RU2300801C2 - Device for finding and correcting errors in codes of polynomial system of residue classes based on zeroing - Google Patents

Abstract

FIELD: computer engineering, in particular, modular neuro-computer means, possible use for finding and correcting errors in modular codes of polynomial residual class system.

SUBSTANCE: in accordance to invention, polynomial residual class system is used, in which as system base minimal polynomials p_i(z), i=1,2,...,7, are used, determined in extended Galois fields GF(2⁵) and neuron network technologies, and also modified zeroing constants determined in current polynomial residual class system are used in parallel.

EFFECT: increased speed of detection and correction of errors in modular codes of polynomial residual class system.

2 dwg, 7 tbl

Description

The invention relates to computer technology, in particular to modular neurocomputer means, and is intended to perform the search and error correction operations in the modular codes of a polynomial residue class system (PSCW).

The aim of the invention is to increase the speed of determining the location and depth of errors in the modular code PSCW to correct the result based on the method of zeroing. The goal is achieved by moving from the sequential character of performing the nullization operation to the parallel subtraction of the nullization constants, as well as using a neural network basis and performing operations in a polynomial system of residue classes of the extended Galois field GF (2 ^ν ).

The technical result achieved by the implementation of the claimed invention is to increase the speed of detection and correction of errors in modular codes PSCW.

The indicated technical result is achieved through the use of a polynomial system of residue classes (PSKV), in which the minimum polynomials p _i (z), i = 1, 2, ..., k + r defined in the extended Galois fields GF are used as the base of the system (2 ^ν ), and neural network technologies, as well as the parallel use of the modified nullization constants defined in this PSKV.

If we choose the minimal polynomials p _i (z) of the field GF (p ^ν ) as the bases of the new algebraic system, then any polynomial A (z) satisfying the condition

A (z) ∈P _floor ,

Where

can be represented as an n-dimensional vector

, i=1, 2, ..., k+r.Where

, i = 1, 2, ..., k + r.

Since comparisons in the same module can be added, subtracted and multiplied term by term, for the sum, difference and product of two polynomials A (z) and B (z) having modular codes (α ₁ (z), α ₂ ( z), ..., α _{k + r} (z)) and (β ₁ (z), β ₂ (z), ..., β _{k + r} (z)) the following relations are valid:

Thus, operations on operands in the extended Galois field GF (p ^ν ) are performed independently for each of the modules p _i (z), which indicates the parallelism of this algebraic system.

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 us to split the full range P of the _full (z) extended Galois field GF (p ^ν ) 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 A (z) ∈P _slave ( z).

The second subset of GF (p ^ν ) 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) ) resolved, or contains erroneous characters.

To determine the location of A (z) = (α ₁ (z), α ₂ (z), ..., α _{k + r} (z)) in (Akushsky I.Ya., Yuditsky DI Machine arithmetic in residual classes. - M .: Sovetskoe Radio, 1968. - 439 p. (pp. 193-194)) it is proposed to use the method of nullification, which consists in switching from the original polynomial to a polynomial of the form

with the help of successive conversions, in which there is no one out of the working range of the system.

According to this method, nullification consists in sequentially subtracting from the initial polynomial represented in the modular code some minimal polynomials — nullization constants such that the polynomial A (z) is subsequently converted to a polynomial of the form

- константа нулевизации по первому основанию p₁(z).Where

is the nullification constant in the first base p ₁ (z).

Then the next nullization constant is subtracted from the result to obtain a polynomial

по второму основанию p₂(z), и так далее. Продолжая данный процесс в течение k итераций, получаетсяWhere

on the second base p ₂ (z), and so on. Continuing this process for k iterations, we obtain

.Application of the method of zeroing allows one to sequentially obtain the smallest polynomial, first multiple p ₁ (z), then a polynomial multiple of p ₁ (z) p ₂ (z), and ultimately a multiple of the operating range

.

If as a result of sequential execution of the nullification procedure a null result is obtained, i.e.

x _{k + 1} (z) = 0, x _{k + 2} (z) = 0, ..., x _{k + r} (z) = 0,

then this indicates that the original combination A (z) represented in the modular code does not contain errors. Otherwise, the modular code A (z) contains errors.

The main disadvantage of the known method of zeroing is the sequential nature of the computing process. This is due primarily to the fact that the zeroing constants are the smallest possible numbers of the form

Where

, возьмем в качестве последних значения произведение остатков рабочих оснований на величину ортогональных базисов безызбыточной системы основанийIt is possible to increase the speed of execution of the nullization procedure by modifying the nullization constants M _i (z). Leaving unchanged the condition for the zeroing constant M _i (z) to be outside the working range

, we take as the last values the product of the residues of the working bases by the value of the orthogonal bases of the redundant system of bases

- ортогональный базис, безызбыточной системы оснований; i=1, 2, ..., k.Where

- orthogonal basis, non-redundant base system; i = 1, 2, ..., k.

, то полином A(z)=(α₁(z),α₂(z)...,α_k(z)) согласно китайской теореме об остатках (КТО) можно представить в видеThen if we put the condition that A (z) ∈P _slave (z), where

, then the polynomial A (z) = (α ₁ (z), α ₂ (z) ..., α _k (z)) according to the Chinese remainder theorem (CTO) can be represented as

Each term of expression (9) represents

We substitute expressions (8) into equality (10). We get

Therefore, the values of the balances on the control grounds will be determined

Therefore, the difference between the polynomial A (z) and the modified nullization constants M _i (z), i = 1, 2, ..., k, of the pseudo-orthogonal forms obtained according to (4.5), determines the magnitude of the normalized trace of the polynomial

Based on the condition that the modified nullization constants M _i (z) are orthogonal bases of the redundant PSKV base system, the nullization operation (13) can be implemented in parallel.

To reduce the volume of stored values of the zeroing constants M _i (z), i = 1, 2, ..., k, we represent the remainder of the number α _i (z) in the form

элементы поля GF(2); j=0, 1, ..., ordp_i(z)-1.Where

elements of the field GF (2); j = 0, 1, ..., ordp _i (z) -1.

Then fair

констант нулевизации M_i(z) достаточно определить ordp_i(z) констант.So instead of storing

nullification constants M _i (z) it is enough to define ordp _i (z) constants.

We consider the PSCW defined in the field GF (2 ⁵ ). Table 1 contains the values of the operating and control bases of the PSKV, as well as the dynamic range for the extended Galois field.

Table 1 Base and dynamic range of the GF field (2 ⁵ ) Foundations of PSKV Working range Workers Control PSKV p ₁ (z) = z + 1 p ₆ (z) = z ⁵ + z ² +1 z ²¹ + z ¹⁹ + z ¹⁶ + z ¹³ + p ₂ (z) = z ⁵ + z ³ +1 p ₇ (z) = z ⁵ + z ³ + z ² + z + 1 + z ¹¹ + z ⁹ + z ⁸ + z ⁶ + p ₃ (z) = z ⁵ + z ⁴ + z ² + z + 1 + z ³ + z ² + z + 1 p ₄ (z) = z ⁵ + z ⁴ + z ³ + z + 1 p ₅ = z ⁵ + z ⁴ + z ³ + z ² +1

The orthogonal bases of the redundant PSKV base system p ₁ (z), p ₂ (z), p ₃ (z), p ₄ (z), p ₅ (z) take the following values

B ₁ ^* (z) = z ²⁰ + z ¹⁹ + z ¹⁵ + z ¹⁴ + z ¹³ + z ¹⁰ + z ⁹ + z ⁷ + z ⁶ + z ² +1;

B ₂ ^* (z) = z ¹⁶ + z ⁸ + z ⁴ + z ² + z + 1;

B ₃ ^* (z) = z ²⁰ + z ¹⁸ + z ¹⁶ + z ¹⁵ + z ¹⁴ + z ¹³ + z ¹² + z ¹¹ + z ¹⁰ + z ⁶ + z ³ + z;

B ₄ ^* (z) = z ¹⁹ + z ¹⁸ + z ¹⁶ + z ¹⁵ + z ¹⁴ + z ¹³ + z ⁸ + z ⁷ + z ⁶ + z ⁵ + z ⁴ + z;

B _l ^* (z) = z ¹⁶ + z ¹⁵ + z ¹⁴ + z ¹³ + z ¹² + z ¹¹ + z ⁹ + z ⁶ + z ⁵ + z ³ + z + 1.

We define all the values of the products of degrees z ^j on the orthogonal bases B _i ^* (z), taking into account the impossibility of going beyond the working range P _slave (z) = z ²¹ + z ¹⁹ + z ¹⁶ + z ¹³ + z ¹¹ + z ⁹ + z ⁸ + z ⁶ + z ³ + z ² + z + 1. The obtained values of the modified nullization constants are presented in table 2.

table 2 Zero Constants for the GF Field (2 ⁵ ) α ₁ (z) α ₂ (z) α ₃ (z) α ₄ (z) α ₅ (z) α ₆ (z) α ₇ (z) z ⁰ B ₁ ^* (z) one 0 0 0 0 z ² z z ⁰ B ₂ ^* (z) 0 one 0 0 0 one one z ¹ B ₂ ^* (z) 0 z 0 0 0 z z z ² B ₂ ^* (z) 0 z ² 0 0 0 z ² z ² z ³ B ₂ ^* (z) 0 z ³ 0 0 0 z ³ z ³ z ⁴ B ₂ ^* (z) 0 z ⁴ 0 0 0 z ⁴ z ⁴ z ⁰ B ₃ ^* (z) 0 0 one 0 0 z ⁴ + z z ⁴ +1 z ¹ B ₃ ^* (z} 0 0 z 0 0 z ³ + z ² +1 z ³ + z + 1 z ² B ₃ ^* (z) 0 0 z ² 0 0 z ⁴ + z ³ + z z ⁴ + z ² + z z ³ B ₃ ^* (z) 0 0 z ³ 0 0 z ⁴ +1 z + 1 z ⁴ B ₃ ^* (z) 0 0 z ⁴ 0 0 z ² + z + 1 z ² + z z ⁰ B ₄ ^* (z) 0 0 0 one 0 z ² z + 1 z ¹ B ₄ ^* (z) 0 0 0 z 0 z ³ z ² + z z ² B ₄ ^* (z) 0 0 0 z ² 0 z ⁴ + z ³ + z ² z ³ + z z ³ B ₄ ^* (z) 0 0 0 z ³ 0 z ⁴ + z z ⁴ + z ² z ⁴ B ₄ ^* (z) 0 0 0 z ⁴ 0 z ³ + z + 1 z ³ + z ² +1 z ⁰ B ₅ ^* (z) 0 0 0 0 one z ⁴ + z z ⁴ z ¹ B ₅ ^* (z) 0 0 0 0 z one z ³ + z ² + z + 1 z ² B ₅ ^* (z) 0 0 0 0 z ² z z ⁴ + z ³ + z ² + z z ³ B ₅ ^* (z) 0 0 0 0 z ³ z ² z ⁴ + z + 1 z ⁴ B ₅ ^* (z) 0 0 0 0 z ⁴ z ³ z ³ +1

If in the ordered excess PSCW of the extended Galois field GF (p ^ν ) for which ord _p1 (z) ≤ordp ₂ (z) ≤ ... ≤ordp _k (z) for two control bases p _{k + 1} (z) and p _{k + 2} (z) we have the relation

then they determine the location and magnitude of the error for any reason.

Consider an example. Let in the field GF (2 ⁵ ), in which the working and control bases are defined according to Table 1, be given - polynomial A (z) = z ⁶ + z ⁵ + z ⁴ +1, This polynomial belongs to P _slave (z). Represent it in modular code

A (z) = z ⁶ + z ⁵ + z ⁴ + 1 = (0, z ³ + z, z ⁴ + z ³ + z ² + z + 1, z ² + z + 1, z ³ + z + 1 , z ⁴ + z ³ + z ² + z, 0).

We carry out the nullization procedure sequentially. At the first stage, by subtracting modulo 2, we obtain

The value of M ₂ (z) is obtained according to expression (15) by summing the values

M ₂ (z) = z ³ B ₂ ^* (z) + zB ₂ ^* (z) = (0, z ³ , 0, 0, 0, z ³ , z ³ ) + (0, z, 0, 0, 0, z, z) = (0, z ³ + z, 0, 0, 0, z ³ + z, z ³ + z).

At the second stage of zeroing we have

At the third stage of zeroing we get

In the fourth stage of zeroing we have

Thus, the polynomial A (z) does not contain an error.

Table 3 Dependence of the location and depth of the error on the results of the nullization procedure Nullization result Error in modular code x ₆ (z) x ₇ (z) depth base z ² z one p ₁ (z) = z + 1 one one one p ₂ (z) = z ⁵ + z ³ +1 z z z z ² z ² z ² z ³ z ³ z ³ z ⁴ z ⁴ z ⁴ z ⁴ + z z ⁴ +1 one p ₃ (z) = z ⁵ + z ⁴ + z ² + z + 1 z ³ + z ² +1 z ³ + z + 1 z z ⁴ + z ³ + z z ⁴ + z ² + z z ² z ⁴ +1 z + 1 z ³ z ² + z + 1 z ² + z z ⁴ z ² z + 1 one p ₄ (z) = z ⁵ + z ⁴ + z ³ + z + 1 z ³ z ² + z z z ⁴ + z ³ + z ² z ³ + z z ² z ⁴ +1 z ⁴ + z ² z ³ z ³ + z + 1 z ³ + z ² +1 z ⁴ z ⁴ + z z ⁴ one p ₅ (z) = z ⁵ + z ⁴ + z ³ + z ² +1 one z ³ + z ² + z + 1 z z z ⁴ + z ³ + z ² + z z ² z ² z ⁴ + z + 1 z ³ z ³ z ³ +1 z ⁴ one 0 one p ₆ (z) = z ⁵ + z ³ +1 z 0 z z ² 0 z ² z ³ 0 z ³ z ⁴ 0 z ⁴ 0 one one p ₇ (z) = z ⁵ + z ³ + z ² + z + 1 0 z z 0 z ² z ² 0 z ³ z ³ 0 z ⁴ z ⁴

Suppose an error occurred on the first ground. Then we have

A * (z) = (1, z ³ + z, z ⁴ + z ³ + z ² + z + 1, z ² + z + 1, z ³ + z + 1, z ⁴ + z ³ + z ² + z, 0).

We carry out the nullization procedure sequentially. At the first stage, by subtracting modulo 2, we obtain

At the second stage of zeroing we have

At the third stage of zeroing we get

In the fourth stage of zeroing we have

In the fourth stage of zeroing we have

As a result of zeroing, a non-zero result was obtained, which indicates the presence of an error in the modular code.

Correction is carried out depending on the magnitude of the error syndrome.

.where (0, ..., Δα _i (z), ..., 0) is the error vector of the modular code; Δα _i (z) is the error depth in the i-th module;

.

According to table 3, where the dependence of the location and depth of the error on the results of the zeroing procedure is given, for the result x ₆ (z) = z ² , x ₇ (z) = z we have that the error occurred on the first basis and the depth is 1. Then the initial polynomial has the form

A * (z) + (1, 0, 0, 0, 0, 0, 0) = (0, z ³ + z, z ⁴ + z ³ + z ² + z + 1, z ² + z + 1, z ³ + z + 1, z ⁴ + z ³ + z ² + z, 0).

The structure of the device for detecting and correcting errors in codes of a polynomial system of residue classes based on nullization is presented in figure 1.

It includes: input of device 1, block of neutralization 2, memory block 3, adders 4, 5, 6, 7, 8, 9, 10, output of device 11.

The operation of the device is as follows.

At input 1 of the device for detecting and correcting errors in codes of a polynomial system of residue classes based on nullification, a controlled number is presented, presented in polynomial form

A (z) = (α ₁ (z), α ₂ (z), α ₃ (z), α ₄ (z), α ₅ (z), α ₆ (z), α ₇ (z)).

where α _i (z) is the remainder of the polynomial A (z) modulo p _i (z); p ₁ (z), p ₂ (z), p ₃ (z), p ₄ (z), p ₅ (z) are the working bases of the PMSC system of the field GF (2 ⁵ ); p ₆ (z), p ₇ (z) are the control bases. The input of the device is connected to the inputs of the nullization block 2. From the output of the nullification block, the calculated values x ₆ (z), x ₇ (z) are fed to the inputs of the memory block 3 and the corresponding error constant (0, ..., Δα _i (z) is selected from there , ..., 0), i = 1, 2, 3, 4, 5, 6, 7. This error constant is fed to the second inputs of the correcting adders 4, 5, 6, 7, 8, 9, 10, respectively, on the basis of p ₁ (z), p ₂ (z), p ₃ (z), p ₄ (z), p ₅ (z), p ₆ (z), p ₇ (z), where it is summed with the values α received at the first inputs ₁ (z), α ₂ (z), α ₃ (z), α ₄ (z), α ₅ (z), α ₆ (z), α ₇ (z) supplied from the input of device 1. Corrected value A (z) according to The property (17) from the output of the correcting adders 4-10 is fed to the output 11 of the device.

Block nullification is presented in figure 2.

It consists of: the first layer of neurons 12-42, the second layer of neurons 43-52.

The nullization block is a two-layer neural network. The first layer contains 31 neurons. The input of neurons 12 in the binary code receives the remainder α ₁ (z) at the base p ₁ (z) = z + 1. At the input of neurons 13-17, the remainder α ₂ (z) is received at the base p ₂ (z) = z ⁵ + z ³ +1, the senior discharge being fed to 13 neuron, and the youngest to 17 neuron. At the input of neurons 18-22, the remainder α ₃ (z) is received at the base p ₃ (z) = z ⁵ + z ⁴ + z ² + z + 1, the senior discharge being fed to 18 neuron, and the youngest being fed to 22 neuron. The input of neurons 23-27 receives the remainder α ₄ (z) on the basis of p ₄ (z) = z ⁵ + z ⁴ + z ³ + z + 1, with the senior discharge being fed to 23 neurons, and the youngest being fed to 27 neurons. At the input of neurons 28-32, the remainder α ₅ (z) is received at the base p ₅ (z) = z ⁵ + z ⁴ + z ³ + z ² +1, the senior discharge being delivered to 28 neuron, and the youngest to 32 neuron. The binary code α ₆ (z) is supplied to neurons 33-37 by the first control module p ₆ (z) = z ⁵ + z ² +1, with the highest level being sent to 33 neurons, and the least to 37 neurons. On binary 38-42 neurons, α ₇ (z) is supplied in binary by the second control module, p ₇ (z) = z ⁵ + z ³ + z ² + z + 1, with the highest level being sent to 38 neurons and the lowest - by 42 neuron. The second layer of the neural network contains 10 neurons that perform the basic summation operation modulo two according to expression (13), the first five neurons 43-47 determining the value x ₆ (z), the remaining neurons 48-52 determining the value x ₇ (z). The inputs of the neuron 43 of the second layer are connected to the outputs of the neurons 13, 19, 20, 22, 24, 25, 32, 33 of the neurons of the first layer. The inputs of the neuron 44 of the second layer are connected to the outputs of the neurons 14, 20, 21, 23, 25, 26, 28, 34 of the neurons of the first layer. The inputs of the neuron 45 of the second layer are connected to the outputs of the neurons 12, 15, 18, 21, 25, 27, 29, 35 of the neurons of the first layer. The inputs of the neuron 46 of the second layer are connected to the outputs of the neurons 16, 18, 20, 22, 23, 30, 32, 36 neurons of the first layer. The inputs of the neuron 47 of the second layer are connected to the outputs of the neurons 17, 18, 19, 21, 23, 24, 31, 37 of the neurons of the first layer. The inputs of the neuron 48 of the second layer are connected to the outputs of the neurons 13, 20, 22, 24, 29, 30, 31, 38 neurons of the first layer. The inputs of the neuron 49 of the second layer are connected to the outputs of the neurons 14, 21, 23, 25, 28, 30, 31, 39 of the neurons of the first layer. The inputs of the neuron 50 of the second layer is connected to the outputs of the neurons 15, 18, 20, 23, 26, 30, 31, 40 of the neurons of the first layer. The inputs of the neuron 51 of the second layer are connected to the outputs of the neurons 12, 16, 18, 19, 20, 21, 24, 25, 26, 27, 29, 30, 31, 41 of the neurons of the first layer. The inputs of the neuron 52 of the second layer is connected to the outputs of the neurons 17, 19, 21, 22, 23, 27, 28, 29, 31, 42 of the neurons of the first layer. The highest values of the results of nullification on the control bases x ₆ (z) and x ₇ (z) are respectively calculated in neurons 43 and 48.

Consider the process of operation of the nullification block with examples. Suppose that a modular code A (z) = (0, z ³ + z, z ⁴ + z ³ + z ² + z + 1, z ² + z-1, z ⁴ + z ³ + z ² +1, 0). This code goes to the inputs of the neurons of the first layer of the nullification block. The signals at the output of neurons of the first layer are presented in table 4.

The signals from the outputs of the neurons of the first layer are fed to the corresponding inputs of the neurons of the second layer. Table 5 presents the values of the signals at the input and output of the neurons of the second layer. The symbol “-” corresponds to the absence of communication between the neurons of the second and first layer. The obtained zero result indicates that this combination does not contain errors.

Assume that the error occurred on the first basis. Then the modular combination has the form

A * (z) = (1, z ³ + z, z ⁴ + z ³ + z ² + z + 1, z ² + z + 1, z ³ + z + 1, z ⁴ + z ³ + z ² + z, 0)

This code goes to the inputs of the neurons of the first layer of the nullification block. The signals at the output of neurons of the first layer are presented in table 6.

The signals from the outputs of the neurons of the first layer are fed to the corresponding inputs of the neurons of the second layer. Table 7 presents the values of the signals at the input and output of the neurons of the second layer.

As a result of executing the procedure parallel to nullification, a result was obtained that is different from zero, i.e. x ₆ (z) = z ² , x ₇ (z) = z. Therefore, the modular combination applied to the input of the device contains an error.

According to table 3, where the dependence of the location and depth of the error on the results of the zeroing procedure is given, for the result x ₆ (z) = z ² , x ₇ (z) = z we have that the error occurred on the first basis and the depth is 1.

Table 4 Signals at the output of neurons of the first layer Neuron Signal 12 0 13 0 fourteen one fifteen 0 16 one 17 0 eighteen one 19 one twenty one 21 one 22 one 23 0 24 0 25 one 26 one 27 one 28 0 29th one thirty 0 31 one 32 one 33 one 34 one 35 one 36 one 37 0 38 0 39 0 40 0 41 0 42 0

Table 5 Signals at the output of neurons of the second layer 52 51 fifty 49 48 47 46 45 44 43 - 0 - - - - - 0 - - 12 - - - - 0 - - - - 0 13 - - - one - - - one - fourteen - - 0 - - - - 0 - - fifteen - one - - - - one - - - 16 0 - - - - 0 - - - - 17 - one one - - one one one - eighteen one one - - - one - - - one 19 - one one - one - one - one one twenty one one - one - one - one one - 21 one - - - one - one - - one 22 0 - 0 0 - 0 0 - 0 - 23 - 0 - - 0 0 - - - 0 24 - one - one - - - one one one 25 - one one - - - - - one - 26 one one - - - - - one - - 27 0 - - 0 - - - - 0 - 28 one one - - one - - one - - 29th - 0 0 0 0 - 0 - - - thirty one one one one one one - - - - 31 - - - - - - one - - one 32 - - - - - - - - - one 33 - - - - - - - - one - 34 - - - - - - - one - - 35 - - - - - - one - - - 36 - - - - - 0 - - - - 37 - - - - 0 - - - - - 38 - - - 0 - - - - - - 39 - - 0 - - - - - - - 40 - 0 - - - - - - - - 41 0 - - - - - - - - - 42 0 0 0 0 0 0 0 0 0 0 Exit

Table 6 Signals at the output of neurons of the first layer (when an error occurs) Neuron Signal 12 one 13 0 fourteen one fifteen 0 16 one 17 0 eighteen one 19 one twenty one 21 one 22 one 23 0 24 0 25 one 26 one 27 one 28 0 29th one thirty 0 31 one 32 one 33 one 34 one 35 one 36 one 37 0 38 0 39 0 40 0 41 0 42 0

Table 7 Signals at the output of neurons of the second layer (when an error occurs) 52 51 fifty 49 48 47 46 45 44 43 - one - - - - - one - - 12 - - - - 0 - - - 0 13 - - - one - - - - one - fourteen - - 0 - - - - 0 - - fifteen - one - - - - one - - - 16 0 - - - - 0 - - - 17 - one one - - one one one - - eighteen one one - - - one - - - one 19 - one one - one - one - one one twenty one one - one - one - one one - 21 one - - one - - one - - one 22 0 - 0 0 - 0 0 - 0 - 23 - 0 - - 0 0 - - - 0 24 - one - one - - - one one one 25 - one one - - - - - one - 26 one one - - - - - one - - 27 0 - - 0 - - - - 0 - 28 one one - - one - - one - - 29th - 0 0 0 0 - 0 - - - thirty one one one one one one - - - - 31 - - - - - - one - - one 32 - - - - - - - - - one 33 - - - - - - - - one - 34 - - - - - - - one - - 35 - - - - - - one - - - 36 - - - - - 0 - - - 37 - - - - 0 - - - - - 38 - - - 0 - - - - - - 39 - - 0 - - - - - - - 40 - 0 - - - - - - - - 41 0 - - - - - - - - - 42 0 one 0 0 0 0 0 one 0 0 Exit

Claims (1)

A device for detecting and correcting errors based on nullification in the codes of a polynomial system of residue classes (PSKV) in the original polynomial A (z) = (α ₁ (z), ..., α _i (z)), where α _i (Z) - the remainder of the polynomial A (z) modulo p _i (z), i = (1, ..., 7), ap ₁ (z), p ₂ (z), p ₃ (z), p ₄ (z), p ₅ (z) are the working bases of the PMSW system of the field GF (2 ⁵ ), p ₆ (z), p ₇ (z) are the control bases, characterized in that the device contains an input that is connected to the inputs of the nullization unit, which is a two-layer a neural network, the first layer of which contains 31 neurons, and the second layer - ten neurons performing bases modulo summation operation, the inputs of the first neuron of the second layer are connected to the outputs 2, 8, 9, 11, 13, 14, 21, 22 of the neurons of the first layer, the inputs of the second neuron of the second layer are connected to the outputs 2, 9, 10, 12, 14 , 15, 17, 23 neurons of the first layer, the inputs of the third neuron of the second layer are connected to the outputs 1, 4, 7, 10, 14, 16, 18, 24 of the neurons of the first layer, the inputs of the fourth neuron of the second layer are connected to the outputs 5, 7, 9 , 11, 12, 19, 21, 25 neurons of the first layer, the inputs of the fifth neuron of the second layer are connected to the outputs 6, 7, 8, 10, 12, 13, 20, 26 of the neurons of the first layer, the inputs of the sixth neuron of the second the loya are connected to the outputs of 2, 9, 11, 13, 18, 19, 20, 27 neurons of the first layer, the inputs of the seventh neuron of the second layer are connected to the outputs of 3, 10, 12, 14, 17, 19, 20, 28 neurons of the first layer, the inputs of the eighth neuron of the second layer are connected to the outputs 4, 7, 9, 12, 15, 19, 20, 29 of the neurons of the first layer, the inputs of the ninth neuron of the second layer is connected to the outputs 1, 5, 7, 8, 9, 10, 13, 14 15, 16, 18, 19, 20, 30 neurons of the first layer, the inputs of the tenth neuron of the second layer are connected to the outputs 6, 8, 10, 11, 12, 16, 17, 18, 20, 31 of the neurons of the first layer, to the inputs of the block nullification feed the values of the residues α _i (z), respectively, the outputs the zeroing block are connected respectively to the inputs of the memory block containing error constants, the outputs of which are connected to the second inputs of the seven correcting adders, respectively, the first inputs of the said adders are connected to the input of the device, and the correcting adders sum the values α _i (z) received at their first inputs the corresponding error constants on the bases p _i (z) received at the second inputs of the said adders, respectively, the outputs of the correcting adders are the output devices.

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