RU2267808C2 - Device for detecting and correcting errors in polynomial residual-class system - Google Patents

Abstract

FIELD: automatics and computer science, possible use for controlling and correcting errors during relaying of information, and also for performing arithmetical operations by computer.

SUBSTANCE: device has two blocks for calculating error syndrome on basis of control bases, made on two-layer neuron network, register, memory block, output adder, and also due to application of polynomial residuals system, in which as system base, minimal polynomials are used, determined in extended Galois fields GF(2^ν) and in terms of neuron network technologies.

EFFECT: decreased dimensions of equipment, higher speed of detection and correction of errors.

3 dwg, 2 tbl

Description

The device relates to the field of automation and computer technology and can be used both for monitoring and correcting errors in the transmission of information, and during arithmetic operations in computers.

A device for detecting and correcting errors in a system of residual classes (AS No. 714399, class G 06 F 11/08, 1980), containing a register, the input of which is connected to the input of the device, two blocks of modular convolution, three adders and the output of the third adder is the output of the device, a memory unit.

A disadvantage of the known device is its complexity and low speed, due to the presence of a large amount of equipment.

The main objective is to reduce equipment and increase the speed of error correction.

The technical result achieved by the implementation of the claimed invention is to increase the speed of detection and correction of errors and reduce the amount of equipment.

The specified technical result is achieved due to the fact that the claimed device contains two blocks for calculating the error syndrome for control reasons, and these blocks are made on a two-layer neural network, with the first output of the register connected to the first outputs of the blocks for calculating the error syndrome, the second and third output of the register are connected, respectively on the second outputs of the first and second blocks of the calculation of the error syndrome, the outputs of which are connected to the inputs of the memory block; and also through the use of a polynomial residue system (PSCW), in which the minimum polynomials p _i (z), i = 1,2, ..., n, defined in the extended Galois fields GF (2 ^ν ) and neural network technology.

Functional diagram of the device shown in figure 1. It includes: register1, input 2, the first block of calculating the syndrome of error 3, the second block of calculating the syndrome of error 4, memory block 5, adder 6, output 7.

The device operates as follows.

At the input 2 of the device a controlled number is presented, presented in polynomial form:

where α _i (z) is the remainder of A (z) modulo P _i (z); P _i (z), ..., P _n (z) - working grounds; P _{n + 1} (z), P _{n + 2} (z) - control bases.

This vector A (z) = (α ₁ (z), α ₂ (z), ..., α _n (z), α _{n + 1} (z), α _{n + 2} (z) is written in register 1. The input of the first block of the calculation of the syndrome of error 3 from the outputs of register 1 is fed:

With the formation of a signal at its output:

Wherein:

α ^* _{n + 1} (z) = λ ⁽¹⁾ ₁ α ₁ (z) + λ ⁽¹⁾ ₂ α ₂ (z) + ... + λ ⁽¹⁾ _n α _n (z),

where λ ⁽¹⁾ ₁ are the constants of the system.

The inputs of the second block of the calculation of the syndrome of error 4 from the outputs of register 1 are fed:

With the formation of a signal output:

Wherein:

α ^* ₂ (z) = λ ⁽²⁾ ₁ α ₁ (z) + λ ⁽²⁾ ₂ α ₂ (z) + ... + λ ⁽²⁾ _n α _n (z),

where λ ⁽²⁾ ₁ are the constants of the system.

The values of δ ₁ (z) and δ ₂ (z) in binary form are fed to the inputs of the memory unit 5 and the corresponding error constant is selected from there. This error constant enters the adder 6, where it is summed with the distorted A (z), presented outside the positional form, from register 1, the corrected representation A (z) from the output of the adder 6 is fed to the output 7 of the device.

As an example, consider the extended Galois field GF (2 ⁴ ), in which the following bases are defined:

P ₁ (z) = z + 1

P ₂ (z) = z ² + z + 1

P ₃ (z) = z ⁴ + z ³ + z ² + z + 1,

where P ₁ (z), P ₂ (z) and P ₃ (z) are the working grounds,

P ₄ (z) = z ⁴ + z ³ +1

P ₅ (z) = z ⁴ + z + 1,

and P ₄ (z) and P ₅ (z) are the control bases.

We have:

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,

B ₃ (z) = z ¹⁴ + z ¹³ + z ¹² + z ¹¹ + z ⁹ + z ⁸ + z ⁷ + z ⁶ + 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,

B _slave (z) = z ⁷ + z ⁶ + z ⁵ + z ² + z + 1,

Then,

B ₁ (z) = (z ⁷ + z ⁴ + z ² + z) P _slave (z) + z ⁶ + z ⁴ + z ³ + z ² +1,

B ₂ (z) = (z ⁷ + z ⁵ + z ² + z + 1) _Slave (z) + z ⁶ + z ⁵ + z + 1,

B ₃ (z) = (z ⁷ + z ⁴ + z ³ + z + 1) P _slave (z) + z ⁵ + z ⁴ + z ³ + z ² + z + 1,

B ₄ (z) = (z ⁷ + z ⁴ + z ³ ) P _slave (z),

B ₄ (z) = (z ⁵ + z ⁴ + z) P _slave (z).

If the polynomial A (z) P is a _slave , then it is true:

(α ₁ (z), α ₂ (z), α ₃ (z)) = (α ₁ (z), α ₂ (z), α ₃ (z), α ₄ (z), α ₅ (z) ),

where the left side of the equality is represented by the working bases P ₁ (z), P ₂ (z), P ₃ (z), and the right - by the polynomial base system P ₁ (z), P ₂ (z), P ₃ (z) , P ₄ (z), P ₅ (z) of the extended Galois field GF (2 ⁴ ).

Then according to the Chinese remainder theorem

Hence,

and

where B ^* _i (z) are orthogonal bases without an excess system of the residue class on the bases P ₁ (z), P ₂ (z), P ₃ (z).

Based on the condition that α ₁ (z) is represented in the form of a binary positional code, then the expression (7) and (8) can be represented in the form:

and

where α ^k _i - values of the k-th category of the i-th residue; k = 0, 1, ord p _i (z) -1; ord P _i (z) is the degree of the i-th base in PSCW.

и

представлены в таблице 1.Constant values

and

presented in table 1.

Table 1 Values α ^k _i (z) Grounds P ₄ (z) = z ⁴ + z ³ +1 P ₅ (z) = z ⁴ + z + 1 α ⁰ ₁ (z) z ³ + z + 1 z α ⁰ ₂ (z) z ² + z + 1 z ³ +1 α ¹ ₂ (z) z ³ + z z ² + z + 1 α ⁰ ₃ (z) z ³ + z ² +1 z ³ + z α ¹ ₃ (z) z + 1 z ² + z + 1 α ² ₃ (z) z z ³ α ³ ₃ (z) z ² z + 1

Then, the difference between the calculated values of α ^* ₄ (z) and α ^* ₅ (z), according to (2), and the remains of the polynomial A (z) belonging to α ₄ (z) and α ₃ (z) on the control bases P ₄ ( z) and P ₅ (z) form an error syndrome.

δ ₁ (z) ≡ α ₄ (z) -a ^* ₄ (z) mod P ₄ (z)

δ ₂ (z) ≡ α ₅ (z) -a ^* ₅ (z) mod P ₅ (z)

Thus, the first block of the calculation of the error syndrome implements the procedure

The second block of error syndrome calculation implements the procedure

If δ ₁ (z) = 0 and δ ₂ (z) = 0, then the non-positional representation of the polynomial A (z) does not contain an error. Otherwise, the location and depth of error are determined from the values of δ ₁ (z) and δ ₂ (z). Let a polynomial A (z) = (1, z + 1, z ³ + z ² + z + 1, z ³ + z ² +1, z ³ + z) be given. Define a convolution:

α ^* ₄ (z) = z ³ + z ² +1

α ^* ₅ (z) = z ³ + z

Define the syndrome of error:

δ ₁ (z) ≡ ((z ³ + z ² +1) + (z ³ + z ² +1)) mod P ₄ (z) = 0

δ ₂ (z) ≡ ((z ³ + z) + (z ³ + z)) mod P ₅ (z) = 0

Therefore, the initial combination (1, z + 1, z ³ + z ² + z + 1, z ³ + z ² +1, z ³ + z) does not contain an error. The memory block will contain the following error constants:

table 2 Base Mistake δ ₁ (z) δ ₂ (z) P ₁ (z) = z + 1 one z ³ + z + 1 z P ₂ (z) = z ² + z + 1 one z ² + z + 1 z ³ +1 z z ³ + z z ² + z + 1 P ₃ (z) = z ⁴ + z ³ + z ² + z + 1 one z ³ + z ² +1 z ³ + z z z + 1 z ² + z + 1 z ² Z z ³ z ³ z ² z + 1

Let a controlled value be fed to input 2 of the device:

A (z) = (1, z + 1, z ² + z + 1, z ³ + z ² +1, z ³ + z)

Then, according to expressions (9) and (10), we obtain:

α ^* ₄ (z) = z ² +1

α ^* ₅ (z) = z ³

Determine the error syndrome:

δ ₁ (z) ≡ (z ³ + z ² + z + z ² +1) mod (z ⁴ + z ³ +1) = z ³ + z + 1

δ ₂ (z) ≡ (z ³ + z + z ³ ) mod (z ⁴ + z + 1) = z

From the memory block 5, in accordance with δ ₁ = z ³ + z + 1 and δ ₂ = z, a quantity (1, 0, 0) is selected, which is added to the controlled number in the adder 6 with the formation of the output:

(1, z + 1, z ² + z + 1, z ³ + z ² + z, z ³ + z) + (1,0,0,0,0) = (0, z + 1, z ² + z + 1, z ³ + z ² + z, z ³ + z).

Note that if A (z) does not contain errors, then the values of the syndrome δ ₁ and δ ₂ are equal to zero. The use in the present invention of two blocks 3 and 4 of the calculation of the error syndrome allows us to simplify the device, because These blocks perform the function of a modular convolution block of a modular adder for each control base. In addition, the use of a two-layer network and the combination of calculation procedures α ^* ₄ (z) (α ^* ₄ (z)) and δ ₁ (z) (δ ₂ (z)) can increase the speed of the device.

The error syndrome calculation unit modulo P ₄ (z) = z ⁴ + z ³ +1 is shown in FIG. It is a two-layer neural network.

The first layer contains 11 neurons. At the inputs of neurons 8, 9-10, 11-14 in binary form, the residues α ₁ (z), α ₂ (z), α ₃ (z) along the working bases P ₁ (z), P ₂ (z), P ₃ (z). The binary code α ₄ (2) modulo P ₄ (z) = z ⁴ + z ³ +1 is supplied to neurons 15-18.

The second layer of the neural network contains 4 neurons performing the basic summation operation modulo 2, and the first neuron 2 of layer 23 is connected to the outputs 8, 9, 11, 12 and 15 of neurons of 1 layer. Neuron 2 of layer 24 is connected to the outputs of 8, 9, 10, 12, 13 and 16 neurons of 1 layer, neuron of 2 layer 25 is connected to the outputs of 9, 11, 14 and 17 neurons of 1 layer, and accordingly neuron of 2 layer 26 is connected to outputs 8 , 10, 11 and 18 neurons of 1 layer.

The error syndrome calculation unit modulo P ₅ (z) = z ⁴ + z + 1 is shown in FIG. It is a two-layer neural network.

The first layer contains 11 neurons. At the inputs of neurons 8, 9-10, 11-14 in binary form, the residues α ₁ (z), α ₂ (z), α ₃ (z) along the working bases P ₁ (z), P ₂ (z), P ₃ (z). The binary code α ₅ (z) modulo P ₄ (z) = z ⁴ + z + 1 is supplied to neurons 19-22.

The second layer of the neural network contains 4 neurons performing the basic summation operation modulo 2, and the first neuron 2 of layer 27 is connected to the outputs 9, 10, 12, 14 and 19 of neurons of 1 layer. A layer 2 neuron 28 is connected to the outputs of 8, 10, 11, 12, 14 and 20 layer 1 neurons, layer 2 neuron 29 is connected to the outputs of 10, 12 and 21 layer 1 neurons, and accordingly layer 2 neuron 30 is connected to outputs 9, 11 , 13 and 22 neurons of 1 layer.

Claims (1)

A device for detecting and correcting errors in a polynomial residue class system, comprising a register, the input of which is the device input, a memory unit and an output adder, the first, second, and third inputs of which are connected to the first, second, and third outputs of the register, and the fourth input is connected to the output of a memory block, characterized in that it contains two blocks for calculating the error syndrome for control reasons, the first output of the register connected to the first inputs of the blocks for calculating the error syndrome, and the second and t The third outputs of the register are connected respectively to the second outputs of the first and second blocks of calculating the error syndrome, the outputs of which are connected to the inputs of the memory block, the first block of calculating the error syndrome is made on a two-layer neural network and contains 11 neurons in the first layer, the inputs of which are binary residuals along three working and one control bases, the second layer of the neural network contains 4 neurons that perform the basic operation of summation modulo 2, the inputs of the first neuron of the second layer are connected to the output odes 1, 2, 4, 5 and 8 of the neurons of the first layer, the inputs of the second neuron of the second layer are connected to the outputs 1, 2, 3, 5, 6 and 9 of the neurons of the first layer, the inputs of the third neuron of the second layer are connected to the outputs 2, 4, 7 and 10 neurons of the first layer, the inputs of the fourth neuron of the second layer are connected to the outputs 1, 3, 4 and 11 of the neurons of the first layer, the outputs of the neurons of the second layer are the outputs of the first adder, the second block of the error syndrome calculation is performed on a two-layer neural network and contains 11 in the first layer neurons to the inputs of which binary residues are fed in m working and second control bases, the second layer of the neural network contains 4 neurons that perform the basic operation of summation modulo 2, the inputs of the first neuron of the second layer are connected to the outputs 2, 3, 5, 7 and 8 of the neurons of the first layer, the inputs of the second neuron of the second layer are connected with outputs 1, 3, 4, 5, 7 and 9 of the neurons of the first layer, the inputs of the third neuron of the second layer are connected to the outputs of 3, 5 and 10 neurons of the first layer, the inputs of the fourth neuron of the second layer are connected to the outputs of 2, 4, 6 and 11 neurons the first layer, the outputs of the neurons of the second layer are output the second block of error syndrome calculation.

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