# Method for decoding cyclic interference-resistant code

FIELD: communications engineering, in particular, engineering of data transfer systems for decoding cyclic interference-resistant codes without preliminary phasing.

SUBSTANCE: during decoding of cyclic interference-resistant code, range of presumed lengths of code combinations [n_{min}-n_{max}] is determined, and assumed phase of beginning of code combination f is set, from phase f in received code series several presumed code combinations S_{i} are selected and pairs are formed from selected combinations in accordance to condition S_{i}≠S_{k}, N of greatest common divisors, represented by polynomials, is calculated, and from calculated polynomials a polynomial of least order is selected, which is considered equal to original polynomial g(x) of cyclic interference-resistant code, if N of greatest common divisors is equal to "1", then length of proposed code combination n is increased by one, phase of proposed beginning of code combination is altered for one, if greatest common divisor, different from "1", is not found for all n∈[n_{min}-n_{max}], combinations of errors are determined in code word and selected code combinations are decoded.

EFFECT: development of method for decoding cyclic interference-resistant code under conditions of adaptation of interference-resistant code to quality of information transfer channel.

3 cl

The invention relates to the field of communication technology, in particular to the processing of digital information, and can be used in a wide class of data transmission systems for decoding cyclic error-correcting codes without prior phasing.

The claimed technical solution expands the Arsenal of tools similar purpose due to the possibility of decoding of cyclic error-correcting codes with variable parameters.

There is a method of decoding a cyclic code [Clark J. ml, Kane, J. Encoding with error correction in digital communication systems: Per. s angl. - M.: Radio and communication, 1987. SS-190], which in the first phase of the received code combination, described by the polynomial S(x)is divided by the known generating polynomial g(x). Then calculated and analyzed modulo r(x). If the remainder r(x)=0, then the received code combination is undistorted. If the remainder r(x)≠0, then the received code combination is erased and a signal is generated "error".

The disadvantage of this method is something that happens only error detection without further correction.

Also there is a method of decoding implemented in the device decoding binary cyclic code [USSR author's certificate No. 1339901, CL H 03 M 13/02. The device for decoding docn the th cyclic code. / Svetsaren, Etherington and Nasuhanova registered 23.09.87], in which the first stage determines the components of the syndrome and calculate the syndrome polynomial. Using the obtained data, solve the key equation, determine the polynomial of the error locator and the position of the erroneous character.

This method has low immunity due to the low probability of correct synchronization.

Closest to the claimed method is (prototype) decoding of cyclic error-correcting code [RF patent 2231216 / Method of decoding a cyclic error correcting code / Kvashennikov VI / published 10.02.2004], namely, that on the transmitting and the receiving side pre-set the parameters of cyclic error-correcting (n, k) code, such as the length of the code combination (n), the number of information symbols (k) and a check polynomial h(x), as well as synchronizing sequence on the transmitting side encodes the information sequence cyclic error-correcting code with the given parameters, recurrently continue code word cyclic error-correcting code of length n1>n and form the output sequence representing the sum modulo two of cyclic error-correcting code and a synchronization sequence at the receiving side does not form a cyclic continuation of the received sequence, multiply adopted consistency check on the well-known polynomial error-correcting code h(x) and compute the synchronization sequence, recognize a unique combination of the synchronizing sequence and determine the beginning of the combination of error-correcting code, subtract the synchronization sequence from the received sequence and the received code word cyclic error-correcting code, determines a combination of errors in the code word and correct errors in the information part of the codeword of a cyclic error-correcting code.

This method potentially has high noise immunity, and also carries out cyclic synchronization of cyclic error-correcting code with no additional synchronization symbols, using the redundancy of the error-correcting code.

However, the disadvantage of the prototype is the loss of its capacity in case of change of parameters of error-correcting code in systems with adaptation according to the method of error-correcting coding. Due to the fact that during the implementation of the method requires knowledge of the parameters used error-correcting code, and in systems with adaptation according to the method of error-correcting coding parameters used by the code can be changed.

The purpose of the claimed technical solution is the I development of a method of decoding a cyclic error correcting code, able to survive when it is used in systems with adaptation according to the method of error-correcting coding without additional settings used error-correcting code, due to their definitions directly from the received code sequence before decoding.

This goal is achieved by the fact that in the proposed method of decoding a cyclic error correcting code on the transmission side set the parameters of cyclic error-correcting (n, k) code, such as the length of the code n, the number of information symbols k and the generating polynomial g(x), encode the information sequence cyclic error-correcting code with the given parameters and transmit the generated sequence over the communication channel to the receiving side. At the receiving side define the likely range of lengths code combinations [n_{min}-n_{max}] and choose the estimated phase of the start code f. With phase f in the received code sequence identified several alleged code combinations S_{i}and form of the selected combinations of pairs of code combinations according to the condition S_{i}≠S_{k}. Calculate the N greatest common divisor (GCD), represented by polynomials, for different pairs of code combinations and choose among in the numerical polynomials,
which of NOD, the polynomial of least degree that has been associated with a generating polynomial g(x) cyclic error-correcting code. If the GCD is equal to "1", increase the length of the proposed code combinations of n per unit. Change the phase of a proposed start code combination by one if the greatest common divisor other than "1", is not found at all n∈[n_{min}-n_{max}]. Determine the combination of errors in the code word and decode the selected code combination.

Thanks to the new essential features in the proposed method will be able to define the parameters used error-correcting code directly from the received code sequence before decoding, which allows the method to survive in case of change of parameters of error-correcting code in systems with adaptation according to the method of error-correcting coding without additional transmission parameters of error-correcting code. In addition, the claimed method allows synchronization code sequence without additional transmission of synchronizing symbols.

The analysis of the level of technology has allowed to establish that the analogues, characterized by a set of characteristics is identical for all features of the claimed technical solution is available, which indicates compliance of the claimed method the condition of patentability "novelty". Search results known solutions in this and related areas of technology in order to identify characteristics that match the distinctive features of the prototype of the features of the declared object, showed that they do not follow explicitly from the prior art. The prior art also revealed no known effect provided the essential features of the claimed invention transformations on the achievement of the technical result. Therefore, the claimed invention meets the condition of patentability "inventive step".

The claimed method can be implemented as follows.

Decoding of cyclic error-correcting code is based on theory of error-correcting coding [Blahut RE Theory and practice codes, controlling errors: TRANS. from English. - M.: Mir, 1986. - 576 C.] and can be set to detect or correct errors.

The basis for the implementation of both regimes are conversion of the received code cyclic error-correcting code with generating or check polynomial that presupposes knowledge of the parameters of cyclic error-correcting code.

In modern conditions the complex electromagnetic environment increases the proportion of systems with adaptation according to the method of error-correcting coding, in which a preference is Agueda the possibility of changing the parameters of error-correcting code depending on the quality of the transmission channel information. In such systems to implement decoding at each change of parameters of error-correcting code is necessary to carry out the transfer on the receiving side, which in turn requires the allocation for these purposes, part of the resource channel information transfer, and also imposes additional requirements on noise immunity when passing parameters of error-correcting code.

To resolve the existing contradictions in the face of changing parameters of cyclic error-correcting code in the process of information transfer is proposed to use the method of decoding of cyclic error-correcting code with a preliminary determination of its parameters directly from the received code sequence.

The essence of the proposed method is as follows.

On the transmission side form the information sequence and set the parameters of cyclic error-correcting code. Next, encode the generated information sequence cyclic error-correcting code with the given parameters and transmit the received code sequence over the communication channel to the receiving side.

At the receiving side define the likely range of lengths code combinations [n_{min}-n_{max}]. In the received code sequence specify the estimated phase n the first code combination f_{
n}choose the length of the code n=n_{min}and there are several code combinations S_{i}, i=1,2,..., length n with phase f_{n}.

Of the selected code combinations form pairs according to the condition S_{i}≠S_{j}, j=1,2,... and i≠j. For selected pairs of code combinations calculate the greatest common divisor (GCD). The GCD computation is performed using the Euclidean algorithm is an iterative algorithm division, the essence of which consists in the following.

If the degree of the polynomial describing the code combination S_{1}greater than or equal to the degree of the polynomial describing the code combination S_{2}the sequence of calculations is

Process is stopped as soon as the result is a balance of zero.

Thus, it is necessary first code combination S_{1}(dividend) divided by the second code combination S_{2}(the divisor) and get the remainder of r_{1}. Then the divisor used in the first stage (the dividend in the second stage), it is necessary to divide the obtained in the first stage, the remainder r_{1}(the divider at the second stage). The process is repeated to obtain a zero balance, with GCD equal to the divisor r_{n}in which turned out to be a zero balance.

After calculation of the N NODES among them choose the one that not only is the h-polynomial of least degree, and identify it with a generating polynomial of the cyclic error-correcting code.

In order to minimize operations calculation number N greatest common divisors believe is equal to 2, which implies the presence of three code words of cyclic error-correcting code. At the first stage search two greatest common divisors GCD_{1}and NOD_{2}. Finding greatest common divisor GCD_{1}and NOD_{2}in the second stage yields a generating polynomial g(x).

Case when GCD is equal to one indicates no common divisor selected code combinations. During this exercise, select the next length code combination n=n_{min}+1 from a specified range and repeat the process of finding the GCD.

If you are searching all possible lengths of the code combinations of the specified range n∈[n_{min}-n_{max}] GCD is not detected, then slip the estimated phase of the start code in the received code sequence and search the NOD for the new phase f=f_{H}+1.

The range of phase change of the beginning of the proposed code combination is determined by the expression f∈[f_{H}f_{H}+n_{max}].

To improve noise immunity, in the case of errors in the received code sequence, the decision about the truth of generating many is a member of g(x) accept the majoritarian why search for g(x) on different parts of the received code sequence.

Achievable technical result of the proposed method is its application in systems with adaptation according to the method of error-correcting coding, namely in terms of possible changes of the parameters of cyclic error-correcting code.

1. The method of decoding of cyclic error-correcting code, namely, that the pre on the transmission side form the information sequence and set the parameters of cyclic error-correcting code, including the length of the code n, the number of information symbols k and the generating polynomial g(x), which encode the information sequence and transmit it over the communication channel at the receiving side, take a transmitted encoded information sequence, determine the beginning of the code combinations of cyclic error-correcting code and combination error code combination, then decode the selected code combination, characterized in that on the transmission side, the combination of cyclic error-correcting code b_{k}is formed by the multiplication of the information sequence a_{k}by the generating polynomial g(x), and on the receiving side before decoding determine product is non polynomial of the cyclic error-correcting code,
why specify the range of the assumed lengths of code combinations [n_{min}-n_{max}]choose the estimated phase of the start code f, isolated from the accepted encoded information sequence several alleged code combinations S_{i}where i=1,2,..., choose from among the selected code combinations of N pairs of code combinations that satisfy the condition S_{i}≠S_{j}where j=1,2,... and i≠j, for each pair of code combinations calculate greatest common divisor, and if the greatest common divisor of these N pairs of code combinations is equal to one, then increase the expected length code combination unit, and repeat the process of finding greatest common divisors, if the enumeration of all possible lengths of the code combinations of the specified range [n_{min}-n_{max}] the greatest common divisor other than one that is not found, change the estimated phase of the beginning of the code combination unit and search N greatest common divisors of a new phase in the beginning of the code combination, then of polynomials, which is the greatest common divisors, choose the polynomial of least degree, and identify it with a generating polynomial of the cyclic error-correcting code g(x), and search the generating polynomial g(x) at different phase is x implementation and the decision about the truth of the generating polynomial take on the majority principle.

2. The method according to claim 1, wherein computing the greatest common divisor is performed using the Euclidean algorithm.

3. The method according to claim 1, characterized in that the number N greatest common divisor is chosen equal to two.

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