RU2319308C1 - Cyclic code synchronization method - Google Patents

Abstract

FIELD: electric communications, possible use for synchronization of message, which is transmitted as a series of words of cyclic code of primitive length under conditions of parametric indeterminacy, demonstrated by absence of any data about coder structure with the exception of code base and code word length.

SUBSTANCE: cyclic code synchronization method includes receiving discrete series of code word symbols using a receiver of discrete information, a fragment of discrete series is extracted which has length equal to length of code word, discrete Fourier-Galois transform is performed over the fragment and presence of synchronous state of discrete information receiver is determined using synchronous state criterion. Synchronous state criterion for the discrete information receiver is the equality to zero of at least one spectral component in the spectrum of the extracted fragment. In case when synchronization is absent before it is established, synchronous state is found by means of successive shifting of received series for one symbol towards one and the same side with following extraction of a new fragment, its discrete Fourier-Galois transform and detection of receiver synchronous state presence based on the synchronous state criterion. After detection of synchronous state criterion, validity check of synchronous state establishment is additionally performed according to presence of phasing validity indication. For that purpose, at least four fragments of the same length are extracted, which are positioned serially after the fragment, extracted at the stage of synchronous state detection, discrete Fourier-Galois transform is performed over additionally selected fragments and presence of phasing validity indication is determined. As phasing validity indication, non-empty intersection of sets of zero component numbers in resulting spectrums is considered. In case when phasing validity indication is absent, the search for synchronous state is continued starting at the moment when synchronous state criterion is fulfilled.

EFFECT: increased number of codes being synchronized under conditions of parametric indeterminacy, apparent from absence of any data about coder structure with the exception of code base and code word length.

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Description

The invention relates to telecommunications and can be used for loop synchronization when receiving transmissions using block cyclic codes of primitive length, in the conditions of parametric uncertainty of the encoder structure.

A known method of code cyclic synchronization in the transmission of information by noise-resistant block codes (phasing according to words) based on the method of successive shifts, which consists in the fact that the received discrete sequence of characters is fed to the input of the discrete information receiver, after which its state is analyzed. In this case, two states are distinguished: synchronous, in which information about the beginning of code combinations is exactly known, and asynchronous, when information about the beginning of code combinations in the received sequence is unknown. As a sign of a synchronous state, the syndrome is equal to zero. In the case of a decision on the asynchronous state, one character is shifted along the received sequence in the same direction. Shifts are made until only code combinations are detected. In this case, a decision is made about the presence of a synchronous state and the process of entering synchronism ends [Losev V.V., Brodskaya E.B., Korzhik V.I. Search and decoding of complex discrete signals. / Ed. V.I.Korzhika. - M .: Radio and communications, 1988, p.132-134].

However, this method cannot be used in the case of parametric uncertainty in the structure of the error-correcting codec encoder, since the calculation of the syndrome requires knowledge of the code check matrix or the generating polynomial [Clark J., Jr., Kane J. Coding with error correction in digital communication systems: Per. from English - M .: Radio and communications, 1986, p. 81; Bleikhut R. Theory and practice of error control codes: Per. from English / Ed. K.Sh. Zigangirova. - M .: Mir, 1986, p.119].

Closest to the proposed method is a method of code cyclic synchronization of Reed-Solomon codes, which consists in the fact that the received discrete sequence of characters is fed to the input of the receiver of discrete information, after which its state is analyzed. In this case, two states are distinguished: synchronous, in which information about the beginning of codewords is exactly known, and asynchronous, when information about the beginning of codewords in the received sequence is unknown. The analysis of the receiver state is based on the calculation of the discrete Fourier Galois transform (DPFG) of the received discrete sequence along the length of the code word. As a sign of a synchronous state, the excess of the number of zero components in the spectra over a threshold value is used [I. Zaitsev Formation of signs for phasing Reed-Solomon codes under conditions of parametric uncertainty of the encoder structure. - News of universities. Instrument making. 1998. T.41, No. 8, p.16]. If a decision is made about the asynchronous state, one character is shifted along the received sequence in the same direction. Shifts are made until a synchronous state is established. Adopted for the prototype.

However, as a result of simulation modeling of the operation of this method on a computer for code synchronization of binary cyclic codes of primitive length [Bleikhut R. Theory and practice of error control codes: Per. from English / Ed. K.Sh. Zigangirova. - M .: Mir, 1986, p.122] it is established that the probability of false phasing sharply increases, ie there is no synchronous state in the presence of a sign, which does not allow the use of this method with respect to binary cyclic codes of primitive length.

Thus, the disadvantage of the prototype (the method of code cycle synchronization based on the feature of the synchronous state of the receiver of discrete information by the excess of the number of zero spectral components over the threshold value) is that it applies only to the Reed-Solomon code.

The technical result is an increase in the number of synchronized codes with respect to the prototype under conditions of parametric uncertainty (only the length of the code word n and the base of the code q are known) and the expansion of the arsenal of tools for similar purposes.

To achieve the technical result in the method of code cycle synchronization, an input discrete sequence of symbols of code words of a cyclic code of primitive length is received using a discrete information receiver, and then its state is analyzed. In this case, two states are distinguished: synchronous, in which the information about the beginning of codewords is exactly known, and asynchronous, when information about the beginning of codewords in the received sequence is unknown. An analysis of the receiver state is made on the basis of a synchronous state by isolating a fragment of length n from the received discrete sequence and calculating the DPSF of this fragment. A sign of the synchronous state of the receiver of discrete information is the vanishing of at least one spectral component in the spectrum of the selected fragment. After identifying this feature, additionally check the truth of the establishment of a synchronous state by the presence of a sign of the truth of phasing. To do this, select at least four fragments of the same length, sequentially located behind the fragment selected at the stage of determining the synchronous state, perform a discrete Fourier Galois transformation of the additionally selected fragments, and determine if there is a sign of true phasing. As a sign of the true phasing, a nonempty intersection of the sets of numbers of zero components in the obtained spectra is used.

As a result of simulation modeling of the operation of this method on a computer for code synchronization of a cyclic code of primitive length, it was found that when analyzing the state of the receiver, it is necessary to isolate and DPFG at least five fragments.

In the absence of synchronization (asynchronous state of the receiver), until it is established, a synchronous state is searched. To do this, make a sequential shift in the received sequence by one symbol in the same direction, followed by the selection of a new fragment, its DPFG and the presence of a synchronous state of the receiver based on the status of a synchronous state, as well as checking the truth of the synchronous state based on the truth of phasing if a sign is detected synchronous state. In the absence of a sign of true phasing, the search for a synchronous state is resumed from the moment a sign of a synchronous state is detected.

In common with the prototype is that using a discrete information receiver, an input discrete sequence is taken, which is sequentially transmitted codeword symbols, a fragment of a discrete sequence equal to the length of the codeword is selected, its DPFG is performed, and the presence of the synchronous state of the discrete information receiver is determined by the sign of the synchronous state . In the absence of synchronization, before it is established, a synchronous state is searched by sequential shift of the received sequence by one symbol in the same direction, followed by the allocation of a new fragment, its DPFG and the presence of a synchronous state of the receiver based on the synchronous state.

The difference from the prototype is that, as a sign of the synchronous state of the receiver of discrete information, the equality to zero of at least one spectral component in the spectrum of the selected fragment is used. After identifying this feature, an additional verification of the truth of establishing a synchronous state by the presence of a sign of the truth of phasing is performed. To do this, select at least four fragments of the same length, sequentially located behind the fragment selected at the stage of determining the synchronous state, perform a discrete Fourier Galois transformation of the additionally selected fragments, and determine if there is a sign of true phasing. As a sign of the true phasing, a nonempty intersection of the sets of numbers of zero components in the obtained spectra is used. In the absence of a sign of the truth of phasing, the search for the synchronous state is resumed from the moment the sign of the synchronous state is detected.

Thanks to a new set of essential features, the technical result is manifested in the possibility of code cyclic synchronization of all types of cyclic codes of primitive length.

It is known [Bleikhut R. Theory and practice of error control codes: Per. from English / Ed. K.Sh. Zigangirova. - M .: Mir, 1986, p.248], that all code combinations of a cyclic code are allowed, in which all spectral components belonging to a given set of test frequencies are equal to zero. Thus, if the receiver is in a synchronous state, then, in the absence of errors, the spectra of all received codewords will contain zero spectral components with the same numbers, that is, you can find the set of zero components contained in each set of spectral components of all received words. In the presence of parametric uncertainty regarding the structure of the encoder, with the exception of the length of the code word and the base of the code, the set of test frequencies is unknown. In the prototype, in properties 1-3, [Zaitsev I.E. Formation of signs for phasing Reed-Solomon codes under conditions of parametric uncertainty of the encoder structure. - News of universities. Instrument making. 1998. Vol. 41, No. 8, pp. 14-16], it is shown that the number of zero components in the spectra of allowed codewords of the Reed-Solomon code does not depend on the choice of the generating code polynomial, the primitive element, and the irreducible polynomial by which the field is constructed. Therefore, in the prototype, the excess of the number of zero components over the threshold value is a sign of the synchronous state of the receiver of discrete information. However, as a result of simulation modeling of the operation of this method on a computer for code synchronization of binary cyclic codes of primitive length (the base of the code is two, the code word is 2 ^m -1, m is the degree of field expansion) it was found that the probability of false phasing sharply increases, i.e. e. there is no synchronous state in the presence of a sign. This does not allow the use of this method with respect to binary cyclic codes of primitive length, especially for codes with low correcting ability (with a small number of check characters in the code word and, therefore, with a small number of zero components in the spectrum). Therefore, to expand the class of synchronized codes, it is proposed to use other features. It is proposed to use the presence of at least one zero spectral component in the spectrum of the fragment selected from the received sequence in the spectrum as a sign of a synchronous state, which will allow synchronizing the receiver of discrete information according to the words of a primitive cyclic code with low correcting ability (from one test character, for example, parity check code). Since the numbers of zero spectral components in the spectra (obtained taking into account the features caused by the parametric uncertainty of the encoder structure) of all the allowed codewords are the same, a sign of the true phasing can be a nonempty intersection of the sets of numbers of zero spectral components in the spectra of several sequentially arranged codewords. As a result of computer simulation for code synchronization of a cyclic code of primitive length, it was established that when analyzing the state of the receiver, it is necessary to extract at least five fragments and DPFG.

The analysis of the level of existing technology has established that analogues that are characterized by a combination of features that are identical to all the features of the claimed technical solution are absent, which indicates the compliance of the claimed method with the condition of patentability "novelty". Search results for known solutions in this and related fields of technology in order to identify features that match the features of the claimed object that are different from the prototype showed that they do not follow explicitly from the prior art. The prior art also did not reveal the popularity of the impact provided by the essential features of the claimed invention, the transformations on the achievement of the specified technical result. Therefore, the claimed invention meets the condition of patentability "inventive step".

The claimed method is illustrated by an illustration, which shows a structural diagram of a method of code cycle synchronization.

The method of code cyclic synchronization of binary cyclic codes of primitive length under conditions of parametric uncertainty (the codeword length n and the base of the code q are known) is as follows:

Step 1. A discrete sequence of characters of code words of a binary cyclic code of primitive length is received using a discrete information receiver.

This stage can be implemented using specialized means of digital signal processing or computer software.

Next, analyze the state of the receiver of discrete information (steps 2, 3, 4, 6, 7, 8).

Stage 2. A fragment of length n is isolated from the received discrete sequence:

Step 3. Calculate the DPFG of the selected fragment:

фрагмента

;where F _j ¹ is the jth spectral component in the spectrum

fragment

;

α is an element of order n over the field GF (2 ^m );

i is the time;

j is the frequency.

In this case, the elements of the binary codeword are transformed into elements of the extended field as follows: 0 → α-∞, 1 → α0.

Step 4. Determine the presence of a synchronous state of the receiver of discrete information on the basis of a synchronous state. As a sign, at least one spectral component in the spectrum of the selected fragment is equal to zero:

Step 5. If F ¹ _j ≠ 0, j = 0,1, ..., n-1 or if the phasing is not true (the transition from step 8), then shift by one character in the received sequence and re-analyze the status of the receiver (return to stage 2).

If there is a sign of a synchronous state, the truth of the synchronous state of the receiver of discrete information is checked (steps 6, 7, 8).

Step 6. Select at least four fragments of the same length, sequentially located behind the fragment selected in step 2.

Step 7. Perform the discrete Fourier Galois transform of the additionally selected fragments:

фрагментов

;where F ^t _j are the jth spectral components in the spectra

fragments

;

α is an element of order n over the field GF (2 ^m );

i is the time;

j is the frequency.

Step 8. Check the truth of the synchronous state of the receiver of discrete information on the basis of the truth of phasing. To do this, calculate the intersection of the sets of zero components of all the obtained spectra:

where Φ ^t is the set of numbers of zero components in the spectrum of the t-th fragment. As a sign of the true phasing, a nonempty intersection of the sets of numbers of zero components in the obtained spectra is used, i.e. if

where | f | is the power of the set f,

it is believed that the receiver is synchronized with the beginning of the code combination; otherwise, the synchronous state search procedure is resumed from the moment the synchronous state sign is detected (go to step 5).

Stages 2-8 can be implemented using specialized computers or software on a computer.

To study the feasibility of the proposed method on a PC, a simulation of its operation was carried out. The program is written in Delphi 7.0.

The results of the solution of the control example using the simulation model are as follows. For example, a discrete information receiver receives a binary discrete sequence containing a seven-element (n = 7) binary (q = 2) cyclic code:

{01110010010111010001110010110001101 ...},

find the synchronous state of the receiver.

To analyze the state of the receiver, using a priori data on the length of the code word n and the basis of the code q, we construct a Galois field in which we will perform DPS. The length of the code word of a primitive binary cyclic code is related to the dimension and the base of the field (the base of the field coincides with the base of the code, since the code words belong to the field GF (q), and their spectra are vectors over GF (q ^m )) by the expression n = q ^m - 1 [Bleikhut R. Theory and practice of error control codes: Per. from English / Ed. K.Sh. Zigangirova. - M .: Mir, 1986, p.122, 248]. Hence we obtain the degree of expansion m of the field GF (q ^m ):

As an irreducible polynomial of the third degree, we choose the polynomial f (x) = x ³ + x + 1. The elements of the extended Galois field GF (2 ³ ) by polynomial are given in Table 1.

Let us analyze the state of the receiver of discrete information. To do this, select a fragment of length 7 from the adopted discrete sequence:

Table 1
Elements of the Galois field GF (2 ³ ) along the polynomial x ³ + x + 1. Decimal number Primitive element degree Binary vector 0 α ^-∞ 000 one α ⁰ 001 2 α ¹ 010 3 α ² one hundred four α ³ 011 5 α ⁴ 110 6 α ⁵ 111 7 α ⁶ 101

Expression (2) can be written in matrix form:

where (f _〈7〉 ) ^T is the transposed vector f _〈7〉 , W is a square matrix of dimension n of the form:

:According to expression (10), we calculate the spectrum of the fragment

:

A sign of a synchronous state was detected, since

Select from the discrete sequence 4 additional fragments of length 7:

According to expression (10), we calculate the spectra of these fragments:

As a result of the calculations, the sets of numbers of the zero components of all spectra were obtained:

The result of the intersection of these sets is a nonempty set Φ = {1, 2, 4}. Since | Ф |> 0, the discrete information receiver is in a synchronous state.

Claims (1)

The method of code cyclic synchronization, which consists in the fact that using a discrete information receiver, an input discrete sequence, which is a sequence of transmitted code words, is received, a fragment of a discrete sequence equal to the length of the code word is extracted, its discrete Fourier Galois transform is performed, and the presence of a synchronous state of the discrete receiver is determined information on the basis of a synchronous state, and in the absence of synchronization before its establishment t search for a synchronous state by sequentially shifting one received symbol in the same direction with the subsequent selection of a new fragment, its discrete Fourier Galois transform and determining the presence of a synchronous state of the receiver based on a synchronous state, characterized in that as a sign of a synchronous state the receiver of discrete information use the vanishing of at least one spectral component in the spectrum of the selected fragment, after identifying this This sign additionally checks the truth of establishing a synchronous state by the presence of a phasing truth sign, for which at least four fragments of the same length are selected sequentially behind the fragment selected at the stage of determining the synchronous state, a discrete Fourier Galois transform of the additionally selected fragments is performed, and the presence of the sign is determined the truth of phasing, which is used as a nonempty intersection of the sets of numbers of zero components in the resulting spectra, and in the absence of a sign of the truth of phasing, the search for a synchronous state is resumed from the moment a sign of a synchronous state is detected.

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