RU2500073C1 - Adaptive decoder for generating 3d codes - Google Patents

Abstract

FIELD: radio engineering, communication.

SUBSTANCE: system for generating three parity-check codes which form a three-dimensional data array. Check ratios relating to parity-check on a third dimension are requested by the decoder only in case of a high level of interfering factors, indicated by the soft solutions relative received symbols with low certainty factors. The disclosed decoder scheme when processing data on the third dimension performs decorrelation of possible errors without using special interleavers or de-interleavers in the encoder-decoder scheme. Received data are processed on each dimension using iterative transformations of soft solutions based on the average value of similar solutions and the dispersion factor of estimates on the length of each code vector.

EFFECT: high reliability and rate of transmitting information.

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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 confidence indices or soft solutions (MR) to increase the reliability of information reception (see R. Morelos-Zaragoza. The art of noise-resistant coding. Methods, algorithms, application. M., Technosphere, p.103 , ..., 105; and also W. Peterson. Codes for correcting errors / W. Peterson, E. Weldon; translated from English; edited by R. L. Dobrushin, S. N. Samoilenko. - M .: Mir, 1976; 594 p .; and also D. Forney. Cascading codes / D. Forney. - M .: Mir, 1970. - 207 p.).

In addition, methods for using hypercodes are known (see Hunt A., “Hyper-Codes: High-Performance Low-Complexity Error-Correcting Codes”, Master's Thesis, Carleton University, Ottawa, Canada, defended March 25, 1998; and Hunt A., Crozier S., Falconer D., “Hyper-Codes: High-performance Low-Complexity Error-Correcting Codes”, 19th Biennial Symposium on Communications, Ontario, Canada, pp. 263-267, May 31-June 3, 1998) as well as devices according to patents of the Russian Federation for inventions No. 2166235; 2209519; 2209520; 2,256,294; 2344556).

The closest device of the same purpose is an erasure correction decoder (see RF patent for inventions No. 2344556), comprising a receiving unit, one output of which is connected to a drive through a signal analyzer, and the other is connected to the input of a code combination drive, the output of which is connected to the first the input of the erasure correction unit, characterized in that the verification switch, the cluster determination unit, the cluster correction unit, the direct coordinate unit, the invariant coordinate unit and the comparison unit, the output of which it is connected to the second input of the erase correction unit, while the first input of the verification switch is connected to the drive output, the second input of the verification switch is connected to the output of the code combination drive, and the output is connected to one of the inputs of the cluster definition block, as well as to the input of the direct coordinate block, one whose output through the block of invariant coordinates is connected to the third input of the comparison block, the second input of which is connected to the output of the block of direct coordinates, while the first output of the cluster definition block is connected to input b a cluster correction lock, the output of which is connected to another input of the cluster definition block, the second output of which is connected to the first input of the comparison block.

The disadvantages of the work of analogues, including the prototype, include the impossibility of using modes of operation with adaptation, by the parameter entered into the redundancy code, the difficulty of implementing the synchronization procedure of the encoder and decoder according to the selected generating polynomial when changing redundancy and the need for situational transformation of software and hardware, implementing the specified code.

In addition, the iterative transformations performed in the analog cluster correction block require a large number of iterations to correct the erroneous cluster symbol due to the need to calculate posterior estimates without taking into account the sign of the corrected symbols and the unproductive first iteration step when the posterior estimates are considered equal to zero.

The technical result consists in increasing the reliability and speed of information transfer. To achieve a technical result, an adaptive decoder for product codes of dimension 3D containing a receiving unit (1), the first output of which is connected through a code combination drive (3) to one input of a data combining unit (4), the other input of which is through one output of a soft decision store ( 2) it is connected to the second output of the receiving unit (1), it is proposed to introduce an additional parameter accumulator ID (5), matrix array (6), 2D parameter block (7), 2D parameter accumulator (8), iterative 2D transformation block (9), data distribution unit (10), a query block (11), a column parameter store (12), a 3D matrix drive (13), a row parameter store (14), an iterative 3D block (15) and an information store (16), while the output of the combining unit data (4) is connected to the input of the parameter drive ID (5), one output of which is connected to the input of the matrix drive (6), the first output of which is connected through a series-connected 2D parameter block (7) and the 2D parameter drive (8) is connected to the third input of the block iterative 2D transforms (9), while its second and first inputs are connected respectively to another output of the matrix storage (6) and to another output of the storage of parameters 1D (5), and the output of the iterative transformation block 2D (9) is connected to the input of the data distribution block (10), while the first output of this block is connected to another input an information storage device (16), while the second output of the data distribution unit (10) is connected to one input of the 3D matrix storage device (13), and the third output of the data distribution unit is connected to the input of the column parameter storage (12), while the fourth output of the data distribution unit (10) connected to another input of the request block (11), the output of which is connected to the feedback channel, and the other output of the column parameter storage (12) is connected to another input of the 3D matrix storage (13), the second output of which is connected to the row parameter storage (14) to the third input of the 3D iterative transformation block (15), while the second and first inputs of this block are connected respectively to one output of the 3D matrix array (13) and to one output of the column parameter storage (12), and the output of the 3D iterative transformation block (15) is connected It is connected to one input of the storage of information (16), and one input of the block of requests (11) is connected to the other output of the storage of soft solutions (2).

We consider the operation of an adaptive decoder using an example of processing 4 × 4 matrices, which are formed by a transmitter as a result of parity verification of three-bit sequences.

Let the transmitter form a sequence of the form:

Matrix 2D No. 1 Matrix 2D No. 2 Matrix 2D No. 3 Matrix 2D No. 4

$$\begin{array}{cccc}\mathrm{one}& \mathrm{one}& \mathrm{one}& \mathrm{one}\\ 0& \mathrm{one}& \mathrm{one}& 0\\ \mathrm{one}& 0& \mathrm{one}& 0\\ 0& 0& \mathrm{one}& \mathrm{one}\end{array}$$

$$\begin{array}{cccc}\mathrm{one}& 0& 0& \mathrm{one}\\ 0& 0& 0& 0\\ 0& \mathrm{one}& \mathrm{one}& 0\\ 0& \mathrm{one}& \mathrm{one}& \mathrm{one}\end{array}$$

$$\begin{array}{cccc}\mathrm{one}& \mathrm{one}& 0& 0\\ 0& 0& \mathrm{one}& \mathrm{one}\\ 0& \mathrm{one}& 0& \mathrm{one}\\ \mathrm{one}& 0& \mathrm{one}& 0\end{array}$$

$$\begin{array}{cccc}\mathrm{one}& 0& \mathrm{one}& 0\\ 0& \mathrm{one}& 0& \mathrm{one}\\ \mathrm{one}& 0& 0& \mathrm{one}\\ 0& \mathrm{one}& \mathrm{one}& 0\end{array}$$

The first three matrices are the products of codes of dimension 2D (parity by rows and columns), the fourth matrix is the parity of the same elements of the first three matrices and together with them determines the product of codes of dimension 3D. After the first three matrices are transmitted over the interference channel, each bit of the binary sequence is fixed by the reception unit in the form of two sequences. (Matrix No. 4 is transmitted only if a request is received by the transmitter from the receiver). The first sequence is represented by a set of hard decisions in the form of logical zeros or ones, and the second sequence is represented by a set of soft decisions whose numbers are synchronous to the numbers of a sequence of hard decisions.

Hard decisions from the first output of receiving unit 1 are transferred to the code combination drive 3 and combined with soft decisions in the data combining unit. Soft decisions based on the parameters of the received signal obtained in block 1 are formed as integer values and are accumulated in the soft decision storage 2, and then transmitted through one output of block 2 to another input of block 4. Block 2 performs the functions of analyzing the state of the communication channel. In this block, the number of threshold symbols is set, overcoming which leads to the refusal to decode the code pattern. Such characters should have low gradations of soft solutions. If the set threshold is reached in block 2, a signal is transmitted to the other output of this block to one input of the block of requests 11, which is a warning signal about the unsatisfactory state of the communication channel. In block 4, information units are replaced by a sign (+), and zeros are replaced by a sign (-), and the received sequence of matrices of dimension 2D takes the form:

Matrix 2D No. 1 Matrix 2D No. 2 Matrix 2D No. 3

$$\begin{array}{cccc}+5& -\widehat{\mathrm{one}}& +7& +7\\ -7& +6& +7& -7\\ +6& +\widehat{3}& +\mathrm{four}& +\widehat{2}\\ -7& -7& +6& +7\end{array}$$

$$\begin{array}{cccc}+6& -3& -2& +2\\ +\widehat{2}& +\widehat{3}& -3& +\widehat{2}\\ +\widehat{\mathrm{one}}& +3& -\widehat{3}& -3\\ +\widehat{2}& -\widehat{2}& +\mathrm{one}& +5\end{array}$$

$$\begin{array}{cccc}+5& -\widehat{2}& -\mathrm{four}& -5\\ -6& -6& +7& +7\\ -7& -\widehat{3}& -\mathrm{four}& +6\\ +7& -7& +7& -7\end{array}$$

отмечены биты, жесткие решения для которых из-за влияния помех в канале связи оказались искаженными. Совмещение данных в блоке 4 происходит по строкам матриц. После обработки все элементы каждой строки данных из блока 4 поступают в накопитель параметров 1D (блок 5), где производится оценка выполнения условия четности принятой последовательности, среднее значение мягких решений и степень их отклонения от этого среднего значения.In the given matrices, the symbol $$(\widehat{x})$$

bits are marked, hard decisions for which, due to the influence of interference in the communication channel, turned out to be distorted. The combination of data in block 4 occurs along rows of matrices. After processing, all the elements of each data row from block 4 go to the parameter accumulator 1D (block 5), where they evaluate the fulfillment of the parity condition of the adopted sequence, the average value of soft decisions, and the degree of their deviation from this average value.

, где λ_i - мягкие решения символов строки (столбца), а степень отклонения от М(λ) как $$\sigma (\lambda )=(1/n-1){\displaystyle {\sum }_{i=1}^n(\left|M(\lambda )\right|-\left|{\lambda }_i\right|}{)}^2$$

. Например, в ходе работы блока 5 для первой строки матрицы 2D №1 будут сформированы следующие данные:When parity is performed in the analyzed row of the matrix, it is assigned an index: sign = (+), otherwise: sign = (-). The average value is estimated by the formula $$M(\lambda )=(\mathrm{one}/n){\displaystyle {\sum }_{i=\mathrm{one}}^n\left|{\lambda }_i\right|}$$

, where λ _i are soft solutions of row (column) symbols, and the degree of deviation from M (λ) as $$\sigma (\lambda )=(\mathrm{one}/n-\mathrm{one}){\displaystyle {\sum }_{i=\mathrm{one}}^n(\left|M(\lambda )\right|-\left|{\lambda }_i\right|}{)}^2$$

. For example, during the operation of block 5, the following data will be generated for the first row of matrix 2D No. 1:

-M(λ)=-5; σ(λ_i)=8. $$\begin{array}{cccc}+5& -\widehat{\mathrm{one}}& +7& +7\end{array}$$

-M (λ) = - 5; σ (λ _i ) = 8.

Similar data is generated for each row of all 2D matrices. In this case, the operational data relating to the symbols of the processed row of the 2D matrix is transmitted sequentially row by row to the matrix drive 6. When 6 all data columns are formed in the drive 6, data similar to the data for the rows is generated in the 2D parameter block (block 7): sign , M (λ), σ (λ), which are synthesized for each column in the 2D parameter accumulator (block 8). After all the operations on the rows and columns of the 2D matrix are completed, its data is transferred to the iterative 2D transformation block (block 9), thus freeing blocks 6, 7 and 8 for processing the next group of data. Therefore, before performing the first iteration step, a block of the form will be fixed in block 9:

$$\begin{array}{cccccc}+5& -\widehat{\mathrm{one}}& +7& -7& -5& 8\\ -7& +6& +7& -7& +6.75& 0.25\\ +6& +\widehat{3}& +\mathrm{four}& +\widehat{2}& +3.75& 2.92\\ -7& -7& +6& +7& +6.75& 0.25\\ +6.25& +4.25& +6& -5.75& 0& 0\\ 0.92& 7.58& 2.0& 6.25& 0& 0\end{array}$$

The block of iterative 2D transformations at the first step selects rows (columns) for which the parity condition is not fulfilled. The efficiency criterion in the selection procedure is an analytical expression of the form:

$$Q\left\{S;M(\lambda );\sigma (\lambda )\right\}\Rightarrow \underset{S\to -\lambda }{sign(M(\lambda ))};\left|\underset{\max }{M(\lambda )}\right|;\underset{\min }{\sigma (\lambda )}$$

In accordance with this criterion, the fourth column is selected in the resulting matrix. Correction in a column (row) is carried out according to the rule:

, $$L({\lambda }_i)+L({\lambda }_p)={(-\mathrm{one})}^{\mathrm{one}-f}\times \left[L({\lambda }_{\mathrm{one}})\right]\times sign\left[L({\lambda }_p)\right]\times \min (\left|L({\lambda }_i)\right|,\left|L({\lambda }_p)\right|)$$

,

, в скобках показан символ, исключаемый из процедуры восстановления.where sign [•] returns the value of its argument; L (λ _i ) is a soft solution for the character involved in the formation of the parity check; Δ (λ _p ) is a soft solution for the check character; f is the number of folding positive soft decisions only among information bits. In the selected row (column), block 9 selects the most reliable characters, and then performs iterative transformations in the row (column). For the reduced matrix and the selected fourth column we get: $$\begin{array}{cccccccc}(+7)& -7& +\widehat{2}& +7& \Rightarrow & -7& +\widehat{2}& +7\end{array}$$

, in brackets the symbol is excluded from the recovery procedure.

For the resulting relation, f = 1, since the most reliable symbol (+7) was removed from the iterative transformation procedure. Hence:

[+ 2-7] + 7 = -5 - a new posterior estimate for (-7);

.[-7 + 2] + 7 = -5 - a new posterior estimate for $$(+\widehat{2})$$

.

Correction results for the line: $$+7(-7-5)(+\widehat{2}-5)+7=+7-13-3+7$$

Index values with an absolute value greater than 7 in the block are replaced with a value of 7 to preserve the bit grid of the representation of MP indices.

The error in the third position is fixed. The matrix takes the form:

$$\begin{array}{cccccc}+5& -\widehat{\mathrm{one}}& +7& +7& -5& 8\\ -7& +6& +7& -7& +6.75& 0.25\\ +6& +\widehat{3}& +\mathrm{four}& -3& -4.00& 2.00\\ -7& -7& +6& +7& +6.75& 0.25\\ +6.25& +4.25& +6& 6.00& 0& 0\\ 0.92& 7.58& 2.0& 4.00& 0& 0\end{array}$$

и f=1.Since the first row in this matrix, the value of M (λ _i ) has a negative sign and M (λ _i ) for it is the largest among the revealed negative ones. For correction, the decoder selects the first line: $$\begin{array}{cccccccc}+5& -\widehat{\mathrm{one}}& (+7)& +7& \Rightarrow & +5& -\widehat{\mathrm{one}}& +7\end{array}$$

and f = 1.

Further according to the iterative conversion:

[-1 + 5] + 7 = + 4 - corrective score for (+5);

.[+ 5-1] + 7 = + 4 - corrective assessment for $$(-\widehat{\mathrm{one}})$$

.

Correction results for the line: (+ 5 + 4) (- 1 + 4) + 7 + 7 = + 9 + 3 + 7 + 7.

In the block, the index values in absolute value greater than 7 are replaced by a value of 7 to preserve the bit grid of the representation of MP indices.

The error in the third line is fixed. The matrix takes the form:

$$\begin{array}{cccccc}+5& +3& +7& +7& 5.50& 3.67\\ -7& +6& +7& -7& +6.75& 0.25\\ +6& +\widehat{3}& +\mathrm{four}& -3& -4.00& 2.00\\ -7& -7& +6& +7& +6.75& 0.25\\ +6.25& -4.75& +6.00& 6.00& 0& 0\\ 0.92& 4.25& 2.00& 4.00& 0& 0\end{array}$$

, при этом f=1. Символ (+3) вычеркнут, поскольку он был подвергнут коррекции на предыдущем шаге, поэтому его достоверность не вызывает сомнений, кроме того, он по абсолютной величине равен другому корректируемому символу с индексом 3.In accordance with the efficiency criterion for error correction in the second column or third row, you must select the row (column) with the largest criterion M (λ). This is the second column, whose average value is higher and the largest λ _p . Therefore, a sequence is highlighted for corrections $$\begin{array}{cccccccc}(+3)& +6& +\widehat{3}& -7& \Rightarrow & +6& +\widehat{3}& -7\end{array}$$

, while f = 1. The symbol (+3) is crossed out because it was corrected in the previous step, therefore its reliability is beyond doubt, in addition, in absolute value it is equal to another correctable symbol with index 3.

циклически сдвигается на шаг влево. Полученная последовательность $$\begin{array}{ccc}+\widehat{3}& -7& +6\end{array}$$

обрабатывается обычным образом.With the same signs of the corrected characters, the iterative transformation process is delayed and becomes ineffective. To reduce the number of iterations, the sequence $$\begin{array}{ccc}+6& +\widehat{3}& -7\end{array}$$

cyclically moves one step to the left. The resulting sequence $$\begin{array}{ccc}+\widehat{3}& -7& +6\end{array}$$

processed in the usual way.

- новая апостериорная оценка для $$(+\widehat{3})$$

; $$\lfloor -7+\widehat{3}\rfloor +6=-\mathrm{four}$$

- new posterior rating for $$(+\widehat{3})$$

;

- новая апостериорная оценка для (-7). $$\lfloor +\widehat{3}-7\rfloor +6=-\mathrm{four}$$

- a new posterior estimate for (-7).

преобразуется к виду $$\begin{array}{ccc}-1& -14& +6\end{array}$$

. Второй шаг итерации дает:After correction, the sequence $$\begin{array}{ccc}+\widehat{3}& -7& +6\end{array}$$

converted to a view $$\begin{array}{ccc}-\mathrm{one}& -\mathrm{fourteen}& +6\end{array}$$

. The second step of the iteration gives:

[-14-1] + 6 = -6 - a new posterior estimate for (-1);

[-1-14] + 6 = -6 is the new posterior estimate for (-14).

и после циклического сдвига вправо $$\begin{array}{ccc}+6& -7& -20\end{array}$$

или окончательно $$\begin{array}{cccc}+3& +6& -7& -7\end{array}$$

.We get the sequence $$\begin{array}{ccc}-7& -\mathrm{twenty}& +6\end{array}$$

and after a cyclic shift to the right $$\begin{array}{ccc}+6& -7& -\mathrm{twenty}\end{array}$$

or finally $$\begin{array}{cccc}+3& +6& -7& -7\end{array}$$

.

$$\begin{array}{cccccc}+5& +3& +7& +7& +5.50& 3.67\\ -7& +6& +7& -7& +6.75& 0.25\\ +6& -7& +\mathrm{four}& -3& +5.00& 3.33\\ -7& -7& +6& +7& 6.75& 0.25\\ +6.25& +5.75& +6.00& +6.00& 0& 0\\ 0.92& \mathrm{3,58}& 2.00& 4.00& 0& 0\end{array}$$

The data of this matrix through the data distribution block 10 is sent to blocks 12 and 13. In block 12 - the column parameter storage device, the column parameters are sent through the third output of the data distribution block. For example:

1 column 2 column 3 column 4 column + 6.25 +5.75 +6.00 +6.00 0.92 3,58 2.00 4.00

The matrix matrix 3D (block 13) through the second output of block 10 receives data on the information symbols of the adjusted matrix. For example:

$$\begin{array}{cccc}+5& +3& +7& +7\\ -7& +6& +7& -7\\ +6& -7& +\mathrm{four}& -3\\ -7& -7& +6& +7\end{array}$$

To form a product of 3D dimensional coefficients, a 3D matrix storage device distributes the obtained data into columns of new matrices. For example:

3D matrix №1 Matrix 3D №2 Matrix 3D №3 Matrix 3D №4

$$\begin{array}{cccc}+5& ...& ...& ...\\ -7& ...& ...& ...\\ +6& ...& ...& ...\\ -7& ...& ...& ...\\ +6.25& ...& ...& ...\\ 0.92& ...& ...& ...\end{array}$$

$$\begin{array}{cccc}+3& ...& ...& ...\\ +6& ...& ...& ...\\ -7& ...& ...& ...\\ -7& ...& ...& ...\\ +5.75& ...& ...& ...\\ 3.58& ...& ...& ...\end{array}$$

$$\begin{array}{cccc}+7& ...& ...& ...\\ +7& ...& ...& ...\\ +\mathrm{four}& ...& ...& ...\\ +6& ...& ...& ...\\ +6.00& ...& ...& ...\\ 2.00& ...& ...& ...\end{array}$$

$$\begin{array}{cccc}+7& ...& ...& ...\\ -7& ...& ...& ...\\ -3& ...& ...& ...\\ +7& ...& ...& ...\\ +6.00& ...& ...& ...\\ 4.00& ...& ...& ...\end{array}$$

At this moment, the soft decision store 2 processes the data of the 2D matrix No. 2 and captures a large number of soft solutions with a low index. The soft decision store 2 through another output and through one input of the query block 11 issues a command to organize a request to the transmitter and transfer additional redundancy, therefore, the data of matrix 2D No. 2 through the matrix drive 6 and the iterative transform block 9 without sending iterative transformations from the output of block 9 at the input of the data distribution block 10, each column of this matrix is accompanied by the values of signM (λ), M (λ), and σ (λ). For example:

3D matrix №1 Matrix 3D №2 Matrix 3D №3 Matrix 3D №4

$$\begin{array}{cccc}+7& +6& ...& ...\\ -7& +\widehat{2}& ...& ...\\ +6& +\widehat{\mathrm{one}}& ...& ...\\ -7& +\widehat{2}& ...& ...\\ +6.75& +2.75& ...& ...\\ 0.25& 0.25& ...& ...\end{array}$$

$$\begin{array}{cccc}+3& -3& ...& ...\\ +6& +\widehat{3}& ...& ...\\ -7& +3& ...& ...\\ -7& -\widehat{2}& ...& ...\\ +5.75& 2.75& ...& ...\\ \mathrm{3,58}& 0.25& ...& ...\end{array}$$

$$\begin{array}{cccc}+7& -2& ...& ...\\ +7& -3& ...& ...\\ +\mathrm{four}& -\widehat{3}& ...& ...\\ +6& +\mathrm{one}& ...& ...\\ +6.00& -2.25& ...& ...\\ 2.00& 0.92& ...& ...\end{array}$$

$$\begin{array}{cccc}+7& +2& ...& ...\\ -7& +\widehat{2}& ...& ...\\ -3& -3& ...& ...\\ +7& +5& ...& ...\\ +6.00& -3.00& ...& ...\\ 4.00& 2.00& ...& ...\end{array}$$

Matrix 2D No. 3 is transformed as a result of iterative transformations to the form. Source Matrix:

$$\begin{array}{cccccc}+5& -\widehat{2}& -\mathrm{four}& -5& -4.00& 2.00\\ -6& -6& +7& +7& +6.50& 0.30\\ -7& -\widehat{3}& -\mathrm{four}& +6& -5.00& 3.30\\ +7& -7& +7& -7& +7.00& 0\\ +6.25& +\mathrm{4,50}& +5.50& +6.25& 0& 0\\ 0.92& 5.67& 3.00& 0.92& 0& 0\end{array}$$

In accordance with the decoding algorithm, a third line is selected for subsequent correction, having a large value of the parameter M (λ _i ).

и f=0, поскольку удаленное мягкое решение имеет отрицательный знак. Последовательность $$\begin{array}{ccc}-\widehat{3}& -4& +6\end{array}$$

циклически сдвигается на шаг вправо. Полученная последовательность $$\begin{array}{ccc}+6& -\widehat{3}& -4\end{array}$$

обрабатывается обычным образом. Тогда:Hence, $$\begin{array}{cccccccc}(-7)& -\widehat{3}& -\mathrm{four}& +6& \Rightarrow & -\widehat{3}& -\mathrm{four}& +6\end{array}$$

and f = 0, since the remote soft solution has a negative sign. Sequence $$\begin{array}{ccc}-\widehat{3}& -\mathrm{four}& +6\end{array}$$

cyclically moves one step to the right. The resulting sequence $$\begin{array}{ccc}+6& -\widehat{3}& -\mathrm{four}\end{array}$$

processed in the usual way. Then:

[-3 + 6] -4 = + 3 - a new posterior estimate for (+6);

.[+ 6-3] -4 = + 3 - a new posterior estimate for $$(-\widehat{3})$$

.

преобразуется к виду $$\begin{array}{ccc}+9& \widehat{0}& -4\end{array}$$

. Второй шаг итерации дает:After correction, the sequence $$\begin{array}{ccc}+6& -\widehat{3}& -\mathrm{four}\end{array}$$

converted to a view $$\begin{array}{ccc}+9& \widehat{0}& -\mathrm{four}\end{array}$$

. The second step of the iteration gives:

[0 + 9] -4 = + 4 - a new posterior estimate for (+9);

.[9 + 0] -4 = + 4- a new posterior estimate for $$(\widehat{0})$$

.

и после циклического сдвига влево $$\begin{array}{ccc}4& -4& 13\end{array}$$

или окончательно $$\begin{array}{cccc}-7& +4& -4& 7\end{array}$$

. Матрица принимает вид:We get the sequence $$\begin{array}{ccc}+13& +\mathrm{four}& -\mathrm{four}\end{array}$$

and after a cyclic shift to the left $$\begin{array}{ccc}\mathrm{four}& -\mathrm{four}& 13\end{array}$$

or finally $$\begin{array}{cccc}-7& +\mathrm{four}& -\mathrm{four}& 7\end{array}$$

. The matrix takes the form:

$$\begin{array}{cccccc}+5& -\widehat{2}& -\mathrm{four}& -5& -4.00& 2.00\\ -6& -6& +7& +7& +6.50& 0.33\\ -7& +\mathrm{four}& -\mathrm{four}& +7& +5.50& 3.00\\ +7& -7& +7& -7& +7.00& 0\\ +6.25& -4.75& +5.50& +6.50& 0& 0\\ 0.92& 4.92& 3.00& 1.00& 0& 0\end{array}$$

и f=0, поскольку удаляется отрицательный символ.In accordance with a particular algorithm, the second column is selected, then - $$\begin{array}{cccccccc}-\widehat{2}& (-6)& +\mathrm{four}& -7& \Rightarrow & -\widehat{2}& +\mathrm{four}& -7\end{array}$$

and f = 0 because the negative character is removed.

Further according to the iterative conversion:

;[+ 4-2] -7 = + 2 - corrective assessment for $$(-\widehat{2})$$

;

[-2 + 4] -7 = + 2 - corrective score for (+4).

преобразуется к виду $$\begin{array}{ccc}\widehat{0}& +6& -7\end{array}$$

. Второй шаг итерации дает:After correction, the sequence $$\begin{array}{ccc}-\widehat{2}& +\mathrm{four}& -7\end{array}$$

converted to a view $$\begin{array}{ccc}\widehat{0}& +6& -7\end{array}$$

. The second step of the iteration gives:

;[+ 6 + 0] -7 = + 6 - corrective assessment for $$(\widehat{0})$$

;

[0 + 6] -7 = + 6 - corrective score for (+6).

или окончательно $$\begin{array}{cccc}+6& -6& +7& -7\end{array}$$

. Матрица принимает вид:We get the sequence $$\begin{array}{ccc}+6& +12& -7\end{array}$$

or finally $$\begin{array}{cccc}+6& -6& +7& -7\end{array}$$

. The matrix takes the form:

$$\begin{array}{cccccc}+5& +6& -\mathrm{four}& -5& +5.00& 0.67\\ -6& -6& +7& +7& +6.50& 0.33\\ -7& +7& -\mathrm{four}& +7& +6.25& 2.25\\ +7& -7& +7& -7& +7.00& 0\\ +6.25& +6.50& +5.50& +6.50& 0& 0\\ 0.92& 0.33& 3.00& 1.00& 0& 0\end{array}$$

Thus, in the 3D matrix drive (block 13), at the time of receiving the requested block, a sequence of characters is formed:

3D matrix №1 Matrix 3D №2

$$\begin{array}{cccc}+7& +6& +5& ...\\ -7& +\widehat{2}& -6& ...\\ +6& +\widehat{\mathrm{one}}& -7& ...\\ -7& +\widehat{2}& +7& ...\\ +6.75& +2.75& +6.25& ...\\ 0.25& 4.91& 0.92& ...\end{array}$$

$$\begin{array}{cccc}+3& -3& +6& ...\\ +6& +\widehat{3}& -6& ...\\ -7& +3& +7& ...\\ -7& -\widehat{2}& -7& ...\\ +5.75& +2.75& +5.50& ...\\ \mathrm{3,58}& 0.25& 0.333& ...\end{array}$$

Matrix 3D №3 Matrix 3D №4 $$\begin{array}{cccc}+7& -2& -\mathrm{four}& ...\\ +7& -3& +7& ...\\ +\mathrm{four}& -\widehat{3}& -\mathrm{four}& ...\\ +6& +\mathrm{one}& +7& ...\\ +6.00& -\mathrm{2,50}& +5.50& ...\\ 2.00& 0.33& 3.00& ...\end{array}$$

$$\begin{array}{cccc}+7& +2& -5& ...\\ -7& -\widehat{2}& +7& ...\\ -3& -3& +7& ...\\ +7& +5& -7& ...\\ +6.00& -3.00& +6.50& ...\\ 4.00& 2.00& 1.00& ...\end{array}$$

According to the errors noted in the above matrices, it is noticeable that decoding at the 3D dimensionality level plays the role of a kind of interleaver and character recovery does not cause difficulties provided that high-quality characters of additional redundancy are transmitted. Let the matrix 2D No. 4 adopted in the form:

$$\begin{array}{cccccc}+7& -5& +7& -7& +6.50& 1.00\\ -5& +6& -6& +6& +5.75& 0.25\\ +6& -7& -7& -7& +6.75& 0.25\\ -7& +6& +7& -7& +6.75& 0.25\\ +6.25& +6.00& +6.75& +6.75& 0& 0\\ 0.92& 0.67& 0.25& 0.25& 0& 0\end{array}$$

After this matrix arrives at block 13, row data related to the mathematical expectation and variance are generated in the row parameter accumulator (14). Based on these data, in the 3D iterative transformation block (15), 3D matrices are processed in parallel. This becomes possible due to the absence of interrelated relationships between matrices. Thus, the block 15 receives the matrix:

3D matrix №1 3D matrix №2

$$\begin{array}{cccccc}+5& +6& +5& +7& +5.75& 0.92\\ -7& +\widehat{2}& -6& -5& -5.00& 4.67\\ +6& +\widehat{\mathrm{one}}& -7& +6& -5.00& 7.33\\ -7& +\widehat{2}& +7& -7& +5.75& 6.25\\ +6.25& +2.75& +6.25& +6.25& 0& 0\\ 0.92& 4.92& 0.92& 0.92& 0& 0\end{array}$$

$$\begin{array}{cccccc}+3& -3& +6& -5& +4.25& 2.25\\ +6& +\widehat{3}& -6& +6& -5.25& 2.25\\ -7& +3& +7& -7& +6.00& 4.00\\ -7& -\widehat{2}& -7& +6& -5.50& 5.67\\ +5.75& +2.75& +6.50& +6.00& 0& 0\\ \mathrm{3,58}& 0.25& 0.33& 0.67& 0& 0\end{array}$$

Matrix 3D №3 Matrix 3D №4

$$\begin{array}{cccccc}+7& -2& -\mathrm{four}& +7& +5.00& 6.00\\ +7& -3& +7& -6& +5.75& \mathrm{3,58}\\ +\mathrm{four}& -\widehat{3}& -\mathrm{four}& -7& -\mathrm{4,50}& 3.00\\ +6& +\mathrm{one}& +7& +7& +5.25& 8.25\\ +6.00& -25& +5.50& +6.75& 0& 0\\ 2.0& 0.92& 3.00& 0.25& 0& 0\end{array}$$

$$\begin{array}{cccccc}+7& +2& -5& -7& +5.25& 5.58\\ -7& +\widehat{2}& +7& +6& -5.50& 5.67\\ -3& -3& +7& -7& +5.00& 5.33\\ +7& +5& -7& -7& +6.50& 1.00\\ +6.00& -3.00& +6.50& -6.75& 0& 0\\ 4.00& 2.00& 1.00& 0.25& 0& 0\end{array}$$

Thus, the proposed decoder makes it possible to implement the principle of parametric adaptation with respect to the parameter introduced into the redundancy code, to perform the error decorrelation procedure without the use of interleavers and deinterleavers. The use of an iterative symbol recovery procedure is supplemented by a calculated parameter of the average estimate of soft decisions along the length of the code vector and the estimate of the spread of soft decisions, which improves the quality of the decoder.

Claims (1)

An adaptive 3D code product decoder comprising a receiving unit, the first output of which is connected via a code combination drive to one input of the data combining unit, the other input of which is connected to the second output of the receiving unit through one output of the soft decision storage unit, characterized in that a parameter storage unit is additionally introduced 1D, matrix storage, 2D parameter block, 2D parameter storage, 2D iterative transformation block, data distribution block, query block, column parameter storage, matrix 3D storage device, string parameters storage device, 3D iterative transformation unit and information storage device, while the output of the data combining unit is connected to the input of the data storage device 1D, one output of which is connected to the input of the matrix storage device, the first output of which is connected via a series-connected 2D parameter block and the data storage device 2D is connected to the third input of the block of iterative transformations 2D, while its second and first inputs are connected respectively to another output of the matrix storage and to another output of the storage By dividing the parameters 1D, the output of the iterative transformation block 2D is connected to the input of the data distribution block, while the first output of this block is connected to another input of the data storage device, while the second output of the data distribution block is connected to one input of the 3D matrix storage device, and the third output of the distribution block the data is connected to the input of the column parameter storage device, while the fourth output of the data distribution block is connected to another input of the request block, the output of which is connected to the feedback channel, and the other output to the column of parameter parameters is connected to another input of the 3D matrix drive, the second output of which is connected to the third input of the iterative 3D transformations through the row parameter drive, while the second and first inputs of this block are connected respectively to one output of the 3D matrix drive and to one output of the column parameter drive and the output of the 3D iterative transformation block is connected to one input of the information storage device, and one input of the request block is connected to the other output of the soft solutions storage device.