signals of the working channels, neuronal 3, the output bus 26, where it is summed with the error constants, chosen so that when the addition is controlled by the number And occurred error number is eliminated. The output of the NJC 21 output bus 22 generates a fixed number.

Neural network for detecting, locating and correcting errors in the system of residual classes (SOC)containing an input layer of neurons, the input of which is fed a controlled number A=(α1that α2, ..., αnthat αn+1that αn+2), where αi=Amod pii=1, 2, ..., n+2, R1, .. Rn- working grounds JUICE, Rn+1, Rn+2control base JUICE, memory block, item, OR, n the output of neural networks finite number of the CA, characterized in that it outputs of the neurons of the input layer on the working grounds branched respectively to the first inputs of the output of neural networks finite rings designed for a fixed number by summing the wrong number with constant error, and to the inputs of the neural network designed to calculate residues α'n+1and α'n+2for control reasons, the outputs of which are connected to the inputs of the neural network forming negative balances control reasons, the outputs of which are connected respectively to the first inputs of the neural networks of the end ring defining the syndrome error δ1=|αn+1-(-α'n+1)|p+1and δ2=|αn+2-(-α'n+2)|p+2the outputs of the neurons of the input layer control bases connected respectively to the second inputs of the neural networks of the end ring defining the syndrome of the error, the outputs of which are connected to the address inputs of the memory block that stores the constants defined syndromes of errors δ1and δ2the outputs of the memory block connected to the tires determine the grounds on which the error occurred and to the element OR forming the signal "there is an error", and respectively to the second inputs of the n output neural networks finite rings, vihodiashiy are the outputs of the neural network detection locating and correcting errors in the JUICE.



 

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