RU2379841C1 - Decoder with erasure correction - Google Patents

Abstract

FIELD: physics; communications.

SUBSTANCE: invention relates to communication engineering and can be used in designing new and upgrading existing digital information transmission systems. Use of the decoder while using a cluster analysis method provides guaranteed correction of n-k erasures in contrast to decoders using Hamming metric, which can correct only d-1<n-k erasures. Complexity of the decoder does not depend on the frequency of the corrected erasures.

EFFECT: more reliable reception of information.

1 dwg, 2 tbl

Description

The invention relates to communication technology and can be used in the design of new and modernization of existing discrete information transmission systems.

Known devices for recovering erasures and correcting errors using symbol reliability indices (symbol reliability estimates) to increase the reliability of information reception (see R. Morelos-Zaragoza. The art of noise-resistant coding. Methods, algorithms, application. M: Technosphere, 2005, p. 103-105; as well as devices according to patents of the Russian Federation for inventions No. 2209519; 2209520; 2256294).

In addition, there are known methods for generating confidence indices of received binary symbols based on an erasing communication channel and using them in the decoding procedure of systematic codes using the cluster analysis method (see Lychagin N.I., Ageev S.A., Gladkikh A.A., Vasiliev A.V. Communication systems, television and radio broadcasting, No. 1, 2, 2006, pp. 49-55; Gladkikh A.A., Teterko V.V. Application of cluster analysis for decoding block codes. // Transactions of LXI -th scientific session of the Russian NTORES named after A.S.Popov. - Moscow, 2006 - p. 381-383), as well as methods of using using these estimates to obtain the logarithmic likelihood ratio when decoding code combinations (see Sklyar, Bernard. Digital Communications. Theoretical Foundations and Practical Applications, 2nd edition: Translated from English. - M.: Publishing House "Williams", 2003 city, p. 500-503).

The closest device for the same purpose is a code sequence recovery device (see RF patent for inventions No. 2256294, H04L 1/20, publ. 2005.07.10), comprising a receiving unit, one output of which is connected to a drive through a signal analyzer, one output of which connected to the first input of the erasure recovery unit, the information output of which is connected to one of the inputs of the erasure correction unit, as well as a code combination drive, a demodulation evaluation unit and a correction unit, the output of which is connected to the second the input of the erasure recovery unit, the control output of which is connected to the second input of the correction unit, the first input of which is connected to the output of the demodulation evaluation unit, the first input of which is connected to another output of the drive, and the second input is connected to the second output of the code combination drive, the input of which is connected to another output of the receiving unit, and the first output to another input of the erasure correction unit.

The disadvantages of the analogs of the proposed device include the incomplete use of the redundancy introduced into the code due to the use of the Hamming metric, when the decoder, using soft decoding methods, corrects the number of errors and erasures allowed by the specified metric. In this case, as a rule, exhaustive methods of restoring erasures are used, which, with each new attempt, require multiplication by the verification matrix of the code.

The disadvantages of the prototype include: the use of the Hamming metric and a complete enumeration of the verification relations determined by the verification matrix of the block code during the application of the logarithm of the likelihood ratio. Along with this, there are known methods of processing block codes that provide decoding of such codes outside of their constructive corrective ability (see R. Morelos-Zaragoza. The art of noise-resistant coding. Methods, algorithms, application. M: Technosphere, 2005, p. 219) )

The technical result is an increase in the reliability of receiving information.

To achieve a technical result, an erasure correction decoder comprising a receiving unit, one output of which is connected to a drive through a signal analyzer and the other is connected to the output of a code combination drive, the output of which is connected to the first input of an erasure correction unit. The peculiarity is that a bit switch, a cluster number analyzer, a coordinate analyzer, a coordinate correction unit, the input of which is connected to one output of the coordinate analyzer, are inserted into it, and the output of the coordinate correction block is connected to the second input of the coordinate analyzer, while the first input of the bit switch is connected to the drive output, the second input of the bit switch is connected to the output of the code combination drive, and the first output of the bit switch through the cluster number analyzer is connected to the first input analyzer coordinate, the third input of which is connected to the second output switch bits, the other output correction unit coordinates of the analyzer is connected to a second input of erasures, and the first input of this unit is connected to the second output of the cluster analyzer numbers.

The drawing shows a structural electrical diagram of the proposed decoder with the correction of erasures.

The deletion correction decoder comprises a receiving unit 1, one output of which is connected to a drive 3 through a signal analyzer 2, and the other is connected to an input of a code combination drive 4, the output of which is simultaneously connected to the second input of the verification switch 5 and to the third input of the erase correction unit 9, the first input of the test switch 5 is connected to the output of the drive 3, and the first output of the test switch 5 is connected to the input of the cluster definition block 6, the second output of block 5 is connected to the third input of the coordination analyzer 7, while one output of this block is connected to the input of the coordinate correction block 8, and the other output is connected to the second input of the erasure correction block 9, while the output of block 8 is connected to the second input of the coordinate correction block 7, and the first output of the cluster number analyzer 6 is connected to the first input of the coordinate analyzer 7, and the second output of block 6 is connected to the first input of the erasure correction block 9.

The operation of the device is considered as an example of a systematic code. Let the generator polynomial of the code g (x) = x ¹⁰ + x ⁸ + x ⁵ + x ⁴ + x ² + x + 1 and n = 15, k = 5, d = 7. In the Hamming metric, this code can fix three errors or restore six erasures.

The verification matrix of the code has the form:

The receiving unit 1 registers the signals coming from the communication channel and transmits their current values in binary form to the drive of the code combination 4. For example, the code code combination was sent from the transmitter:

101110000101001.

In block 1, this combination is distinguished from the general data stream (shown by direct inverse brackets) and is recorded in block 4 with possible errors. Errors are shown in italics.

... 01] 1 10 1 0 0 1 0 1 101001 [00 ....

The last ten characters in the combination are verifying.

In addition, in the receiving unit 1, an erasure signal is generated, which arrives as a logical unit in the signal analyzer 2 over the symmetrical erasure interval ρ. The input of the receiving unit 1 is the information input of the device. In the receiving unit 1, the joint information symbol stream and the erasure stream are separated, but between them the correspondence by bit numbers is always preserved.

In the erasure stream, a value of zero is not erased in the primary sequence of information symbols, and a value of one is assigned to the erased symbol positions.

Let the erasure configuration for the received code vector have the form:

... 00] 001100101000000 [00 ...,

here, the erased elements are denoted by units, and correctly received characters are indicated by zeros.

To determine the symbol confidence index, two sliding intervals of sizes K ₁ and K ₂ bits each are assigned, with K ₁ = K ₂ . The intervals follow the sequence of erasures extracted from the data stream, one after another, overlapping each other, at the position of one estimated bit, for example, when K ₁ = K ₂ = 3 we get:

- стирание, то от общей оценки отнимется единица. Это усиливает различимость индексов достоверности символов (см. Гладких А.А., Мансуров А.И., Черторийский С.Ю. Статистическая оценка индексов достоверности символов, формируемых в системе с мягким декодированием. // Периодический научно-технический и информационно-аналитический журнал «Инфокоммуникационные технологии», том 6, №1, 2008 г. Поволжская государственная академия телекоммуникаций и информации, г.Самара. - С.39-43). Таким образом, оценка надежности вычисляется для анализируемого символа

попавшего в оба окна в соответствии с выражениемEach interval is assigned a weight of K ₁ +1 and K ₂ +1, but if there are i erasures on the length of the interval, then the weight of the window is reduced by this value. The total score is defined as the sum of the ratings of the first and second interval. If the analyzed character

- erasure, then the unit will be subtracted from the total score. This enhances the distinguishability of character confidence indices (see Gladkikh A.A., Mansurov A.I., Chertorysky S.Yu. Statistical evaluation of character confidence indices formed in a system with soft decoding. // Periodical scientific, technical and information-analytical journal “Infocommunication Technologies”, Volume 6, No. 1, 2008. Volga State Academy of Telecommunications and Information, Samara. - P.39-43). Thus, the reliability score is calculated for the analyzed symbol

caught in both windows in accordance with the expression

- символ, подлежащий оценке. При К₁=К₂=3 наибольшей оценкой является оценка с индексом 8, а наименьшей оценкой является оценка с индексом 1.here R is the character confidence index expressed as an integer, K ₁ , K ₂ is the width of the estimated intervals, x _i are the characters that fell into these intervals, a

- The character to be evaluated. When K ₁ = K ₂ = 3, the largest score is the score with index 8, and the lowest score is the score with index 1.

The output of the signal analyzer 2 is connected to the input of the drive 3, which accumulates the symbols confidence indices (reliability estimates) R _j for each symbol of the code combination. After the processing of the characters of the next code combination, the estimates of R _j from the drive 3 are simultaneously read into the switch of bits 5 simultaneously with the combination from block 4. For example, when K ₁ = K ₂ = 3 for the analyzed code combination we get:

- a tuple of erasures from block 1 ... 00] 001100101000000 [00 ...;

- estimates in drive 3 ...] 764456464778888 [...;

- characters in the drive 4 ...] 1 10 1 0 0 1 0 1 101001 [....

, то любая кодовая комбинация может быть представлена последовательностью разрядов:Bit switch 5 is programmed to divide the n-bit combination into three groups. The highest digits of the combination are on the left. The first group, consisting of the first ƒ high order bits, is intended to determine the cluster (a list of combinations belonging to a particular group). In total, 2 ^ƒ clusters (ƒ≤k) can be formed. The second group, representing half the digits for an even value of the difference n-ƒ, determines the X coordinate of the two-dimensional Euclidean space. In the case of an odd n-ƒ value, the X coordinate is assigned an extra bit. The remaining bits of the code combination determine the third group and the Y coordinate itself. If we designate the bits in decreasing order of degrees x ⁱ , where

, then any code combination can be represented by a sequence of bits:

x ¹⁴ , x ¹³ , x ¹² , x ¹¹ , x ¹⁰ , x ⁹ , x ⁸ , x ⁷ , x ⁶ , x ⁵ , x ⁴ , x ³ , x ² , x ¹ , x ⁰ .

In the switch of discharges 5 for the example under consideration for ƒ = 3 we obtain combinations of groups of discharges

1 group x ¹⁴ , x ¹³ , x ¹² - cluster number;

2 group x ¹¹ , x ⁹ , x ⁸ , x ⁷ , x ⁶ , x ⁵ - X coordinate;

3 group x ¹⁰ , x ⁴ , x ³ , x ² , x ¹ , x ⁰ - Y coordinate.

It is noticeable that the symbols of the cluster number and the most significant bits of the coordinates are located at the places of the information bits of the systematic code, this approach provides the best combination of check ratios. As a result, we get:

- a combination of ratings ...] 764 464647 578888 [...;

- a combination of characters ...] 1 10 10 1 0 1 1 0 01001 [....

The digit switch 5 sends all three groups of symbols to the analyzer of the cluster number 6 and to the coordinate analyzer 7.

The cluster number analyzer 6 is designed to determine the degree of reliability of cluster bits. If all the digits of the first of the three groups of symbols have grades no lower than six, then it is considered that the cluster number is likely to be determined correctly. If the symbol confidence indices have values lower than seven, the cluster determination unit 6 carries out an unambiguous correction of the symbols due to the information contained in the digits with high confidence indices. For this, the procedure of simultaneous cyclic shift of the generating polynomials g (x) and h (x) is used. The first represents the generating polynomial of the code, and the second represents many combinations of the dual code. Combinations of the first polynomial will have constant weight (in the example this parameter is 7), and the dual code represents combinations with another weight (in the example this weight is 8). The cluster number analyzer 6 determines that the least significant bit of the cluster number has a confidence index of 4, therefore, a system of cyclic shifts of the generating polynomials is started. The operation of the system is presented in Tables 1 and 2. During the analysis, in this block, those bits that have a confidence index of less than seven are crossed out. It is easy to verify that complete coincidence in the remaining digits appears only for the only combination highlighted in Table 1. The number of shifts 11 of the polynomial g (x) unambiguously indicates cluster 5. This means that x ₁ = 1, x ₂ = 0, x ₃ = 1. The cluster number analyzer 6 transfers this data to the coordinate analyzer 7 and the erasure correction unit 9. The converted sequence has the form:

- a combination of ratings ...] 888 464647 578888 [...;

- a combination of characters ...] 101 10 1 0 1 1 0 01001 [....

The coordinate analyzer 7, having received a sequence of symbols and confidence indices, checks the level of estimates and, if they have low indices at the highest bits of coordinates, transmits data to the coordinate correction block 8. In this example, the highest digit of the binary representation of the coordinate X has a confidence index of 4, therefore, this symbol requires correction. The leading digit of the Y coordinate has an index of 5, which means that this digit also requires correction. To correct the coordinates, side 8 operates with data from the verification matrix. For the higher digits, the following relations are selected from the check matrix.

For X coordinate:

x ¹⁴ ⊕x ¹³ ⊕x ¹¹ = x ⁹ ;

x ¹³ ⊕x ¹² ⊕x ¹¹ = x ⁶ ;

x ¹⁴ ⊕x ¹² ⊕x ¹¹ = x ³ .

For Y coordinate:

x ¹³ ⊕x ¹² ⊕x ¹⁰ = x ⁸ ;

x ¹⁴ ⊕x ¹³ ⊕x ¹⁰ = x ⁴ ;

x ¹⁴ ⊕x ¹² ⊕x ¹⁰ = x ⁰ .

It is noticeable that in all test relations the first two characters are considered reliable after processing them in block 6, and the unknown bit z _i , located in the third position of the left side of the equations, can be found by the most reliable representative of the right side of the equations or by the majority method.

For the X coordinate, the best character is x ³ , which has a confidence index of 8. For the Y coordinate, the best character is x ⁰ , which has a confidence index of 8.

Since the symbols x ¹⁴ = 1, x ¹³ = 0, x ¹² = 1 after restoration in block 6 are reliable, the solution of the corresponding linear equations leads to the correction of the most significant bits of the coordinates. For the coordinate X: x ¹⁴ ⊕x ¹² ⊕z _x = x ³ or 1⊕1⊕z _x = 1, therefore, z _x = 1, i.e. the highest bit of the X coordinate is not distorted, here ⊕ is the addition operation modulo two. For the coordinate Y: x ¹⁴ ⊕x ¹² ⊕z _y = x ⁰ or 1⊕1⊕z _y = 1, therefore, z _y = 1. An error has been fixed. For the final restoration of the combination, the values of the least significant bits of the coordinates do not play a role (see Lychagin N.I., Ageev S.A., Gladkikh A.A., Vasiliev A.V. Communication systems, television and radio broadcasting, No. 1, 2 , 2006, p. 49-55).

The erasure correction unit 9 compares the data from blocks 6 and 7 and transfers the combination 10111 to the output, which corresponds to the transmitted information vector. The output of this block is the information output of the decoder.

The application of the cyclic shift procedure of generating polynomials in block 6 cannot be attributed to the exhaustive search of the erasure recovery method, since it does not require algebraic operations, but is a trivial operation of bitwise comparison of two vectors.

Thus, the use of a decoder using the cluster analysis method allows guaranteed correction of n-k erasures in contrast to decoders using the Hamming metric, which are able to correct only d-1 <n-k erasures. The complexity of the decoder does not depend on the multiplicity of correctable erasures.

Claims (1)

An erasure correction decoder comprising a receiving unit, one output of which is connected through a signal analyzer to a drive and the other is connected to an input of a code combination drive, the output of which is connected to the third input of an erasure correction unit, characterized in that a bit switch and a cluster number analyzer are additionally introduced , coordinate analyzer, coordinate correction block, the input of which is connected to one output of the coordinate analyzer, and the output of the coordinate correction block is connected to the second input of the coordinate analyzer at, while the first input of the switch of discharges is connected to the output of the drive, the second input of the switch of discharges is connected to the output of the drive of the code combination, and the first output of the switch of discharges through the analyzer of the cluster number is connected to the first input of the coordinate analyzer, the third input of which is connected to the second output of the switch of discharges, while the other output of the coordinate analyzer is connected to the second input of the erasure correction unit, and the first input of this block is connected to the second output of the cluster number analyzer.