RU2340091C2 - Method of decoding serial cascade code (versions) - Google Patents

Abstract

FIELD: information technology.

SUBSTANCE: for the received code implementation, extended syndromes are calculated for each code word of the component code of the cascade code, and, using an extended test matrix, the sets of lines which take part in the generation of any nonzero element of the extended syndrome (the number of lines of the extended test matrix, included in the set of lines, corresponds to the positions of single and two-fold errors of the distorted code word) are determined. Further successively inspecting extended syndromes of one of the code components, arrays of isolated errors are defined, which are joined in alternative groups of isolated errors, and during decoding with a "solid" solution, the most probable correction vector chosen is that alternative group, which has the least weight and all syndromes of component codes are nullified. During decoding with a "soft" solution, that alternative group with maximum modified metric is chosen, and those elements of the systematic part of the code word of the cascade code are inverted, the number of which corresponds to the positions of nonzero elements in the correction vector.

EFFECT: realisation of an optimum decoding procedure, increased authenticity of decoding and reduced device and computational complexity and provision for decoding turbo-codes with component cyclic linear block codes.

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Description

The invention relates to the field of communication technology, in particular to information transmission systems in which cascading codes with serial connection through an interleaver of cyclic linear block codes or turbo codes with component cyclic linear block codes are used to protect it from distortion in the communication channel. The invention can be used in codecs (encoder-decoder) of data transmission systems, as well as in error-correcting coding devices for transmitting and storing discrete information.

There is a method of decoding cascade codes with serial connection through an interleaver of component cyclic linear block block codes [1, 3-5], which includes two decoding procedures for a two-component cascade code, which are SISO modules (“soft” input, “soft” output) , and two interleaving procedures for mixing “soft” information exchanged by decoding procedures. The input of the first SISO module receives two sequences: a priori information about the sequence of information symbols and a “soft” output of the communication channel (demodulator), and “soft” solutions are formed at the output, which are the ratio of posterior probabilities of the information elements of the code and which, after interleaving, serve as a priori information about information elements for the second SISO module. The second SISO module refines the values of the analyzed information elements and calculates its “soft” estimates of the information elements, which, after deinterleaving, enter the input of the first SISO module, and the iterative process continues. After each iteration, a priori information about each information element is increased. The decoding process ends either after performing a given number of iterations, or after the correction value of the decoding result reaches a certain threshold value.

The main disadvantages of this decoding method are its great computational complexity and long decoding delay time, since a long codeword is decoded (several tens of thousands of elements), and several iterations are necessary to process the distorted codeword. In addition, this decoding method relates to quasi-optimal decoding methods.

The aim of the invention is to increase the reliability (quality) of decoding, reduce the hardware and computational complexity of decoding, reduce the delay time, and, in particular, implement the optimal decoding procedure with both “soft” and “hard” solutions.

To achieve the goal, a method is proposed for the coding of a cascade code syndrome with serial connection through an interleaver of cyclic linear block codes, in which the most probable value of the systematic part of the code word is formed not as a result of an iterative procedure involving cyclic processing of the code word using SISO modules, but as a result search for the optimal correction vector, which is based on the representation of the n-bit extended syndrome s of the component code in the form of linear combinations th rows extended check matrix H _{n, n,} and representation of the error vector e _kc distort codeword in a set of primitive (indecomposable) correction vectors.

The expanded verification matrix H _{n, n} is the transposed verification matrix [1], in which the jth row consists of coefficients for the unknown polynomial h _j (x) = x ^j h (x) mod (x ⁿ +1) (where h ( x) = (x ⁿ +1) / p (x) is the verification polynomial of the cyclic (n, k) code, p (x) is the generating polynomial of the code, and j = 0,1, ... n-1). The transposed extended verification matrix H _{n, n} differs from the verification matrix H _{n, nk} [1] only in that it adds k more rows, each of which is also a cyclic shift of the previous row by one digit to the right. The line number of the extended check matrix indicates the number of the distorted position of the received distorted codeword.

Primitive correction vectors have a configuration of single localized errors, chains of localized errors, as well as localized errors having a configuration of code words of component codes. A single localized error is such an error in the code word of the cascading code, which is the only one in all the code words of the component codes that it has distorted. A chain of localized errors is a sequence of errors in a code word of a cascading code that has a weight of at least two and which is uniquely determined by the syndromes of those code words of component codes that it distorts.

To decode a cascade code with a serial connection through an interleaver of cyclic linear block codes, a method is proposed, which consists in the following.

(где: s_j ⁽ⁱ⁾ - расширенный синдром j-го кодового слова i-го компонентного кода, b_l ⁽ⁱ⁾ - j-е кодовое слово i-го компонентного кода, е_j ⁽ⁱ⁾ - вектор ошибки, исказивший в канале связи - j-е кодовое слово i-го компонентного кода,

- расширенная проверочная матрица i-го компонентного кода), которые заносятся в таблицу (см. фиг.1). Кроме того, для каждого расширенного синдрома вычисляют вектор HN_j ⁽ⁱ⁾, элементами которого являются номера строк расширенной проверочной матрицы, которые могли участвовать в формировании одного из (например, крайнего слева) ненулевого элемента расширенного синдрома. В векторе HN_j ⁽ⁱ⁾ особо помечают номер строки, который соответствует номеру строки расширенного синдрома s_j ⁽ⁱ⁾ (см. фиг.1). Номер особо помеченной строки указывает на позицию возможной однократной ошибки в b_j ⁽ⁱ⁾-м кодовом слове компонентного кода, а каждый непомеченный номер строки указывает на позицию одного из искаженных элементов возможной двукратной ошибки в том же b_j ⁽ⁱ⁾-м кодовом слове компонентного кода.For adopted possibly distorted code implementing the concatenated code (b⊕e _CS) codeword for which the bicomponent code presented in Figure 1, extended calculated syndromes for each codeword component codes

(where: s _j ⁽ⁱ⁾ is the extended syndrome of the j-th codeword of the i-th component code, b _l ⁽ⁱ⁾ is the j-th code word of the i-th component code, e _j ⁽ⁱ⁾ is the error vector distorted in communication channel - the j-th code word of the i-th component code,

- extended verification matrix of the i-th component code), which are entered in the table (see figure 1). In addition, for each extended syndrome, the vector HN _j ^{(i) is} calculated, the elements of which are the line numbers of the extended check matrix that could participate in the formation of one of (for example, the leftmost) non-zero element of the extended syndrome. The vector HN _j ⁽ⁱ⁾ a particularly marked line number that corresponds to the line number of extended syndrome s _j ^{(i) (see} FIG. 1). The number of the especially marked line indicates the position of a possible one-time error in the b _j ⁽ⁱ⁾ -th codeword of the component code, and each unmarked line number indicates the position of one of the distorted elements of the possible two-time error in the same b _j ⁽ⁱ⁾ -m codeword component code.

Further, the search for the correction vector of the code word of the cascading code is performed in stages.

At the first stage, a search is performed for localized errors in the code word of the cascading code, which begin with a single error in the code words of one of the component codes.

To do this, choose any ith component code, and for each distorted codeword (s _j ⁽ⁱ⁾ ≠ 0) in the vector HN _j ⁽ⁱ⁾ find the number of the especially marked line, which indicates the position of a single error in the jth codeword i-th component code. Then, for all codewords of the component codes that this error has distorted, the specially marked line numbers of the vector HN _g ^{(q) are} compared with the position number of the error in question.

If the numbers match for all component codes, then this error is considered a one-time localized error of the cascading code. It is remembered along with the codeword numbers of the component codes that it has distorted, and the extended syndromes of these codewords are considered conditionally zero (zero only for this localized error).

If the numbers do not coincide, for example, for the codeword b _g ^{(q) of the} qth component code, then we proceed to search for chains of localized errors that may have a double error in this codeword. It should be noted that the position r of the first double-error error in the codeword b _g ^{(q) is} known. It is given by the position of a single error in the jth codeword of the ith component code. The combination of double errors is formed as follows. For the distorted codeword of the component code, the current expanded syndrome s _g ^(q) = s _g ^(q) ⊕h _r and the corresponding vector HN _g ^(q) are calculated in which the number of the especially marked row m of the extended verification matrix indicates the second distorted position of the double errors in the b _g ^(q) codeword. Thus, a combination of the double error e _{r, g} ↔ e _{m, g} in the gth codeword of the qth component code is constructed. Moreover, the extended syndrome s _g ^(q) for the desired chain of errors is considered conditionally zero.

A double error e _{r, g} ↔ e _{m, g} is considered completed in the mth direction if the extended syndromes of all codewords of component codes corrected by the error e _{m, g} become zero. A chain of localized errors is formed until all directions are completed. After that, the chain of localized errors is stored along with the codeword numbers of the component codes that it has distorted, and the extended syndromes of these codewords for this chain of errors are considered conditionally zero.

The search for a localized error chain is terminated when the second error e _{m, g of a} double error falls into one of the code words of the component codes, which already has a conditionally zero syndrome for the constructed chain of localized errors.

If the second error e _{m, g of the} double error falls into the codeword of the component code with zero syndrome s _f ^(u) = 0, then this codeword is possibly distorted by an error that has the configuration of the codeword (for cyclic Hamming codes, the minimum weight of the codeword is three ) In this case, the vector HN _f ^(u) contains the positions of the second errors of the desired triple errors, if we exclude from the consideration the specially marked line number. Therefore, it is necessary to consider w-1 possible combinations of triplicate errors (where w is the number of nonzero coefficients with an unknown code verification polynomial), for which two positions are already known. The third last position of the triple error is determined similarly to the search above for the second last position of the double error.

After considering all the code words of the i-th component code with non-zero extended syndromes, we proceed to the second stage of the search for localized errors.

At the second stage, a search is performed for localized errors in the code word of the cascading code, which begin with a twofold error in the code words of the ith component code. Before performing a search for chains of localized errors from vectors HN _j ^{(i) of} all codewords with s _j ⁽ⁱ⁾ ≠ 0, especially marked line numbers are excluded. Thus, in the vectors HN _j ⁽ⁱ⁾ , only those line numbers of the extended check matrix remain that indicate the position of one of the distorted elements of the alleged two-time codeword error. Then, for each codeword with s ⁽ⁱ⁾ _j ≠ 0, w-1 of possible pairs of double error combinations are generated, which may be the beginning of the alleged chains of localized errors. The second error is found in accordance with the above method. After the pairs of errors e _{r, j} ↔ e _{m, j} are determined, the search for error chains is performed similarly to the search for localized errors in the code word of the cascade code at the first stage. Moreover, the search is carried out in parallel for errors e _{r, j} and e _{m, j} .

After considering all codewords with nonzero syndrome of the ith component code, it is necessary to identify repeating e _p = e _m and intersecting (one or more elements in the selected pair of localized errors coincide) pairs of localized errors among the found localized errors.

To determine the repeated pairs of localized errors e _p = e _{m, it} suffices to calculate NK:

- сумма суммы по mod 2 элементов векторов А и В с одинаковыми индексами i;Where

- the sum of the sum over mod 2 of elements of vectors A and B with the same indices i;

- вектор позиций условно нулевых синдромов r-того компонентного кода для j-ой локализованной ошибки (где j=(p,m)), причем:

is the position vector of conditionally zero syndromes of the r-th component code for the j-th localized error (where j = (p, m)), and:

If NK = 0, then the localized errors are e _p = e _m , and if NK ≠ 0, then the localized errors are e _p ≠ e _m .

To determine the overlapping localized errors e _p and e _{m it is} enough to calculate NN:

or

.

.

или

ненулевыми элементами (где (А∧В) - логическое умножение элементов векторов А и В с одинаковыми индексами i).If NN = 0, then the localized errors e _p and e _m do not intersect, and if NN ≠ 0, then the localized errors e _p and e _m intersect. Intersection positions in the rth component code are indicated in vector

or

nonzero elements (where (А∧В) is the logical multiplication of elements of the vectors A and B with the same indices i).

Then, among the repeated errors, we leave one of them, and exclude the rest from consideration.

After that, alternative groups of localized errors are determined in which intersecting errors are spaced into different groups.

At the third stage, they search for localized errors having the configuration of the code words of the ith component code for each alternative group of localized errors. The need to complete the 3rd stage arises after the completion of the 1st and 2nd stages, when all the extended syndromes of the i-th component code of the cascading code become zero (both initially zero and conditionally zero). In this case, the specially marked line numbers of the vectors HN _r ^{(u) of} nonzero extended syndromes of other component codes either all or in groups indicate one or a group of code words of the ith component code. Moreover, the positions indicated by specially marked line numbers form error chains having a codeword configuration. They should be chosen as the most probable chains of localized errors.

The group of localized errors that has zero and conditionally zero syndromes for all codewords of component codes and has the smallest weight is chosen as the optimal correction vector.

And at the end of the decoding process of the cascading codeword, those elements of its systematic part are inverted whose numbers correspond to the positions of nonzero elements in the correction vector.

In the case when “extended” cyclic codes for decoding with a “hard” solution are used as component codes of the cascade code, a variant of the method described above is proposed in which the extension element is removed in the code words of the component codes before calculating the extended syndromes.

In the case when “shortened” cyclic codes are used as component codes of the cascade code for decoding with a “hard” solution, the methods described above are proposed in which zero elements are added to the beginning of each code word of the “shortened” component code, number which is equal to the value of shortening. Moreover, it is obvious that the zero positions added to the beginning cannot be distorted in the communication channel, since they were not transmitted through it. This fact reduces the number of localized errors, which leads to a decrease in the computational complexity of decoding.

In the case when the cascade code is decoded with a “soft” solution, variants of the methods described above are proposed in which, for the localized error e _{m, the} modified metric v _{m is} calculated for all codewords of the component codes into which the elements of the localized error e _m fall:

or

where p (y _j / b _{j, c} ) is the conditional probability that the value y _{j is} obtained at the output of the demodulator when transmitting through the communication channel at the jth position the code word of the component code of element c, which for the binary code can take the value 0 or one,

e _{i, j} is a localized error element that has distorted the j-th element of the codeword of the i-th component code.

The modified metric is the ratio of the generally accepted metric [1-3] of the i-th code word to the metric received from the communication channel with the “hard” solution of the distorted code word. Those elements of the cascaded code received with a “hard” solution are corrected that are specified by an alternative group of localized errors with a maximum metric v _m and which resets all component codes of the cascade code.

In the case when a cascade code with “shortened” component codes is decoded with a “soft” solution, a variant of the method described above is proposed, in which, before decoding to the beginning of the “shortened” code words of the component codes, zero elements are added, the number of which is equal to the shortening value, with conditional probabilities p (y _j / b _{j, 0} ) = 1 and p (y _j / b _{j, 1} ) = 0.

The proposed technical solutions allow us to solve the problem of optimal syndromic decoding of a cascade code with serial connection through an interleaver of cyclic linear block codes with both hard and soft solutions with less computational and hardware complexity than known decoders [1-5]. In addition, the proposed method can also be applied in syndromic decoding with both “hard” and “soft” solutions of turbo codes with component cyclic linear block block codes.

The invention is illustrated in the drawing (figure 2), which shows a structural diagram of an optimal syndromic decoder cascade code with a serial connection through an interleaver of cyclic linear block codes.

A cascade code syndromic decoder with serial connection through an interleaver of cyclic linear block codes contains: an extended syndrome calculation unit 20, a non-zero element search unit 40, a line number generation unit 60, a table storage unit 80, a first localized error chain search unit 100, 2- the first block of searching for chains of localized errors 120, the block for storing localized errors of 140, the block for generating alternative groups of localized errors 160, the third block for searching for chains of localized errors 180, the block for selecting the vector of correl section 200, a unit for generating decoded information 220.

The extended syndrome calculation unit 20 is designed to calculate the extended syndromes of the code words of the cascade code component codes s _r ^(u) by the formula s _r ^(u) = (b _r ^(u) ⊕e _r ^(u) ) × H _{n, n} .

The non-zero element search block 40 is designed to determine the position N of any non-zero element of the expanded syndrome s _r ^(u) . It can be implemented in the form of a shift register, in which the leading digit for the presence of 0 is analyzed. In this case, the current syndrome s _r ^{(u) is} entered into the shift register and its shifts are performed towards the senior bit until a nonzero one appears in it element. The number of shifts is the position number of one of the nonzero elements N, which is fixed by the counter.

The block for generating line numbers 60 is used to determine the line numbers of the extended check matrix H _{n, n} , for which one of the nonzero elements is located at position N. Block 60 can be made in the form of a shift register, in which the highest order for the presence of 0 is analyzed, and counters line numbers, the number of which is equal to w (the number of nonzero coefficients of the verification polynomial h (x)). The Nth column of the expanded verification matrix H _{n, n is} entered into the shift register, which is shifted towards the high order until it is reset to zero. Line number counters count the number of shifts and when a nonzero element appears in the high order of the shift register, they are sequentially disabled. When the shift register is reset to zero, the numbers of the required rows of the extended verification matrix correspond to the counters.

The storage unit of table 80 is designed to store the expanded syndromes s _r ^(u) and the corresponding vectors HN _r ^(u) , which indicate the row numbers of the extended check matrix H _{n, n} that took part in the formation of the syndrome s _r ^(u) , and when soft decision decoding and metrics v _{r, u} . Block 80 is a random access memory device, in which each row consists of two (three) fields for storing the current vectors s _r ^(u) , HN _r ^(u) , and when decoding with a “soft” solution, the metrics v _{r, u} .

The 1st block of searching for chains of localized errors 100 is designed to search for localized errors in the code word of a cascading code that begin with a single error in the code words of the i-th component code, in accordance with the steps that are provided for stage 1 of searching for localized errors of the proposed method.

The 2nd block of searching for chains of localized errors 120 is designed to search for localized errors in the code word of the cascading code that begin with a double error in the code words of the i-th component code, in accordance with the steps that are provided for the 2 stages of searching for localized errors of the proposed method.

The localized error storage unit 140 is designed to store localized errors e _m and their corresponding position vectors of conditionally zero syndromes N _m . Block 160 can be implemented in the form of random access memory, in which each line consists of two (three) fields for storing localized errors e _m and vectors N _m , and, when decoding with a “soft” solution, the metric v _m .

The block for generating alternative groups of localized errors 160 is designed to detect and remove duplicate errors, identify overlapping localized errors, and generate alternative groups of localized errors in which intersecting errors are distributed in different groups. Block 160 can be implemented as a special calculator for determining repeated and intersecting localized errors, containing random access memory, in which each line consists of two (three) fields for storing groups of localized errors, the number of conditionally zero extended syndromes corresponding to each group, and when soft decision decoding and metrics for each group.

The 3rd block of searching for localized error chains 180 is designed to search for localized errors having the configuration of the code words of the i-th component code for each alternative group of localized errors generated in the second stage, in accordance with the steps that are provided for the 3 stages of searching for localized errors the proposed method.

The correction vector selection block 200 is designed to determine the optimal correction vector of the distorted cascading code.

The unit for generating decoded information 220 is designed to invert the elements in the systematic part of the cascade code word, which are indicated in the correction vector, and transmit to the decoder output the corrected systematic part of the cascade code word.

The proposed device operates as follows.

The received, possibly distorted in the communication channel, code word (b⊕e _ks ) is received from the output of the communication channel (demodulator) via bus 10 to the extended syndrome calculation unit 20, and via bus 11 to the decoded information generation unit 220.

If all the syndromes calculated in the extended codeword syndrome calculation unit for component codes 20 are equal to zero, then the cascading codeword is not distorted and information about this is transmitted via bus 32 to the decoded information generation unit 220, in which the systematic part of the codeword is allocated and via bus 230 arrives at the output of the decoder. This completes the process of decoding the code word.

If at least one of the extended syndromes of the code words of the component codes is not a zero vector, then via bus 31 it enters the storage unit of table 80, and through bus 30 to the search unit of a nonzero element 40, in which any nonzero position of the extended syndrome is determined by the bus 50 is transmitted to the line number generating unit 60.

The line number generation unit 60 finds the numbers of those lines of the extended check matrix that contain a nonzero element at the position obtained via bus 50. The generated vector with the line numbers of the extended check matrix is transmitted via bus 70 to the storage unit of table 80.

Upon completion of the calculation of extended syndromes for all codewords of component codes and entering them together with their vectors with row numbers of the extended verification matrix in the storage unit of table 80, the first block for searching for chains of localized errors 100 is launched.

The 1st block of searching for chains of localized errors 100 sequentially reads along the bus 90 extended codeword syndromes of one of the component codes and performs a sequence of actions that involves the 1st stage of searching for localized errors described in the above method. As a result, localized errors are detected in the codeword of the cascading code, which begin with a one-time error in the codewords of the selected component code, which with the position vector of conditionally zero extended syndromes of this localized error are transmitted via bus 110 to the localized error storage unit 140. After it is completed viewing all extended codeword syndromes of the selected component code, the second block of searching for chains of localized errors 120 starts.

The 2nd block of searching for chains of localized errors 120 sequentially reads through the bus 91 extended codeword syndromes of the selected component code and performs a sequence of actions that involves the 2nd stage of searching for localized errors described in the above method. As a result, localized errors in the code word of the cascading code are detected, which begin with a twofold error in the code words of the selected component code. Localized errors along with the position vector of conditionally zero extended syndromes are transmitted via bus 130 to the localized error storage unit 140. After the viewing of all extended codeword syndromes of the selected component code is completed, the block for generating alternative groups of localized errors 160 is launched.

The block for generating alternative groups of localized errors 160 via bus 150 sequentially scans for localized errors stored in the block for storing localized errors 140, removes repeated localized errors and generates alternative groups of localized errors, taking into account the fact that the found intersecting errors must be included in different groups. For each group of localized errors in block 160, the number of conditionally zero syndromes and their positions are calculated, which, together with their group of localized errors, are stored in the storage device of block 160 ..

Upon completion of the formation of alternative groups of localized errors, the third block for searching for chains of localized errors 180 is launched. The third block for searching for chains of localized errors 180 sequentially reads 160 groups of localized errors from the block for generating alternative groups of localized errors 160. For each group of localized errors, the syndrome table is modified, coming on the bus 92 from the storage unit of table 80, taking into account conditionally zero syndromes and performs the sequence of actions that involves the 3rd stage of the search for localized errors described in the above method. As a result, localized errors that have a codeword configuration in the codewords of the selected component code are detected. The newly received localized errors are included in the group and, together with the number of conditionally zero syndromes via bus 190, are returned to the block for generating alternative groups of localized errors 160.

After the viewing of all groups of localized errors has been completed, a block for selecting a correction vector 200 is started, which, on the bus 171, sequentially reads groups of localized errors and selects, when decoding with a “hard” solution, one that contains all zero and conditionally zero codeword syndromes of component codes and has the smallest weight. Next, the selected group of localized errors via bus 210 enters the block for generating decoded information 220, in which those elements in the systematic part of the code word of the cascade code that are indicated in the localized group of errors are inverted. The adjusted systematic part of the cascading codeword is sent to the decoder via bus 230.

For decoding a cascade code with "shortened" code words of component codes, another design option is to modify the extended syndrome 20 calculation unit, in which zero elements are added to the beginning of each code word before calculating the extended syndromes of "shortened" code words of component codes s _r ^(u) ( when decoding with a “soft” solution with conditional probabilities p (y _j / b _{j, 0} ) = 1 and p (y _j / b _{j, 1} ) = 0), the number of which is equal to the amount of code shortening. In addition, in the 1st block of searching for chains of localized errors 100, in the 2nd block of searching for chains of localized errors 120 and in the 3rd block of searching for chains of localized errors 180, the fact that a localized error cannot contain the positions of elements added in block 20. This design solution allows not only to decode cascading codes with "shortened" component codes, but also to increase the speed of the decoder.

To decode a cascade code with “extended” code words for component codes, another design option is to modify the extended syndrome calculation unit 20, in which the last element (extension element or codeword parity element ^{) is} deleted before computing the extended syndromes of component code words s _r ^(u ) in the code words for “advanced” component codes. When decoding with a “hard” solution, this element is not taken into account in any of the blocks. When decoding with a “soft” solution, the conditional probabilities of the extension element are used in calculating the metrics in the block for generating alternative groups of localized errors 160. This constructive solution allows decoding cascading codes with “extended” component codes.

For decoding a cascade code with a “soft” solution, another constructive option is to modify the extended syndrome calculation unit 20, which, before computing the extended syndromes of component codes, generates a cascade code code word with a “hard” solution. In the 1st block of searching for chains of localized errors 100, in the 2nd block of searching for chains of localized errors 120 and in the 3rd block of searching for chains of localized errors 180, the least reliable positions of the code words of component codes are considered, which will lead to higher performance decoder. In the block for generating alternative groups of localized errors 160, a metric is calculated for each alternative group of localized errors, which is the sum of the metrics of the code words of the component codes distorted by this group of localized errors. In the block of selection of the correction vector 200, the group of localized errors that has the maximum metric and has all zero or conditionally zero syndromes is selected as the optimal error vector.

The implementation of the described device can be hardware, software or hardware-software and can be used for both binary and q-ary codes.

Achievable technical result of the proposed method for decoding a cascade code with serial connection through an interleaver of cyclic linear block codes is to increase the reliability (quality) of decoding with a “soft” solution, increase its speed, reduce hardware complexity and reduce decoding delay time compared to known decoders [1- 3], in addition, it is an optimal decoding method with both a “hard” and a “soft” solution. The proposed syndromic decoder with both a “hard” and a “soft” solution can be successfully applied for decoding turbo codes with component cyclic linear block block codes.

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Claims (4)

1. The method of decoding a cascade code with a serial connection through an interleaver of cyclic linear block codes, namely, that the received code sequence is divided into component codes and iteratively decodes each component code using a decoder with a “soft” input and a “soft” output, characterized the fact that the received code sequence is divided into component codes, extended syndromes are calculated for each codeword of the component codes, and localized errors are found bqs from which alternative groups of localized errors are formed, moreover, for each group of localized errors, a metric is calculated, which, when decoding with a “hard” solution, is its weight, then, to correct the most probable cascade code error, an alternative group of localized errors is selected that resets all component codes and has a minimum metric, then invert the elements of the systematic part of the code word of the cascading code, the numbers of which correspond to the positions of nonzero elements an alternative group of localized errors. 2. The method according to claim 1, characterized in that when decoding with a “hard” solution of a cascade code with "shortened" component codes, zero elements are added to the beginning of each code word, the number of which is equal to the shortening value. 3. A method for decoding a cascade code with a serial connection through an interleaver of cyclic linear block codes, namely, that the received code sequence is divided into component codes and iteratively decodes each component code using a decoder with a “soft” input and a “soft” output, characterized the fact that the received code sequence is divided into component codes, extended syndromes are calculated for each codeword of the component codes, and localization chains are found errors, from which alternative groups of localized errors are formed, moreover, for each group of localized errors, a metric is calculated, which, when decoding with a “soft” solution, is a modified metric, then, to correct the most probable cascade code error, an alternative group of localized errors is selected, which resets all syndromes component codes and has a maximum metric, then invert the elements of the systematic part of the code word of the cascading code, the numbers of which correspond to nitions of nonzero elements of an alternative group of localized errors. 4. The method according to claim 3, characterized in that when decoding with a “soft” solution of a cascade code with “shortened” component codes, zero elements are added to the beginning of each codeword, the number of which is equal to the value of shortening, with conditional probabilities equal to one.

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