RU2660609C1 - Pseudorandom code scale - Google Patents

Abstract

FIELD: measuring equipment.

SUBSTANCE: device contains an information track made in the form of gradations of a pseudo-random binary sequence of the maximum length of the period M=2ⁿ-1, constructed by means of a primitive polynomial h(x) degree, where n is the digit of scale, n information and k+1 corrective reading elements placed along the information track with angular steps, multiples of the quantum of the scale δ= 360°/M, with the possibility of obtaining from them M different (n+k+1) - bit code combinations, representing a correction code with correction of single and double error detection, k_d additional corrective reading elements placed along the information track with angular steps, multiples of the quantum of the scale δ, with the possibility of obtaining from them together with (n+k+1) reading elements M different (n+k+k_d+1) - bit code combinations, which representing a correction code with a double error correction, the outputs of the reading elements are pseudo-random code scale outputs.

EFFECT: increase of information reliability of pseudo-random code scale due to the formation of a correction code with double errors correction.

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Description

The invention relates to measuring equipment, in particular to analog-to-digital conversion, and in particular to the code scales of digital angle converters (CPU).

CPUs are used in various technical systems for a wide range of purposes. Naturally, the reliability of the converter affects the reliability of the entire system. The main components of the CPU are the code scale and reading elements. During the operation of the CPU, malfunctions of the reading elements are possible. In this case, information from the scale will be read with errors. To compensate for such errors, the CPUs are equipped with additional (corrective) reading elements, the number of which is determined by the scale capacity and the frequency of corrected errors. The solution to this problem is based on the use of the theory of codes that correct errors. The most suitable code scales in which corrective codes can be applied are pseudo-random code scales.

A known pseudo-random code scale (see Ozhiganov A.A., Lukyanov V.D. Code scales based on recurrence sequences for displacement transducers of increased information reliability // Sensors and Systems. - Moscow, 2012. - No. 2. - P. 13- 17) - [1], containing an information track made in the form of gradations of a pseudo-random binary sequence of the maximum period length M = 2 ⁿ -1, constructed by means of a primitive polynomial h (x) of degree n , where n is the scale capacity, n of information reading elements, posted along ormatsionnoy paths with angular steps which are multiples of the value scale quantum δ = 360 ° / M, to obtain them with M different n-bit codewords (see. Ozhiganov AA placement algorithm sensing elements on a pseudorandom code scale // Math. USSR universities Instrument Engineering, 1994. T. 37. No. 2. P. 22-27) - [2], k corrective reading elements placed along the information track with the possibility of receiving together with n information reading elements M different ( n + k ) - bit code combinations representing Dr. Hemming with detection and correction of a single error.

The disadvantage of this scale is the low information reliability, since it does not provide the opportunity not only to correct, but even to detect double errors.

The closest technical solution and chosen by the authors for the prototype is a pseudo-random code scale (see. Pseudo-random code scale. Patent RU 2510572 C1, IPC Н03М 1/24. Published: 03/27/2014. Bull. No. 9) - [3], containing information a track made in the form of gradations of a pseudorandom binary sequence of the maximum period length M = 2 ⁿ -1, constructed by means of a primitive polynomial h (x) of degree n , where n is the scale capacity, n of information reading elements located along the information track with angular steps, multiples of the quantum of the scale δ = 360 ° / M , with the possibility of obtaining from them M different n bit code combinations, k corrective reading elements located along the information track with the possibility of receiving together with n information reading elements M different ( n + k ) - bit codewords representing the Hamming code detecting and correcting a single error, the read control member disposed along the information track to derive from it, together with (n + k) MF Pipeline various elements M (n + k +1) - bit codewords representing the Hamming code correcting single and double error detection, the outputs of n information sensing elements outputs k correcting sensing elements and an output controlling the read element are the outputs of the pseudorandom code scale.

The disadvantage of the prototype is the low information reliability, since it does not provide the ability to correct double errors.

The present invention solves the problem of increasing the information reliability of the pseudo-random code scale by generating corrective codes from it with correction of double errors.

To achieve a technical result, the pseudo-random code scale contains an information track made in the form of gradations of a pseudo-random binary sequence of the maximum period length M = 2 ⁿ -1, constructed by means of a primitive polynomial h (x) of degree n , where n is the scale capacity, n information and k + 1 corrective reading elements located along the information track with angular steps that are multiples of the quantum of the scale δ = 360 ° / M , with the possibility of obtaining from them M different ( n + k +1) - bit code combinations, representing a correction code with the correction of a single and the detection of a double error, k _d additional corrective reading elements located along the information track with angular steps that are multiples of the quantum of the scale δ, with the possibility of receiving together with ( n + k +1) reading elements M different ( n + k + k _d +1) - bit code combinations, which are a correcting code with double error correction, the outputs of the readout elements are the outputs of the pseudo-random code scale.

New in the invention is:

- supply of a pseudo-random code scale k _{d with} additional corrective reading elements;

- appropriate placement of all readout elements along the information track with angular steps that are multiples of the quantum of the scale δ, with the possibility of obtaining from them M different ( n + k + k _d +1) - bit code combinations, which are a correction code with the detection and correction of double mistakes.

The set of essential features in the present invention has improved the information reliability of the pseudo-random code scale.

As a result of this, we can conclude that the invention has an inventive step and allows to obtain a technical result.

The invention is new, since the prior art on available sources of information did not reveal analogues with a similar set of features.

The invention is industrially applicable, as it can be used in all areas where high-precision positional determination of the angular position of an object is required using digital angle converters of increased information reliability based on the claimed pseudo-random code scales.

The invention is illustrated in FIG. 1, which shows a linear scan of a circular five-digit pseudo-random code scale.

The inventive pseudo-random code scale contains an information code track 1, information reading elements 2, 3, 4, 5, 6 ( n = 5), correcting reading elements 7, 8, 9, 10, 11, 12, 13, 14 ( k = 8 )

To clarify the essence of the invention, we give some theoretical background.

In [1, 2 and 3], as well as in (see Ozhiganov A.A. Pseudorandom code scales // Izv. Universities of the USSR. Instrument Making, 1987. V. 30. No. 2. P. 40-43) - [4 ] the code scales used in the invention, called pseudo-random (PSCS), and constructed on the basis of the theory of M-sequences, are considered. PCSS have only one information code track, made in accordance with the symbols M - the sequence a = a ₀ a ₁ ... a _{M -1} and n information reading elements (SE), located along the track. Reading elements make it possible to obtain, with a full turn of the scale M = 2 ⁿ -1, various n- digit code combinations, which provides the resolution of the PCSH δ = 360 ° / M. In general terms, the problem of placing informational SCs on PCSS was solved in [2].

To generate an M-sequence with a period of M = 2 ⁿ -1, a primitive irreducible polynomial h (x) of degree n with Galois field coefficients GF (2) is used (see Macuilliams FD, Sloan ND Pseudorandom sequences and tables / / TIIER. 1976. T. 64. No. 12. P. 80-95) - [5], i.e.

The symbols of the M-sequence a _{n + j} satisfy the recurrence expression

означает суммирование по модулю два, а индексы при символах М-последовательности берутся по модулю М. Начальные значения символов М-последовательности a ₀ a ₁ …a _{n -1} могут выбираться произвольно, за исключением нулевой комбинации. Для определенности при построении круговой ПСКШ символы М-последовательности a ₀ a ₁ …a _{M - 1} отображаются на информационной дорожке по ходу часовой стрелки.where is the sign

means summation modulo two, and the indices for the symbols of the M-sequence are taken modulo M. The initial values of the symbols of the M-sequence a ₀ a ₁ ... a _{n -1} can be chosen arbitrarily, with the exception of the zero combination. For definiteness, when constructing a circular PCSS, the symbols of the M-sequence a ₀ a ₁ ... a _{M - 1 are} displayed on the information track clockwise.

M-sequences belong to the class of cyclic codes and can be specified using the generating polynomial g (x) = ( x ^M +1) / h (x) , where h (x) is determined in accordance with the expression (1), M = 2 ⁿ -one.

For each M-sequence of length M, there are exactly M different cyclic shifts that can be obtained by multiplying the generating polynomial g (x) by x ^j , where j = 0,1, ..., M -1.

М-последовательности.Since PCSS are constructed in accordance with the symbols of the M-sequence, it is possible by cyclic shifts to determine the order in which n information reading elements are placed on the scale, i.e. m- th FE, m = 1,2, ..., n , is mapped to j _m- th cyclic shift

M-sequences.

Then the polynomial that determines the order of placement of n informational FEs on the scale has the form:

Setting j ₁ = 0, according to polynomial (3), we obtain the positions of the 2nd, 3rd, ..., n- th information SCs shifted relative to the first SC by j ₂ , j ₃ , ..., j _n quanta of the information track of the scale, respectively.

In the table. Figure 1 shows polynomials h (x) up to n = 11 inclusive, which can be used to generate the corresponding M-sequences [5].

Let us explain the embodiment of the PCSS shown in FIG. one.

In the example, for simplicity, n = 5 is taken and, accordingly, from the table. 1, a primitive irreducible polynomial h (x) = x ⁵ + x ² +1 is chosen, where h ₀ = h ₂ = h ₅ = 1, h ₁ = h ₃ = h ₄ = 0. Here, the period of the M-sequence is M = 2 ⁵ -1 = 31, and the M-sequence itself is a = a ₀ a ₁ ... a _{2 9} a _{3 0} = 0000100101100111110001101110101. For the initial values of the M-sequence a ₀ = a ₁ = a ₂ = a ₃ = 0, and ₄ = 1, the remaining characters of the sequence are obtained in accordance with the recurrence relation (2), which in this example has the form a _{5+ j} = a _{2 + j} ⊕ a _j , j = 0,1, ..., 25. The placement of the five information reading elements SE ₁ (in Fig. Position 2), SE ₂ (in Fig. Position 3), SE ₃ (in Fig. Position 4), SE ₄ (in Fig. Position 5) and SE ₅ (in Fig. . position 6) along the information track of the scale is set according to (3) by the polynomial r _u (x) = 1 + x + x ² + x ²⁹ + x ³⁰ .

When constructing the information track 1, the M-sequence with a period of M = 31 should be plotted on the scale in the form of passive (zeros of the M-sequence) and active (units of the M-sequence) sections of the information track, for example, clockwise, and on the information track scale is applied only one period of the M-sequence. M-sequence with a period of M = 2 ⁿ -1 determines the number of quanta of the information track of the scale, which in this example is equal to M = 31. Hence, the quantum value is δ = 360 ° / M = 360 ° / 31 = 11.6129032280645 °. Information reading elements, number 5, should be placed along the information track according to r (x) with an angular step that is a multiple of the quantum of the scale δ, for example, clockwise. Moreover, SE _{1 is} set exactly at the beginning of the scale, SE ₂ - with a shift of 1 quantum relative to the beginning of the scale, SE ₃ - with a shift of 2 quanta relative to the beginning of the scale, SE ₄ - with a shift of 29 quanta relative to the beginning of the scale, and SE ₅ - with a shift of 30 quanta relative to the beginning of the scale. Note that other options for placing informational solar cells along the track of the scale are also possible [2].

Consistently fixing five-digit code combination by informational SCs when moving the scale one quantum counterclockwise, we get 31 different five-digit code combination. These code combinations corresponding to 31 different angular positions of the PCSS are shown in Table. 2.

The technical result of the invention (improving information reliability) is achieved through the use of cyclic corrective codes with the correction of double errors known by:

Bleikhut R. Theory and practice of error control codes: Per. from English - M .: Mir, 1986 .-- 576 p. - [6];

Peterson W., Weldon E. Error Correcting Codes: Per. from English - M .: Mir, 1976 .-- 594 p. - [7];

Coding Theory / T. Kasani, N. Takura, E. Ivadari, Y. Inagaki: Transl. with japan. - M .: Mir, 1978.- 576 p. - [8].

In order for the correction code to be able to correct double errors, its minimum code distance must be at least 5, i.e. d ≥5. Methods for generating corrective codes with d ≥5 are considered in detail in [6, 7, 8] and other available literature on coding theory.

In our example, the number of information symbols is n = 5 (this is a five-digit code that is removed from 5 informational SEs).

To obtain a correction code with d ≥5, the generator of the cyclic code polynomial g (x) = 1 + x + x ³ + x ⁴ + x ⁸ with the number of significant terms equal to 5 is selected.

Further, by means of the generating polynomial g (x) = 1 + x + x ³ + x ⁴ + x ⁸ , the generating matrix of the cyclic correction code is formed

For each column of the matrix G , the numbers of cyclic shifts M are determined — the sequences used to find installation locations on the SC scale.

Then the placement polynomial of corrective FE will have the form (determined by columns 4 ÷ 11) r _k (x) = x ⁶ + x ⁷ + x ⁸ + x ¹⁰ + x ¹⁶ + x ¹⁷ + x ¹⁹ + x ²⁴ .

The placement polynomial of both informational and corrective FE r (x) = r _u (x) + r _k (x) = 1 + x + x ² + x ⁶ + x ⁷ + x ⁸ + x ¹⁰ + x ¹⁶ + x ¹⁷ + x ¹⁹ + x ²⁴ + x ²⁹ + x ³⁰ .

Therefore, corrective SC, number 8, should be placed along the information track according to r _k (x) with angular steps that are multiples of the quantum of the scale δ, for example, clockwise. Moreover, SSC _{1 is} set relative to the beginning of the scale with a shift of 6 quanta, SSC ₂ - with a shift of 7 quanta, SSC ₃ - with a shift of 8 quanta, SSC ₄ - with a shift of 10 quanta, SSC ₅ - with a shift of 16 quanta, KSE ₆ with a shift of 17 quanta, KSE ₇ with a shift of 19 quanta, and KSE ₈ with a shift of 24 quanta.

The placement of solar cells, determined according to the above procedure, is not the only possible, since any non-trivial linear combination of rows of the matrix G defines a block code with similar characteristics.

Consistently fixing thirteen-digit code combination with information and corrective FE when moving the scale one quantum counterclockwise, we get 31 different thirteen-digit code combinations of a cyclic correction code with a minimum code distance of d = 5. It is known [6, 7, 8] that such a code allows correcting a double error. These code combinations corresponding to 31 different angular positions of the PCSS are shown in Table. 3.

Thus, in the present invention, the problem of increasing the information reliability of the PCSS by solving correcting codes with correcting double errors is solved from it. As noted earlier, under the error in the operation of the CPU based on PCSS in the present invention refers to the failure of the reading elements. Another application of the invention is its use where information from a PCB based CPU should be directly transmitted to the processing device via a communication channel subject to interference.

The proposed PCSS can be the basis for the construction of a CPU with increased information reliability. In turn, it is advisable to use such converters in various control systems for aircraft or special-purpose equipment, where ensuring the reliability of their operation is a paramount requirement.

Literature

1. Ozhiganov A.A., Lukyanov V.D. Code scales based on recurrence sequences for displacement transducers of increased information reliability // Sensors and Systems. - Moscow, 2012. - No. 2. - S. 13-17.

2. Ozhiganov A.A. Algorithm for placing reading elements on a pseudo-random code scale // Izv. universities of the USSR. Instrument Engineering, 1994. T. 37. No. 2. S. 22-27.

3. Pseudo-random code scale. Patent RU 2510572 C1, IPC Н03М 1/24. Published: 03/27/2014. Bull. No. 9. - The prototype.

4. Ozhiganov A.A. Pseudorandom code scales // Izv. universities of the USSR. Instrument Engineering, 1987. T. 30. No. 2. S. 40-43.

5. McWilliams FD, Sloan ND Pseudorandom sequences and tables // TIIER. 1976.V. 64. No. 12. S. 80-95.

6. Bleikhut R. Theory and practice of error control codes: Per. from English - M .: Mir, 1986 .-- 576 p.

7. Peterson W., Weldon E. Codes for correcting errors: Per. from English - M .: Mir, 1976 .-- 594 p.

8. The coding theory / T. Kasani, N. Takura, E. Ivadari, Y. Inagaki: Trans. with japan. - M .: Mir, 1978.- 576 p.

Claims (1)

A pseudo-random code scale containing an information track made in the form of gradations of a pseudo-random binary sequence of maximum period length M = 2 ⁿ -1, constructed by means of a primitive polynomial h (x) of degree n, where n is the scale capacity, n information and k + 1 corrective reading elements placed along the information track with angular steps that are multiples of the quantum of the scale δ = 360 ° / M, with the possibility of obtaining from them M different (n + k + 1) -bit code combinations, which are a correction code with spravleniya single and detecting double errors, characterized in that the pseudo-random code scale is provided with k _d is further corrected with reading elements arranged along the information track with angular steps which are multiples of the value of the quantum δ scale, to derive from them, together with (n + k + 1) read element M different (n + k + k _d + 1) -bit codewords representing code correction double error correction, outputs the read elements are the outputs of the pseudorandom code w Ala.

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