RU2327297C2 - Method of block codes decryption with elements deleting - Google Patents

Abstract

FIELD: information technologies.

SUBSTANCE: invention relates to the communication technology and can be used in digital information transmitting systems. While processing of binary digits in the method, supplied from data channel, reliability figure of every symbol is fixed and lee reliable symbols are deleted. According to another group of more reliable symbols one of 2^N clusters is defined (where N - natural value), to which accepted code vector can belong. At the same time remained part of coding combination is divided on two groups of binary symbols, conversing each group into m integral numbers with commonly accepted method, from high-order digits to low order digits, and accept them as two direct coordinates, belonging to separate cluster flatness, as well as into m-numbers from low order digits into high ordered, accepting them as stable coordinates of the same coding vector. Evaluating of accepted code vector deleting configuration in each group is defined, setting priorities of deleted symbols reconstruction. In case of beating with deleting of high ordered digits of direct coordinates one transfers to stable coordinates, defining in any case according Euclid's distance the nearest enabled code vector of chosen cluster.

EFFECT: time rate increasing and authenticity of information recovering.

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Description

The invention relates to communication technology and can be used in the design, new and modernization of existing discrete information transmission systems. The claimed method can be used to decode noise-resistant block codes, providing high speed and reliability of information recovery.

The claimed technical solution expands the arsenal of application of noise-resistant block codes.

Known methods for decoding block codes (see, for example, J. Clark, Jr., J. Kane "Coding with error correction in digital communication systems" M .: Radio and communication, 1987, p.96-128), in which combinations of errors are searched by different from the procedure for multiplying the received code vector by a check matrix. Such non-algebraic algorithms can be easily generalized to the case of soft solutions and prove to be very useful.

The disadvantage of such methods is the complexity of the decoder, which increases relatively quickly with the multiplicity of correctable errors. Therefore, they usually turn out to be useless when correcting more than three random errors or more than one packet of errors. Another disadvantage is the difficulty of finding a test set covering a combination of errors or a set of test sets covering all sets of errors of a given type (the so-called coverage).

The closest in technical essence to the claimed one is the Viterbi decoding method (see, for example, Sklyar, Bernard “Digital Communication. Theoretical Foundations and Practical Applications”. Ed.2-ed., Revised M .: Ed. House Williams, 2003 , p.443, 444), which does not use a Hamming distance metric with limited resolution, but uses the Euclidean code distance between a point with noise and a point without noise by converting the processed binary vector from a binary number system to numbers with the required m-ary the system number, for example, in octal.

The disadvantage of the prototype lies in the narrow scope of its application. It is developed only for convolutional codes, although blocking codes are widely used in many practically important applications, especially in systems that do not suffer delays in the exchange of information. The method is not suitable for correcting erasures, although when they are corrected, the correcting capabilities of the code are doubled.

The aim of the invention is to develop a method for decoding code combinations of block codes, which allows to increase the decoding speed and reliability of the received information when correcting errors and erasures.

This goal is achieved by the fact that when receiving binary characters coming from the communication channel, they fix the reliability indicator of each symbol (for example, the ratio indicator of the likelihood function - see Sklyar, Bernard “Digital Communication. Theoretical Foundations and Practical Applications”, 2nd, Rev .: Translated from English - M .: Williams Publishing House, 2003, p. 500) and the least reliable characters are erased, and the group of the most reliable characters determines one of 2 ^N clusters (where N is a natural number) ( see Kremer N.Sh. Probability Theory and Mathematical Stats tika: Textbook for high schools. - 2nd ed., revised and add. - M .: Unity-Dana, 2004, p. 496), to which the accepted code vector may belong, while the remainder of the code combination is divided into two groups of binary symbols, translating each group into m-ary integers in a generally accepted way, from the highest digits to the lowest digits, and take them for two direct coordinates belonging to the plane of the selected cluster, as well as m-ary integers from the least significant digits in the group to the highest taking them for the invariant coordinates of the same code vector, during the estimation of pr of the incomprehensible code vector, the configuration of the erasures in each group is determined, setting priorities for correcting erased characters, and in the case of defeat by erasures of the highest digits of the direct coordinates, they switch to invariant coordinates, determining in any case the closest allowed code vector of the selected cluster from the Euclidean distance.

Due to the new set of essential features in the claimed method, when decoding block codes, the reliability indicators of the received symbols are taken into account, on the basis of which erasures are formed and their correction priorities are determined by correlating the received code vector to a particular cluster within which the number of combinations to be analyzed is sharply reduced , which allows for faster and more accurate recovery of erased characters in the received code combination and thus extends the range of The application of the claimed method for both synchronous and asynchronous transmission systems.

The analysis of the prior art made it possible to establish that analogues that are characterized by a combination of features 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 method is illustrated by the example of the BCH code (15, 5, 7) and is applicable to any block code.

The claimed method is illustrated by drawings:

figure 1 is a table of allowed code combinations of the block code (15, 5, 7);

figure 2 - configuration of the code clusters (15, 5, 7) in the direct coordinate system;

figure 3 - combination of cluster No. 0 in the direct coordinate system;

figure 4 - combination of cluster No. 0 in the invariant coordinate system.

The goal is achieved as follows.

Many block code combinations are clustered. As a cluster attribute, any combination of binary symbols along the length of the code combination can be selected. In the above example, a combination of the adjacent three bits of any code combination is selected as such a feature (see FIG. 1). Then the remaining 12 bits form two equal (optional requirement) groups of binary characters. The first group of bits represents the X coordinate, and the second represents the Y coordinate. In each group, the highest digit in the direct coordinate system is on the left. The conversion of coordinate values from the binary number system to m-decimal is carried out in the usual way. For example, the accepted code combination No. 14 has the form: 011101100101000 (high-order bits on the left). The last three bits 000 - determine whether this combination belongs to cluster No. 0. Symbols: 011101 - determine the X coordinate, and symbols: 100101 - determine the Y coordinate.

Writing an arbitrary coordinate X or Y in the m-ary positional number system is based on the representation of this integer in the form of a polynomial.

For example,

X ₁₀ = a _n m ⁿ + a _n-1 m ^n-1 + ... + a ₁ m ¹ + a ₀ m ⁰ ,

where each coefficient a _i can be one of the basic numbers and is represented by one digit (see Ostreykovsky V.A. Informatics: Textbook for high schools. - Higher school, 2001, p. 59). In our case, a _i , depending on the value of the bit in X or Y, takes the value either 0 or 1, and m = 2.

Therefore, the conversion of coordinate values from the binary number system to the decimal number system has the form:

X = 011101 ₂ = 0 · 2 ⁵ + 1 · 2 ⁴ + 1 · 2 ³ + 1 · 2 ² + 0 · 2 ¹ + 1 · 2 ⁰ = 29 ₁₀ ;

Y = 100 101 ₂ = 1 · 2 ⁵ + 0 · 2 ⁴ + 0 · 2 ³ + 1 · 2 ² + 0 · 2 ¹ + 1 · 2 ⁰ = 37 ₁₀ .

It is noticeable that the price of each binary character is different. It depends on the place of the symbol in the group and is a multiple of 2 ^Z , where Z is a positive integer, including zero. Subsequently, this property will determine the priorities in the erasure correction procedure. The table (see Fig. 1) shows the cluster numbers and direct coordinates for all code vectors (15, 5, 7). Combinations of one cluster for clarity are connected by a continuous line. Since code combinations can be divided into orthogonal sets, all clusters form pairs with a certain type of symmetry (see figure 2). If the selected binary characters determining the cluster number are not received reliably, you should select other characters with high reliability indicators, for example, at the beginning of the code combination. In the configuration of clusters, changes will not follow due to the cyclic properties of the code, however, combination No. 14 will be correlated with combinations of other numbers, which does not matter.

On the receiving side, each bit of the code vector is accompanied by a reliability estimate. The characters with the lowest ratings are erased, and several basic erasure configurations are possible along the length of groups X and Y of the code vector:

Option 1. There are no erasures.

Option 2. All characters are erased.

Option 3. Erasures coincided with the lower digits of the groups that determine the coordinates of X and Y.

Option 4. Erasures coincided with the senior bits of the groups that determine the coordinates of X and Y.

Option 5. Erasures coincided with the least significant bits defining the X coordinate and the highest bits defining the Y coordinate.

Option 6. Erasures coincided with the high order bits that determine the X coordinate and the low order bits that determine the Y coordinate

In the first case, decoding the code pattern is not in doubt.

In the second case, it is advisable to abandon decoding.

In the third case, the search for the transferred combination is not difficult, since the price of the erasures is low. Possible erasure correction options are grouped near the significant point for the i-th cluster combination. For example, for combination No. 14 of the zero cluster, the X and Y coordinates when restoring the erasures can be of the form:

Figure 3 shows a slight deviation in the Euclidean metric of coordinate variations from the true value (29; 37), the decoding of the combination is not in doubt and can be done without iterating over the positions of the erased characters and multiplying the vector by the check matrix, which sharply increases the performance of the decoder.

In the fourth case, actions in direct coordinates can lead to gross errors, since the price of erasures in high orders is high. For example, in the following cases we get:

Figure 3 in the form of triangles shows points No. 3 and No. 4, which are erroneously identified with other combinations of the cluster. Such a combination of erasures in case No. 3 can easily be transformed into combination No. 19 (Euclidean metric is ≈25 versus similar metric ≈27 to combination No. 29) or in case No. 4 into combination No. 29 (noticeably without additional calculations). To avoid erroneous restoration of the combination, the decoder, when the signs indicated in the fourth case are manifested, switches to inverse coordinates, i.e. Defines the most significant bits not on the left, but on the right. In this case, the cluster is transformed and has the form shown in Fig.4. Moreover, the error in reconstructing combination No. 14 is minimal, and the decoding procedure is similar for the third case. For example, figure 4 shows the restoration of combinations of erasures for case 3 and case 4, but in invariant coordinates.

In the fifth and sixth cases, the decoder operates with the coordinate at which the erasures are concentrated in the lower digits of the direct coordinate system, which allows you to uniquely decode the received vector. The success of decoding is based on the fact that in none of the eight clusters adjacent points associated with the coordinates of the allowed code combinations do not lie in pairs on straight lines parallel to the coordinate axes (see Fig. 2), i.e. they do not have the same coordinates in either X or Y. This suggests that if one of the coordinates is deleted with erased characters (six binary characters), the combination is restored to another coordinate. At least, this is no worse than restoring the erasures in the Hamming metric.

Application of the proposed method for decoding combinations of block codes with erasing elements eliminates the exhaustive methods of restoring erasures and the repeated procedure in this case of multiplying the next version of the iteration procedure by a verification matrix. The method allows you to purposefully use the priorities of erased characters when correcting one or another of their configurations, which increases the speed of recovery of code combinations by erasures and ensures the implementation of potential code error correction capabilities.

Claims (1)

The method of decoding block codes with erasing elements, which consists in the fact that a fixed sequence of binary symbols is taken from the communication channel, which is converted into two m-th numbers and these numbers are taken as the coordinates of a point on the plane, determining the location of this point relative to the previously set points of this planes in the Euclidean metric, characterized in that during processing of binary symbols coming from the communication channel, the reliability indicator of each symbol is fixed and the least reliable symbols are erased, and the group of the most reliable characters is determined by one of 2 ^N clusters (where N is a natural number), to which the received code vector may belong, while the rest of the code combination is divided into two groups of binary characters, converting each group into m-th integers in a generally accepted way , from the highest digits to the lowest digits, and take them for two direct coordinates belonging to the plane of the selected cluster, as well as in the mth number from the least significant digits in the group to the highest, taking them for the invariant coordinates of the same code vector, in the course of The wedges of the received code vector determine the erasure configuration in each group, setting priorities for correcting erased characters, and in the case of defeat by erasures of the higher digits of the direct coordinates, they switch to invariant coordinates, determining in any case the closest allowed code vector of the selected cluster from the Euclidean distance.

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