RU2761058C1 - Pseudo-random code scale - Google Patents

Abstract

FIELD: measuring technology.SUBSTANCE: invention relates to measuring technology. The pseudo-random code scale contains an information track made in the form of gradations of a pseudo-random binary sequence of the maximum length of the period М=2n-1, built by means of a primitive polynomial h(x) of degree n, where n is the capacity of the scale, n informational and (k+kb+3) corrective reading elements placed along the information track with angular steps that are multiples of the scale quantum δ=360°/М, with the possibility of obtaining from them M different (n+k+kb+3) - bit code combinations, representing a correction code with the possibility of correcting triple errors, the outputs of the reading elements are the outputs of a pseudo-random code scale.EFFECT: increasing the information reliability of the pseudo-random code scale.1 cl, 3 tbl, 1 dwg

Description

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

CPUs are used in various technical systems for a wide variety 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 readout elements. During the operation of the CPU, the reading elements may fail. In this case, information from the scale will be read with errors. To compensate for such errors, the CPU is equipped with additional (correcting) readout elements, the number of which is determined by the capacity of the scale and the frequency of corrected errors. The solution to this problem is based on the use of the theory of error-correcting codes. The most suitable code scales in which correction codes can be applied are pseudo-random code scales.

Known pseudo-random code scale (see. Pseudo-random code scale. Patent RU 2660609 C1, IPC N03M 1/24. Published: 06.07.2018. Bull. No. 19.) - [1], containing an information track made in the form of gradations of a pseudo-random binary sequence the maximum length of the period М = 2 ⁿ -1, constructed by means of a primitive polynomial h (x) of degree n, where n is the capacity of the scale, n information reading elements (see A.A. Ozhiganov, Algorithm for placing reading elements on a pseudo-random code scale, Izv. Universities of the USSR Instrument Engineering, 1994. V. 37. No. 2. P. 22-27.) - [2], (k + 1) correcting reading elements, k _d additional correcting reading elements, where all reading elements are located along the information tracks with angular steps, 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 a double error correction, outputs The elements are the outputs of the pseudo-random code scale.

The disadvantage of such a scale is low information reliability, since it does not provide the ability to detect and correct triple errors.

The closest in technical solution and chosen by the authors for the prototype is a pseudo-random code scale (see. Pseudo-random code scale. Patent RU 2709666 C1, IPC Н03М 1/24 (2006.01). Published: 19.12.2019. Bull. No. 35.) - [ 3], containing an information track, made in the form of gradations of a pseudo-random binary sequence of the maximum length of the period M = 2 ⁿ -1, built by means of a primitive polynomial h (x) of degree n, where n is the capacity of the scale, n informational and (k + k _d + 2) correcting 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 + k _d +2) - bit code combinations, which are correcting code with the possibility of correcting double and (or) detecting triple errors, the outputs of the reading elements are the outputs of a pseudo-random code scale.

The disadvantage of the prototype is its low informational reliability, since it does not provide the possibility of correcting triple errors.

The proposed invention solves the problem of increasing the information reliability of a pseudo-random code scale by generating correcting codes from it with the possibility of correcting triple errors.

To achieve the technical result, the pseudo-random code scale (the essence of the invention) contains an information track made in the form of gradations of a pseudo-random binary sequence of the maximum length of the period M = 2 ⁿ -1, built by means of a primitive polynomial h (x) of degree n, where n is the capacity of the scale, n information and (k + k _d +3) 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 + k _d +3 ) - bit code combinations, representing a correcting code with the ability to correct triple errors, the outputs of the reading elements are the outputs of a pseudo-random code scale.

New in the proposed invention is:

- supplying the pseudo-random code scale with an additional correcting reading element;

- appropriate placement of all reading elements along the information track with angular steps that are multiples of the quantum of the δ scale, with the possibility of obtaining from them M different (n + k + k _d +3) - bit code combinations, which are a correction code with the possibility of correcting triple errors ...

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

As a result, it can be concluded that the proposed invention has an inventive step and allows you to obtain a technical result.

The invention is new, since no analogues with a similar set of features have been identified from the prior art according to available sources of information.

The invention is industrially applicable, since 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 with increased information reliability based on the claimed pseudo-random code scales.

The invention is illustrated by the figure, which shows a linear scan of a circular five-bit pseudo-random code scale.

The claimed 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, 15, 16 number 10.

To clarify the essence of the invention, we present some theoretical prerequisites.

In [1, 2 and 3], as well as in (see Ozhiganov AA Pseudo-random code scales // Proceedings of the USSR Universities. Instrument-making, 1987. V. 30. No. 2. P. 40-43) - [4 ], the code scales used in the invention are considered, which are called pseudo-random (PSCS), and are built on the basis of the theory of M - sequences. PSSCH 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. The reading elements make it possible to obtain, at a full turn of the scale M = 2 ⁿ -1, various n-bit code combinations, which ensures the resolution of the PSCS δ = 360 ° / M. In general, the problem of placing information ESSs on PSCS was solved in [2].

To generate an M-sequence with a period M = 2 ⁿ -1, a primitive irreducible polynomial h (x) of degree n with the coefficients of the Galois field GF (2) is used (see McWuillams F.D., Sloan N.D. Pseudo-random sequences and tables / / ТИИЭР. 1976. T. 64. No. 12. S. 80-95) - [5], i.e.

The symbols of the M-sequence a _{n + J} satisfy the recursive expression

означает суммирование по модулю два, а индексы при символах М-последовательности берутся по модулю М. Начальные значения символов М-последовательности a₀a₁…..a_n-1 могут выбираться произвольно, за исключением нулевой комбинации. Для определенности при построении круговой ПСКШ символы М-последовательности a₀a₁…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 PSCS, the symbols of the M-sequence a ₀ a ₁ ... a _{M-1 are} displayed on the information track in a clockwise direction.

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 expression (1), M = 2 ⁿ -one.

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

Since PSCS are constructed in accordance with the symbols of the M-sequence, it is possible, by means of cyclic shifts, to determine the arrangement order of n information reading elements on the scale, i.e. The m-th SE, m = 1, 2, ..., n, is assigned to the j _m- th cyclic shift x ^jm g (x) of the M-sequence.

Then the polynomial that determines the order of placement of n information SEs on the scale has the form:

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

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

Let us explain the variant of constructing the PSCS, shown in the figure of graphic materials.

In the example, for simplicity, n = 5 is taken and, accordingly, from table. 1, a primitive irreducible polynomial h (x) = x ⁵ + x ³ +1 is chosen, where h ₀ = h ₃ = h ₅ = 1, h ₁ = h ₂ ⁼ 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 ₂₉ a ₃₀ = 0000101011101100011111001101001. With the initial values of the M-sequence a ₀ = a ₁ = a ₂ = a ₃ = 0, and ₄ = 1, the remaining symbols of the sequence are obtained in accordance with the recurrence relation (2), which in this example has the form a _{5 + j} = a _{3 + j} ⊕a _j , j = 0, 1, ..., 25. Placement of five information reading elements SE ₁ (in the figure, position 2), SE ₂ (in the figure, position 3), SE ₃ (in the figure, position 4), SE ₄ (in the figure, position 5) and SE ₅ (in the figure, 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 ³ + x ³⁰ .

When constructing 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 only one period of the M-sequence is applied to the scale. The M-sequence with the period 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 quantum value δ = 360 ° / M = 360 ^0/31 = 11.6129032280645 ^0. 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 value of the quantum of the δ scale, 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 3 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 information SE along the track of the scale are also possible [2].

Sequentially fixing a five-bit code combination with information SEs when moving the scale one quantum counterclockwise, we get 31 different five-bit code combinations. These code combinations, corresponding to 31 different angular positions of the PSCS, are given in table. 2.

The technical result of the claimed invention is to improve information reliability. The technical result is achieved through the use of cyclic correcting codes with correcting triple errors known from:

- Bleihut 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. Iwadari, J. Inagaki: Per. from japan. -M .: Mir, 1978 .-- 576 p. - [eight].

In order for the correcting code to have the ability to correct triple errors, its minimum code distance must be at least 7, i.e. d≥7. Methods for generating correction codes with d≥7 are discussed 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 information SE).

To obtain a correction code with d≥7, the generating polynomial of the cyclic code g (x) = l + x + x ² + x ⁴ + x ⁵ + x * + x ¹⁰ is selected with the number of significant terms equal to 7.

Further, by means of the generating polynomial g (x) = l + x + x ² + x ⁴ + x ⁵ + x ^g + x ¹⁰ , the generating matrix of the cyclic correcting code is formed

For each column of the matrix G, the numbers of cyclic shifts of the M-sequence are determined, which are used to find the installation locations on the SE scale.

Then the polynomial for the placement of corrective SE will have the form (determined by columns 5 ÷ 14) r _k (x) = x ⁶ + x ⁷ + x ⁹ + x ¹² + x ¹⁹ + x ²¹ + x ²² + x ²³ + x ²⁵ + x ²⁶ .

The polynomial of placement of both informational and corrective SE is r (x) = r _u (x) + r _k (x) = 1 + x + x ² + x ³ + x ⁶ + x ⁷ + x ⁹ + x ¹² + x ¹⁹ + x ²¹ + x ²² + x ²³ + x ²⁵ + x ²⁶ + x ³⁰ .

Therefore, the correcting SEs, 10 in number, must be placed along the information track according to r _k (x) with angular steps that are multiples of the quantum of the δ scale, for example, clockwise. Moreover, QSE _{1 is} set relative to the beginning of the scale with a shift of 6 quanta, QSE ₂ - with a shift of 7 quanta, QSE ₃ - with a shift of 9 quanta, _QSE4 - with a shift of 12 quanta, QSE ₅ - with a shift of 19 quanta, QSE ₆ - with a shift of 21 quanta, QSE ₇ - with a shift of 22 quanta, QSE ₈ - with a shift of 23 quanta, QSE ₉ - with a shift of 25 quanta, and QSE ₁₀ - with a shift of 26 quanta.

The SE placement performed according to the above procedure is not the only possible one, since any nontrivial linear combination of rows of the matrix G defines a block code with similar characteristics.

Sequentially fixing a fifteen-bit code combination with information and correcting SEs when moving the scale one quantum counterclockwise, we obtain 31 different fifteen-bit code combinations of a cyclic correcting code with a minimum code distance d≥7. It is known from [6, 7, 8] that such a code allows one to correct a triple error. These code combinations, corresponding to 31 different angular positions of the PSCS, are given in table. 3.

Thus, the proposed invention solves the problem of increasing the information reliability of the PSCS by generating correcting codes from it with the possibility of correcting triple errors. As noted earlier, an error in the operation of the CPU based on the PSCS is understood as the failure of the reading elements. Another application of the contemplated invention is its use where information from the CPU based on the PSCR is to be directly transmitted to the processing device over a communication channel subject to interference.

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

Sources of information

1. Pseudo-random code scale. Patent RU 2660609 C1, IPC Н03М 1/24. Published: 06.07.2018. Bul. No. 19.

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

3. Pseudo-random code scale. Patent RU 2709666 C1, IPC Н03М 1/24 (2006.01). Published: 19.12.2019. Bul. No. 35 - Prototype.

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

5. Macwilliams F.D., Sloan N.D. Pseudo-random sequences and tables // ТИИЭР. 1976. T. 64. No. 12. S. 80-95.

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

7. Peterson W., Weldon E. Error-correcting codes: Per. from English - M .: Mir, 1976 .-- 594 p.

8. Coding theory / T. Kasani, N. Takura, E. Iwadari, J. Inagaki: Per. from 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 the maximum length of the period M = 2 ⁿ -1, built by means of a primitive polynomial h (x) of degree n, where n is the capacity of the scale, n informational and (k + k _d +2) 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 + k _d +2) - bit code combinations, which are a correcting code with the possibility of correcting double and (or) detecting triple errors, characterized in that the pseudo-random code scale is equipped with an additional correcting reading element located along the information track with an angular step that is a multiple of the magnitude of the quantum of the δ scale, with the possibility of obtaining from it, together with (n + k + k _q + 2) reading elements of M different (n + k + k _q +3) - bit code combinations, which are Correcting code with the ability to correct triple errors, the outputs of the reading elements are the outputs of a pseudo-random code scale.

Images