CN115632662B - Syndrome calculation method, device, equipment and medium in RS decoding - Google Patents
Syndrome calculation method, device, equipment and medium in RS decoding Download PDFInfo
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Abstract
The application discloses a syndrome calculation method, a syndrome calculation device, syndrome calculation equipment and a syndrome calculation medium in RS decoding, which relate to the field of computer communication, and the method comprises the following steps: deforming the determined syndrome polynomial by using a preset multiplication strategy to obtain an iterative syndrome polynomial s; determining a syndrome expression S = Ar + bs by using a preset periodic iteration formula based on a preset parallelism p and an iteration syndrome polynomial S; determining (n-k) × 2p calculated values corresponding to A by using a preset calculation tool according to a preset equivalent circuit splitting method; determining (n-k) calculated values corresponding to the Chang Jishu matrix A by using a preset data iterative segmentation method, determining a simplified expression of the constant coefficient matrix A based on the (n-k) calculated values, and finally determining a syndrome so as to finish RS decoding error correction by using the syndrome. The method improves the syndrome calculation efficiency by using an equivalent circuit splitting method and a data iteration segmentation method.
Description
Technical Field
The present invention relates to the field of computer communications, and in particular, to a syndrome calculation method, apparatus, device, and medium in RS decoding.
Background
RS (Reed-Solomon) decoding is an FEC (Forward Error Correction) decoding technology, which is widely applied to coding technology in a communication system to ensure the accuracy of data, and its basic idea is to re-encode information to be transmitted at a transmitting end, add certain redundant check information to form a codeword with a longer length, and after reaching a receiving end, if an Error is within a correctable range, correct the Error after decoding check, thereby reducing the Error rate and improving the reliability of the communication system. In an optical communication system, through FEC processing, the error rate of the system can be effectively reduced with small redundancy overhead, the transmission distance is prolonged, and the purpose of reducing the system cost is realized. FEC "Forward error correction" is not available at 400G level and in all future data center communication standards, and FEC requirements in IEEE802.3bs are in all scenarios of 400GAUI-16 and 400GAUI-8, always turning on the FEC function.
Although RS parallel decoding has been widely used, most of the applications to RS (255, 239) and the like, although the applications to RS (544,514) are limited to 100G. In the 400G RS decoding syndrome, due to the high parallelism, the complexity is high, the time sequence convergence is difficult to converge, the decoding efficiency cannot be met, and the system transmission efficiency cannot reach 400G.
From the above, how to avoid the situation that the syndrome complexity is high and the decoding efficiency is low in the 400G RS decoding process is a problem to be solved in the art.
Disclosure of Invention
In view of the above, an object of the present invention is to provide a syndrome calculation method, device, apparatus and medium in RS decoding, which can split a constant coefficient multiplier by using the idea of an equivalent circuit, and solve the problem of difficult timing convergence in the syndrome calculation process by combining a data iterative segmentation method, thereby reducing the logic area, and enabling the syndrome calculation efficiency to stably operate at more than 400G. The specific scheme is as follows:
in a first aspect, the present application discloses a syndrome calculation method in RS decoding, including:
deforming the syndrome polynomial determined based on the received code word polynomial r by using a preset multiplication strategy to obtain an iterative syndrome polynomial s;
determining a syndrome expression S = Ar + bs by using a preset periodic iteration formula based on a preset parallelism p and the iteration syndrome polynomial S; wherein A is a constant coefficient matrix of (n-k) rows and p columns, b is a constant coefficient matrix of (n-k) rows and 1 column, n represents that one code block in the received code element information corresponds to n code elements, and k represents that k information code elements exist in the n code elements in the code element information;
determining (n-k) × 2p calculated values corresponding to (n-k) × p coefficients in the Chang Jishu matrix A by using a preset calculation tool according to a preset equivalent circuit splitting method; wherein each of the n-k rows corresponds to 2p calculated values;
performing array segmentation on the (n-k) × 2p numerical values by using a preset data iterative segmentation method, determining a calculated value corresponding to each group of data based on a preset exclusive-or algorithm until (n-k) calculated values corresponding to the Chang Jishu matrix A are determined, and then determining a simplified expression of the Chang Jishu matrix A based on the (n-k) calculated values;
and determining a syndrome by using the simplified expression, the iterative syndrome polynomial and the syndrome expression so as to complete RS decoding error correction by using the syndrome.
Optionally, the method determines (n-k) × 2p calculated values corresponding to (n-k) × p coefficients in the Chang Jishu matrix a by using a preset calculation tool according to a preset equivalent circuit splitting method; wherein each of the n-k rows corresponds to 2p calculated values, including:
determining (n-k) × 2p calculated values corresponding to (n-k) × p coefficients in the Chang Jishu matrix A by utilizing matlab according to a preset equivalent circuit splitting method; wherein each of the n-k rows corresponds to 2p calculated values.
Optionally, the calculating the syndrome by using the simplified expression, the iterative syndrome polynomial and the syndrome expression includes:
inputting n symbols of the received symbol information into the simplified expression, the iterative syndrome polynomial, and the syndrome expression to determine a syndrome.
Optionally, the syndrome calculating method in RS decoding further includes:
the preset parallelism p is set to 64.
Optionally, the performing array segmentation on the (n-k) × 2p values by using a preset data iterative segmentation method, and determining a calculated value corresponding to each group of data based on a preset exclusive or algorithm until determining (n-k) calculated values corresponding to the Chang Jishu matrix a, and then determining a simplified expression of the Chang Jishu matrix a based on the (n-k) calculated values includes:
and performing array segmentation on the (n-k) × 2p numerical values by using a preset data iterative segmentation method based on a preset segmentation number, determining a calculated value corresponding to each group of data based on a preset exclusive-or algorithm until (n-k) calculated values corresponding to the Chang Jishu matrix A are determined, and then determining a simplified expression of the Chang Jishu matrix A based on the (n-k) calculated values.
Optionally, the method determines (n-k) × 2p calculated values corresponding to (n-k) × p coefficients in the Chang Jishu matrix a by using a preset calculation tool according to a preset equivalent circuit splitting method; wherein each of the n-k rows corresponds to 2p calculated values, including:
determining a first divided circuit and a second divided circuit corresponding to the Chang Jishu matrix A by using a preset calculation tool according to (n-k) p coefficients in the Chang Jishu matrix A and a preset equivalent circuit splitting method;
calculating initial values of the first divided circuit and the second divided circuit to determine an initial value of an LUT edge checking circuit corresponding to the Chang Jishu matrix A;
substituting the preset parallelism p into the Chang Jishu matrix a of which the initial value is calculated to determine (n-k) × 2p calculated values corresponding to the Chang Jishu matrix a; wherein each of the n-k rows corresponds to 2p calculated values.
Optionally, the determining, based on (n-k) × p coefficients in the Chang Jishu matrix a and according to a preset equivalent circuit splitting method and by using a preset calculation tool, a first split circuit and a second split circuit corresponding to the Chang Jishu matrix a includes:
respectively calculating Chang Jishu multipliers of (n-k) p coefficients in the Chang Jishu matrix A on a Galois field by using a preset calculation tool;
and performing equivalent division on the (n-k) p constant coefficient multipliers by using a preset equivalent circuit division method to determine a first divided circuit and a second divided circuit corresponding to the Chang Jishu matrix A.
In a second aspect, the present application discloses a syndrome calculating apparatus in RS decoding, comprising:
a polynomial determining module, configured to utilize a preset multiplication strategy to deform a syndrome polynomial determined based on the received codeword polynomial r to obtain an iterative syndrome polynomial s;
the expression determining module is used for determining an adjoint expression S = Ar + bs by using a preset periodic iteration formula based on a preset parallelism p and the iteration adjoint polynomial S; wherein A is a constant coefficient matrix of (n-k) rows and p columns, b is a constant coefficient matrix of (n-k) rows and 1 columns, n represents that one code block in the received code element information corresponds to n code elements, and k represents that k information code elements exist in the n code elements in the code element information;
the circuit splitting module is used for determining (n-k) × 2p calculated values corresponding to (n-k) × p coefficients in the Chang Jishu matrix A by using a preset calculating tool according to a preset equivalent circuit splitting method; wherein each of the n-k rows corresponds to 2p calculated values;
the data segmentation module is used for performing array segmentation on the (n-k) × 2p numerical values by using a preset data iterative segmentation method, determining a calculated value corresponding to each group of data based on a preset exclusive-or algorithm until (n-k) calculated values corresponding to the Chang Jishu matrix A are determined, and then determining a simplified expression of the Chang Jishu matrix A based on the (n-k) calculated values;
and the syndrome determining module is used for determining a syndrome by using the simplified expression, the iterative syndrome polynomial and the syndrome expression so as to complete RS decoding error correction by using the syndrome.
In a third aspect, the present application discloses an electronic device, comprising:
a memory for storing a computer program;
and the processor is used for executing the computer program to realize the syndrome calculating method in the RS decoding.
In a fourth aspect, the present application discloses a computer storage medium for storing a computer program; wherein the computer program when executed by a processor implements the steps of the syndrome calculation method in the RS decoding disclosed in the foregoing.
In the application, a preset multiplication strategy is utilized to deform a syndrome polynomial determined based on a received code word polynomial r so as to obtain an iterative syndrome polynomial s; determining a syndrome expression S = Ar + bs by using a preset periodic iteration formula based on a preset parallelism p and the iteration syndrome polynomial S; wherein A is a constant coefficient matrix of (n-k) rows and p columns, b is a constant coefficient matrix of (n-k) rows and 1 column, n represents that one code block in the received code element information corresponds to n code elements, and k represents that k information code elements exist in the n code elements in the code element information; determining (n-k) × 2p calculated values corresponding to (n-k) × p coefficients in the Chang Jishu matrix A by using a preset calculation tool according to a preset equivalent circuit splitting method; wherein each of the n-k rows corresponds to 2p calculated values; performing array segmentation on the (n-k) × 2p numerical values by using a preset data iterative segmentation method, determining a calculated value corresponding to each group of data based on a preset exclusive-or algorithm until (n-k) calculated values corresponding to the Chang Jishu matrix A are determined, and then determining a simplified expression of the Chang Jishu matrix A based on the (n-k) calculated values; determining a syndrome by using the simplified expression, the iterative syndrome polynomial and the syndrome expression so as to complete RS decoding error correction by using the syndrome. Therefore, the embodiment can greatly reduce the calculation amount in the syndrome calculation process through the preset equivalent circuit splitting method and the preset data iteration segmentation method, reduce the logic use area, reduce the LUT table look-up complexity, and facilitate the time sequence convergence. The high-parallelism syndrome computing mode improves the computing efficiency and solves the problem of low efficiency of serial and low-parallelism syndromes.
Drawings
In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the embodiments or the prior art will be briefly described below, it is obvious that the drawings in the following description are only embodiments of the present invention, and for those skilled in the art, other drawings can be obtained according to the provided drawings without creative efforts.
Fig. 1 is a flowchart of a syndrome calculating method in RS decoding according to the present application;
FIG. 2 is a flowchart of a syndrome calculation method in RS decoding according to an embodiment of the present disclosure;
FIG. 3 is a block diagram of a syndrome computing device for RS decoding according to the present application;
fig. 4 is a block diagram of an electronic device provided in the present application.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
In the prior art, although RS parallel decoding is widely applied, most of RS (255, 239) and the like are applied, and although the RS (544,514) is applied, the application is limited to 100G. In the 400G RS decoding syndrome, due to the high parallelism, the complexity is high, the time sequence convergence is difficult to converge, the decoding efficiency cannot be met, and the system transmission efficiency cannot reach 400G. In the method, the constant coefficient multiplier can be split by using the idea of an equivalent circuit, the problem of difficult time sequence convergence in the syndrome calculation process is solved by combining a data iteration segmentation method, the logic use area is reduced, and the syndrome calculation efficiency can stably operate above 400G.
The embodiment of the invention discloses a syndrome calculation method in RS decoding, which is described with reference to FIG. 1 and comprises the following steps:
step S11: and deforming the syndrome polynomial determined based on the received code word polynomial r by using a preset multiplication strategy to obtain an iterative syndrome polynomial s.
In this embodiment, the number of information symbols input to the RS high-speed decoding circuit is denoted by k, the bit width of the symbols is denoted by m, the total bit width of each codeword input to the RS high-speed decoding circuit is k · m, the total bit width serial input is converted into p-way parallel input, and the bit width of each way is a symbol _ size bit.
In general, it is commonly seen that FEC decoding occurs in the form of RS (n, k, t, m), where the meaning of the different letters is:
n is frame size [ symbol ], which indicates that a code block has n symbols;
the message size [ symbol ] represents that k information symbols exist in n symbols, namely the number of the information symbols;
t is corrected symbol error per frame, denoted as correctable symbol data, and n-k =2t;
symbol size [ bit ], indicates that a single symbol comprises an m-bit binary number, i.e., bit width.
In this embodiment, p is the parallelism of parallel decoding. In a specific embodiment, if P can be divided by n, the decoding period c is c = n/P, and if P cannot be divided by n, the decoding period c = n/P is rounded and added by 1, here, in the syndrome calculation, we adopt a pre-zero-filling manner, i.e. parallelism P in the first period, but the effective data bit width is n-P × c-1.
In this step, the preset multiplication strategy is preferably a Horner criterion. The received codeword polynomial is
The adjoint polynomial is
Using Horner's rule to formula s i And (3) carrying out deformation to obtain an iterative adjoint polynomial s:
in this example, the above formula is given as formula 1, where i =0,1 …, n-k-1;
wherein, the input P (c-1) data of the previous zero padding are all 0;
step S12: determining a syndrome expression S = Ar + bs by using a preset periodic iteration formula based on a preset parallelism p and the iteration syndrome polynomial S; wherein A is a constant coefficient matrix of (n-k) rows and p columns, b is a constant coefficient matrix of (n-k) rows and 1 column, n represents that one code block in the received code element information corresponds to n code elements, and k represents that k information code elements exist in the n code elements in the code element information.
In this embodiment, the syndrome calculating method in RS decoding may further include: the preset parallelism p is set to 64. That is, the predetermined parallelism p in the present embodiment is preferably 64.
The expression of the syndrome in this step is as follows:
in this example, the above formula is expressed as formula 2. Wherein is s' 0 Is s is 0 The result of the calculation in the previous cycle indicates addition in the Galois field, and r in Ar + bs is r 0 To r p-1 The column vector of (2).
From equation 2 we can obtain the constant coefficient matrix a for solving the syndrome:
the matrix a is an (n-k) x p matrix in which each coefficient is solved, each coefficient being a constant coefficient multiplier.
From equation 2 we can get the constant coefficient matrix b solving the syndrome:
the matrix b is an (n-k) row 1 column matrix in which each coefficient can also be found. We will calculate a and b in the following steps.
Step S13: determining (n-k) × 2p calculated values corresponding to (n-k) × p coefficients in the Chang Jishu matrix A by using a preset calculation tool according to a preset equivalent circuit splitting method; wherein each of the n-k rows corresponds to 2p calculated values.
As shown in the formula 2, the syndrome is that Ar and bs are added in Galois field, and m is the bit number of each symbol in Galois field GF (2^m), and RS (544, 514) is in GF (2) 10 ) In the field, m is 10, and the parallel input bit width is determined to be 10 × P by combining the preset parallelism, so that each 10-bit coefficient in the matrix a can be calculated, and (n-k) × P coefficients are calculated in total, and each coefficient is a constant coefficient multiplier. In a specific embodiment, each 10bit coefficient in MATrix a may be calculated using MATLAB (i.e., MATrix laboraty) as a pre-set calculation tool.
In the step, a concept of splitting each coefficient based on a preset equivalent circuit splitting method is provided, and the concept can also be understood as split input, wherein the split input is not split randomly, but is combined with an m value of a galois field to perform two-split input, if m is 8, 4-split can be adopted, if m is 10, 5-split can be adopted, and the split aims at splitting one symbol into 2 symbols, so that the bit width of a single input can be reduced, and the time sequence convergence is facilitated.
Such as GF (2) 10 ) On the field, 64 parallel, then 640bit is input, each inputIf the input is 10 bits, the 10bit 2 is divided into 2 pieces of 5-bit data; if input r 0 Is 10' d788, then it is divided into r 1 =5'b11000，r 2 =5'b10100。
Specifically, GF (2) is added in the present example 10 ) In the field, 523 constant coefficients are taken as an example, and the constant coefficient common multiplier expression is formula 3:
y[0] = x[0] ⨁ x[1] ⨁ x[7] ⨁ x[8] ⨁ x[9];
y[1] = x[0] ⨁ x[1] ⨁ x[2] ⨁ x[8] ⨁ x[9];
y[2] = x[1] ⨁ x[2] ⨁ x[3] ⨁ x[9];
y[3] = x[0] ⨁ x[1] ⨁ x[2] ⨁ x[3] ⨁ x[4] ⨁ x[7] ⨁ x[8] ⨁ x[9];
y[4] = x[1] ⨁ x[2] ⨁ x[3] ⨁ x[4] ⨁ x[5] ⨁ x[8] ⨁ x[9];
y[5] = x[2] ⨁ x[3] ⨁ x[4] ⨁ x[5] ⨁ x[6] ⨁ x[9];
y[6] = x[3] ⨁ x[4] ⨁ x[5] ⨁ x[6] ⨁ x[7];
y[7] = x[4] ⨁ x[5] ⨁ x[6] ⨁ x[7] ⨁ x[8];
y[8] = x[5] ⨁ x[6] ⨁ x[7] ⨁ x[8] ⨁ x[9];
y[9] = x[0] ⨁ x[6] ⨁ x[7] ⨁ x[8] ⨁ x[9];
wherein y 0 is the lowest order bit of 10 bits and y 9 is the highest order bit.
In this embodiment, the above formula can be equivalent to the following two equivalent circuits:
circuit 1, equation 4:
y1[0] = x[0] ⨁ x[1];
y1[1] = x[0] ⨁ x[1] ⨁ x[2];
y1[2] = x[1] ⨁ x[2] ⨁ x[3];
y1[3] = x[0] ⨁ x[1] ⨁ x[2] ⨁ x[3] ⨁ x[4];
y1[4] = x[1] ⨁ x[2] ⨁ x[3] ⨁ x[4];
y1[5] = x[2] ⨁ x[3] ⨁ x[4];
y1[6] = x[3] ⨁ x[4];
y1[7] = x[4]];
y1[8] = 0;
y1[9] = x[0];
and circuit two, equation five:
y2[0] = x[7] ⨁ x[8] ⨁ x[9];
y2[1] = x[8] ⨁ x[9];
y2[2] = x[9];
y2[3] = x[7] ⨁ x[8] ⨁ x[9];
y2[4] = x[5] ⨁ x[8] ⨁ x[9];
y2[5] = x[5] ⨁ x[6] ⨁ x[9];
y2[6] = x[6] ⨁ x[7];
y2[7] = x[5] ⨁ x[6] ⨁ x[7] ⨁ x[8];
y2[8] = x[5] ⨁ x[6] ⨁ x[7] ⨁ x[8] ⨁ x[9];
y2[9] = x[6] ⨁ x[7] ⨁ x[8] ⨁ x[9]。
after the equivalent circuit is split, 1024 situations of original 10bit input of the LUT edge checking circuit are changed into 32 situations, the LUT edge checking difficulty is greatly reduced, the number of LUT units is greatly reduced, and the logic occupied area is reduced.
Each coefficient is divided into 2 equivalent circuits by using MATLAB according to the above equivalent circuit splitting method, and then the circuit 1 and the circuit 2 are initialized. Specifically, the initialization is to substitute each value a of 0 to 31 into the circuit 1 in a 2-ary form (for example, 28=5 =b 11100) to obtain 32 10bit values, and similarly, substitute a into the circuit 2 to obtain 32 10bit values, and the obtained 64 values are initial values (truth table) of LUT lookup tables of the circuit 1 and the circuit 2, and then each coefficient equivalence of the matrix a can be obtained and a truth table is calculated, and we can obtain the initialization value of the matrix a.
Then, the parallelism p is input into the matrix a which is divided and has calculated the initial value, we can get (n-k) × 2p 10-bit values, here we can understand (n-k) rows, each row has 2 × p data, the 2 × p data of each row can get the corresponding value by directly adding, if a certain row 2p 10 bits is directly added on the galois field, if p is 64 parallelism, then 2 × p =128 10 bits directly do xor, the logical calculation amount is very large, and the logic is complex, and the time sequence convergence is very poor. By using the equivalent circuit splitting method in the embodiment, the calculation amount can be greatly reduced, the logic use area is reduced, the LUT table look-up complexity is reduced, and the time sequence convergence is facilitated.
That is, in this embodiment, the method determines (n-k) × 2p calculated values corresponding to (n-k) × p coefficients in the Chang Jishu matrix a by using a preset calculation tool according to a preset equivalent circuit splitting method; wherein each of the n-k rows corresponds to 2p calculated values, which may include: determining a first divided circuit and a second divided circuit corresponding to the Chang Jishu matrix A by using a preset calculation tool according to a preset equivalent circuit splitting method based on (n-k) × p coefficients in the Chang Jishu matrix A; calculating initial values of the first divided circuit and the second divided circuit to determine an initial value of an LUT edge checking circuit corresponding to the Chang Jishu matrix A; substituting the preset parallelism p into the Chang Jishu matrix A with the calculated initial value to determine (n-k) × 2p calculated values corresponding to the Chang Jishu matrix A; wherein each of the n-k rows corresponds to 2p calculated values.
That is, in this embodiment, the determining, based on (n-k) × p coefficients in the Chang Jishu matrix a and according to a preset equivalent circuit splitting method and using a preset calculation tool, a first split circuit and a second split circuit corresponding to the Chang Jishu matrix a may include: respectively calculating Chang Jishu multipliers of (n-k) p coefficients in the Chang Jishu matrix A on a Galois field by using a preset calculation tool; and performing equivalent division on the (n-k) p constant coefficient multipliers by using a preset equivalent circuit division method to determine a first divided circuit and a second divided circuit corresponding to the Chang Jishu matrix A.
Step S14: performing array segmentation on the (n-k) × 2p numerical values by using a preset data iterative segmentation method, determining a calculated value corresponding to each group of data based on a preset exclusive-or algorithm until (n-k) calculated values corresponding to the Chang Jishu matrix A are determined, and then determining a simplified expression of the Chang Jishu matrix A based on the (n-k) calculated values.
In this embodiment, a preset data iterative segmentation method may be used to divide 2 × p values of each row in n-K rows by a preset segmentation number, if the values cannot be completely divided, zero padding is performed, w groups of data may be obtained by segmentation, n-K rows have (n-K) × w groups of data, a calculated value corresponding to each group of data is determined by using a preset exclusive-or algorithm, so as to obtain (n-K) × w values, then the w values of each row are divided by the preset segmentation number, the array is continuously segmented, then the calculated value … corresponding to each group of data is calculated by using the preset exclusive-or algorithm again, and the data segmentation process is repeated until an n-K value K1 is obtained, the calculation of a is completed, and the simplified expression of the Chang Jishu matrix a may be determined.
Step S15: determining a syndrome by using the simplified expression, the iterative syndrome polynomial and the syndrome expression so as to complete RS decoding error correction by using the syndrome.
In this embodiment, after the simplified expression of a is obtained through calculation, the iterative syndrome polynomial S and the syndrome expression S = Ar + bs may be used to calculate the syndrome S, and then the RS decoding error correction may be completed by using S.
In this embodiment, a preset multiplication strategy is used to deform a syndrome polynomial determined based on a received codeword polynomial r to obtain an iterative syndrome polynomial s; determining a syndrome expression S = Ar + bs by using a preset periodic iteration formula based on a preset parallelism p and the iteration syndrome polynomial S; wherein A is a constant coefficient matrix of (n-k) rows and p columns, b is a constant coefficient matrix of (n-k) rows and 1 column, n represents that one code block in the received code element information corresponds to n code elements, and k represents that k information code elements exist in the n code elements in the code element information; determining (n-k) × 2p calculated values corresponding to (n-k) × p coefficients in the Chang Jishu matrix A by using a preset calculation tool according to a preset equivalent circuit splitting method; wherein each of the n-k rows corresponds to 2p calculated values; performing array segmentation on the (n-k) × 2p numerical values by using a preset data iterative segmentation method, determining a calculated value corresponding to each group of data based on a preset exclusive-or algorithm until (n-k) calculated values corresponding to the Chang Jishu matrix A are determined, and then determining a simplified expression of the Chang Jishu matrix A based on the (n-k) calculated values; determining a syndrome by using the simplified expression, the iterative syndrome polynomial and the syndrome expression so as to complete RS decoding error correction by using the syndrome. Therefore, in the embodiment, through the preset equivalent circuit splitting method, the preset data iteration segmentation method and the initialization value method, the calculation amount in the syndrome calculation process can be greatly reduced, the logic use area is reduced, the LUT table look-up complexity is reduced, and the time sequence convergence is facilitated. The high-parallelism syndrome calculation mode improves the calculation efficiency, solves the problem of low efficiency of serial and low-parallelism syndromes, and ensures that the syndrome calculation efficiency can stably run above 400G.
Fig. 2 is a flowchart of a syndrome calculating method in RS decoding according to an embodiment of the present disclosure. Referring to fig. 2, the method includes:
step S21: and deforming the syndrome polynomial determined based on the received code word polynomial r by using a preset multiplication strategy to obtain an iterative syndrome polynomial s.
For a more specific processing procedure of step S21, reference may be made to corresponding contents disclosed in the foregoing embodiments, and details are not repeated here.
Step S22: determining a syndrome expression S = Ar + bs by using a preset periodic iteration formula based on the 64 parallelism and the iteration syndrome polynomial S; wherein A is a constant coefficient matrix of (n-k) rows and p columns, b is a constant coefficient matrix of (n-k) rows and 1 column, n represents that one code block in the received code element information corresponds to n code elements, and k represents that k information code elements exist in the n code elements in the code element information.
That is, in the present embodiment, the preset parallelism may be 64. By adopting the parallelism 64 syndrome calculation, the maximum clock frequency of the circuit can be ensured to be larger than 390Mhz, under the condition that the width of a data interface is 1280 bits, the data throughput rate of more than 425G/bits is achieved, and compared with the method that the logic is reduced by 25% by directly adopting the multiplier calculation.
Step S23: and determining a first segmented circuit and a second segmented circuit corresponding to the Chang Jishu matrix A by using MATLAB according to a preset equivalent circuit splitting method based on (n-k) × p coefficients in the Chang Jishu matrix A.
For a more specific processing procedure of step S23, reference may be made to corresponding contents disclosed in the foregoing embodiments, and details are not repeated here.
Step S24: calculating initial values of the first divided circuit and the second divided circuit to determine initial values of the LUT edge checking circuit corresponding to the Chang Jishu matrix A, and then substituting the preset parallelism p into the Chang Jishu matrix A with the calculated initial values to determine (n-k) 2p calculated values corresponding to the Chang Jishu matrix A; wherein each of the n-k rows corresponds to 2p calculated values.
For a more specific processing procedure of step S24, reference may be made to corresponding contents disclosed in the foregoing embodiments, and details are not repeated here.
Step S25: and performing array segmentation on the (n-k) × 2p numerical values by using a preset data iterative segmentation method based on a preset segmentation number, determining a calculated value corresponding to each group of data based on a preset exclusive-or algorithm until (n-k) calculated values corresponding to the Chang Jishu matrix A are determined, and then determining a simplified expression of the Chang Jishu matrix A based on the (n-k) calculated values.
In this embodiment, the preset number of divisions is preferably 6. Specifically, the preset data iterative segmentation method is a 6-segmentation method, that is, dividing 2 × p values of each line in n-k lines by 6, and if the 2 × p values cannot be divided by 6, zero padding is performed, so that w groups of data can be obtained. If 128/6=21, the remaining 2 are complemented by 4 10bit 0 values, and w =22 groups of data can be formed. Wherein, every 6 10 bits are a group, and each 10bit in the 6 10bit data is subjected to bit exclusive OR logic; each bit is 6 bits input, 6 bits input is 0 to 63, and substituting y = x [0] ⨁ x [1] ⨁ x [2] ⨁ x [3] ⨁ x [4] ⨁ x [5] (formula 6) can obtain an initial VALUE VALUE _ P of 64' h6996699669966996.
If a certain set of 6 values is: a [9:0], b [9:0], c [9:0], d [9:0], e [9:0], f [9:0]
Then the sum of the 6 10 bits of the group is:
f[0]= a[0]⨁b[0]⨁c[0]⨁d[0]⨁e[0]⨁f[0]；
f[1]= a[1]⨁b[1]⨁c[1]⨁d[1]⨁e[1]⨁f[0]；
f[2]= a[2]⨁b[2]⨁c[2]⨁d[2]⨁e[2]⨁f[0]；
……
f[9]= a[9]⨁b[9]⨁c[9]⨁d[9]⨁e[9]⨁f[0]；
in this embodiment, the above expression is expressed as expression 7, and each bit in expression 7 is a VALUE _ P, so that the VALUE v of the group can be obtained 1 Calculating w values by calculating w groups of the row according to the formula 7, and then calculating w groups of n-k rows to obtain (n-k) xw values; then, continuously dividing and calculating w numerical values of each row according to a 6-division method, and obtaining a (n-k) x u numerical value, wherein if u can be divided by 6, u = w/6, and if u cannot be divided by 6, u = w/6+1; and (4) repeatedly using the 6 segmentation method to segment the array until the n-K numerical value K1 is obtained, and finishing the calculation of A.
Step S26: inputting n code elements in the received code element information into the simplified expression, the iteration syndrome polynomial and the syndrome expression to determine a syndrome, and completing RS decoding error correction by using the syndrome.
In this embodiment, before inputting the n symbols in the received symbol information into the simplified expression, the iterative syndrome polynomial and the syndrome expression, the method may further include:
and calculating a constant coefficient matrix b by using the preset calculation tool. Wherein MATLAB can also be used as a pre-set calculation tool.
Specifically, a constant coefficient multiplier is adopted for the b matrix to carry out operation.
In the present invention, the syndrome of the present period is calculated by using the syndrome calculation result of the previous period, and the specific operation rule is as follows:
in the first period: calculating S is S 1 Then S is 1 The n-K numerical value K1 is obtained through the calculation;
and a second period: s 2 n-K values K1 plus S which can be calculated by Ar 1 ⊗ b to yield K2;
the third cycle: s 3 n-K values K2 plus S which can be calculated by Ar 2 ⊗ b to yield K3; and so on.
In this embodiment, when all the n symbols in all the code blocks are input, the value obtained by equation 2 is the determined syndrome value.
In the embodiment, a method for equivalence of a division input constant coefficient multiplier 2 is provided, and the problems that the calculation logic is complex and the time sequence convergence is difficult when a constant coefficient multiplier is directly adopted in an adjoint expression are solved. The method not only reduces the logic use area, but also reduces the complexity of LUT table lookup, and is beneficial to timing sequence convergence; in addition, the 6-segmentation method provided in the embodiment solves the problems of large occupation of syndrome computing logic resources and difficult timing convergence. Moreover, the maximum clock frequency of the circuit can be ensured to be larger than 390Mhz by adopting the syndrome calculation of the parallelism 64, under the condition that the width of a data interface is 1280 bits, the data throughput rate of more than 425G/bits is achieved, and compared with the method that the multiplier is directly adopted for calculation, the logic is reduced by 25%.
Referring to fig. 3, an embodiment of the present application discloses a syndrome calculating device in RS decoding, which may specifically include:
a polynomial determining module 11, configured to deform a syndrome polynomial determined based on the received codeword polynomial r by using a preset multiplication strategy to obtain an iterative syndrome polynomial s;
the expression determining module 12 is configured to determine an expression of an adjoint expression S = Ar + bs based on a preset parallelism p and the iterative adjoint polynomial S and by using a preset periodic iterative formula; wherein A is a constant coefficient matrix of (n-k) rows and p columns, b is a constant coefficient matrix of (n-k) rows and 1 columns, n represents that one code block in the received code element information corresponds to n code elements, and k represents that k information code elements exist in the n code elements in the code element information;
a circuit splitting module 13, configured to determine (n-k) × 2p calculated values corresponding to (n-k) × p coefficients in the Chang Jishu matrix a by using a preset calculation tool according to a preset equivalent circuit splitting method; wherein each of the n-k rows corresponds to 2p calculated values;
the data segmentation module 14 is configured to perform array segmentation on the (n-k) × 2p values by using a preset data iterative segmentation method, determine a calculated value corresponding to each group of data based on a preset exclusive or algorithm until (n-k) calculated values corresponding to the Chang Jishu matrix a are determined, and then determine a simplified expression of the Chang Jishu matrix a based on the (n-k) calculated values;
and a syndrome determining module 15, configured to determine a syndrome by using the simplified expression, the iterative syndrome polynomial, and the syndrome expression, so as to complete RS decoding error correction by using the syndrome.
In the application, a preset multiplication strategy is utilized to deform a syndrome polynomial determined based on a received code word polynomial r so as to obtain an iterative syndrome polynomial s; determining a syndrome expression S = Ar + bs by using a preset periodic iteration formula based on a preset parallelism p and the iteration syndrome polynomial S; wherein A is a constant coefficient matrix of (n-k) rows and p columns, b is a constant coefficient matrix of (n-k) rows and 1 column, n represents that one code block in the received code element information corresponds to n code elements, and k represents that k information code elements exist in the n code elements in the code element information; determining (n-k) × 2p calculated values corresponding to (n-k) × p coefficients in the Chang Jishu matrix A by using a preset calculation tool according to a preset equivalent circuit splitting method; wherein each of the n-k rows corresponds to 2p calculated values; performing array segmentation on the (n-k) × 2p numerical values by using a preset data iterative segmentation method, determining a calculated value corresponding to each group of data based on a preset exclusive-or algorithm until (n-k) calculated values corresponding to the Chang Jishu matrix A are determined, and then determining a simplified expression of the Chang Jishu matrix A based on the (n-k) calculated values; and determining a syndrome by using the simplified expression, the iterative syndrome polynomial and the syndrome expression so as to complete RS decoding error correction by using the syndrome. Therefore, the embodiment can greatly reduce the calculation amount in the syndrome calculation process through the preset equivalent circuit splitting method and the preset data iteration segmentation method, reduce the logic use area, reduce the LUT table look-up complexity, and facilitate the time sequence convergence. The high-parallelism syndrome computing mode improves the computing efficiency and solves the problem of low efficiency of serial and low-parallelism syndromes.
Further, an electronic device is also disclosed in the embodiments of the present application, fig. 4 is a block diagram of the electronic device 20 shown in the exemplary embodiments, and the content in the diagram cannot be considered as any limitation to the scope of the application.
Fig. 4 is a schematic structural diagram of an electronic device 20 according to an embodiment of the present disclosure. The electronic device 20 may specifically include: at least one processor 21, at least one memory 22, a power supply 23, a display 24, an input-output interface 25, a communication interface 26, and a communication bus 27. The memory 22 is used for storing a computer program, and the computer program is loaded and executed by the processor 21 to implement the relevant steps in the syndrome calculating method in RS decoding disclosed in any of the foregoing embodiments. In addition, the electronic device 20 in the present embodiment may be specifically an electronic computer.
In this embodiment, the power supply 23 is configured to provide an operating voltage for each hardware device on the electronic device 20; the communication interface 26 can create a data transmission channel between the electronic device 20 and an external device, and a communication protocol followed by the communication interface is any communication protocol applicable to the technical solution of the present application, and is not specifically limited herein; the input/output interface 25 is configured to obtain external input data or output data to the outside, and a specific interface type thereof may be selected according to specific application requirements, which is not specifically limited herein.
In addition, the storage 22 is used as a carrier for storing resources, and may be a read-only memory, a random access memory, a magnetic disk, an optical disk, or the like, the resources stored thereon may include an operating system 221, a computer program 222, virtual machine data 223, and the like, and the virtual machine data 223 may include various data. The storage means may be a transient storage or a permanent storage.
The operating system 221 is used for managing and controlling each hardware device on the electronic device 20 and the computer program 222, and may be Windows Server, netware, unix, linux, or the like. The computer program 222 may further include a computer program that can be used to perform other specific tasks in addition to the computer program that can be used to perform the syndrome calculating method in RS decoding disclosed in any of the foregoing embodiments by being executed by the electronic device 20.
Further, the present application discloses a computer-readable storage medium, wherein the computer-readable storage medium includes a Random Access Memory (RAM), a Memory, a Read-Only Memory (ROM), an electrically programmable ROM, an electrically erasable programmable ROM, a register, a hard disk, a magnetic disk, or an optical disk or any other form of storage medium known in the art. Wherein the computer program, when executed by a processor, implements the syndrome calculation method in RS decoding disclosed above. For the specific steps of the method, reference may be made to the corresponding contents disclosed in the foregoing embodiments, which are not described herein again.
The embodiments are described in a progressive manner, each embodiment focuses on differences from other embodiments, and the same or similar parts among the embodiments are referred to each other. The device disclosed by the embodiment corresponds to the method disclosed by the embodiment, so that the description is simple, and the relevant points can be referred to the method part for description. Those of skill would further appreciate that the various illustrative elements and algorithm steps described in connection with the embodiments disclosed herein may be implemented as electronic hardware, computer software, or combinations of both, and that the various illustrative components and steps have been described above generally in terms of their functionality in order to clearly illustrate this interchangeability of hardware and software. Whether such functionality is implemented as hardware or software depends upon the particular application and design constraints imposed on the implementation. Skilled artisans may implement the described functionality in varying ways for each particular application, but such implementation decisions should not be interpreted as causing a departure from the scope of the present application.
The steps of a method or algorithm described in connection with the embodiments disclosed herein may be embodied directly in hardware, in a software module executed by a processor, or in a combination of the two. A software module may reside in Random Access Memory (RAM), memory, read Only Memory (ROM), electrically programmable ROM, electrically erasable programmable ROM, registers, hard disk, a removable disk, a CD-ROM, or any other form of storage medium known in the art.
Finally, it should also be noted that, in this document, relational terms such as first and second, and the like are used solely to distinguish one entity or action from another entity or action without necessarily requiring or implying any actual such relationship or order between such entities or actions. Also, the terms "comprises," "comprising," or any other variation thereof, are intended to cover a non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements does not include only those elements but may include other elements not expressly listed or inherent to such process, method, article, or apparatus. Without further limitation, an element defined by the phrase "comprising a … …" does not exclude the presence of another identical element in a process, method, article, or apparatus that comprises the element.
The syndrome calculating method, apparatus, device and storage medium in RS decoding provided by the present invention are described in detail above, and a specific example is applied in this document to illustrate the principle and implementation of the present invention, and the description of the above embodiment is only used to help understanding the method and core idea of the present invention; meanwhile, for a person skilled in the art, according to the idea of the present invention, there may be variations in the specific embodiments and the application scope, and in summary, the content of the present specification should not be construed as a limitation to the present invention.
Claims (10)
1. A syndrome calculation method in RS decoding, comprising:
deforming the syndrome polynomial determined based on the received code word polynomial r by using a preset multiplication strategy to obtain an iterative syndrome polynomial s;
determining a syndrome expression S = Ar + bs by using a preset periodic iteration formula based on a preset parallelism p and the iteration syndrome polynomial S; wherein A is a constant coefficient matrix of (n-k) rows and p columns, b is a constant coefficient matrix of (n-k) rows and 1 column, n represents that one code block in the received code element information corresponds to n code elements, and k represents that k information code elements exist in the n code elements in the code element information;
determining the Chang Jishu matrix A by using a preset calculation tool according to a preset equivalent circuit splitting method
Number of coefficients corresponds to->
(ii) a calculated value; wherein each of the n-k rows corresponds to 2p calculated values;
using preset data iteration segmentation method to the
Carrying out array segmentation on the numerical values, determining a calculation value corresponding to each group of data based on a preset exclusive-or algorithm until (n-k) calculation values corresponding to the Chang Jishu matrix A are determined, and then determining a simplified expression of the Chang Jishu matrix A based on the (n-k) calculation values;
determining a syndrome by using the simplified expression, the iterative syndrome polynomial and the syndrome expression so as to complete RS decoding error correction by using the syndrome;
wherein the preset multiplication strategy is a Hornor criterion; the preset equivalent circuit splitting method splits each coefficient and performs two-division input by combining the m value of a Galois field; the preset data iteration segmentation method comprises the following steps: corresponding to each of n-k lines
Dividing the calculated value by a preset division number, if the calculated value cannot be divided completely, filling zero to obtain w groups of data, wherein each preset division number m bits is a group, each bit of each m bit is in exclusive OR logic according to a bit, each bit is input by the preset division number bits, and the calculated value is obtained through calculationAnd (5) circuit initial values.
2. The syndrome calculation method of claim 1, wherein the determining of the matrix A of Chang Jishu by a predetermined equivalent circuit splitting method using a predetermined calculation tool is performed according to a predetermined equivalent circuit splitting method
Corresponding to a coefficient
Each calculated value; wherein each of the n-k rows corresponds to 2p calculated values, including:
determining the matrix A of Chang Jishu by matlab according to a preset equivalent circuit splitting method
Number of coefficients corresponding>
(ii) a calculated value; wherein each of the n-k rows corresponds to 2p calculated values.
3. The syndrome calculation method in RS decoding according to claim 1, wherein said calculating syndromes using the simplified expression, the iterative syndrome polynomial, and the syndrome expression includes:
inputting n symbols of the received symbol information into the simplified expression, the iterative syndrome polynomial, and the syndrome expression to determine a syndrome.
4. The syndrome calculation method in RS decoding according to claim 1, further comprising:
the preset parallelism p is set to 64.
5. The syndrome calculation method in RS decoding according to claim 1, wherein the utilizing is performed by using a syndrome calculation methodPreset data iterative segmentation method for
Carrying out array segmentation on the numerical values, determining a calculation value corresponding to each group of data based on a preset exclusive-or algorithm until (n-k) calculation values corresponding to the Chang Jishu matrix A are determined, and then determining a simplified expression of the Chang Jishu matrix A based on the (n-k) calculation values, wherein the method comprises the following steps:
based on the preset segmentation number, the preset data iteration segmentation method is used for aligning the data
And carrying out array segmentation on the numerical values, determining a calculation value corresponding to each group of data based on a preset exclusive-or algorithm until (n-k) calculation values corresponding to the Chang Jishu matrix A are determined, and then determining a simplified expression of the Chang Jishu matrix A based on the (n-k) calculation values.
6. The syndrome calculation method in RS decoding according to any one of claims 1 to 5, wherein the determining of the Chang Jishu matrix A in the Chang Jishu matrix A by a preset calculation tool according to a preset equivalent circuit splitting method is performed
Number of coefficients corresponding>
(ii) a calculated value; wherein each of the n-k rows corresponds to 2p calculated values, including:
based on in the Chang Jishu matrix A
Determining a first divided circuit and a second divided circuit corresponding to the Chang Jishu matrix A by using a preset calculation tool according to the coefficient and a preset equivalent circuit splitting method;
calculating initial values of the first divided circuit and the second divided circuit to determine an initial value of an LUT edge checking circuit corresponding to the Chang Jishu matrix A;
substituting the preset parallelism p into the Chang Jishu matrix A with the calculated initial value to determine the Chang Jishu matrix A corresponding to the Chang Jishu matrix A
(ii) a calculated value; wherein each of the n-k rows corresponds to 2p calculated values.
7. The syndrome calculation method in RS coding according to claim 6, wherein the syndrome calculation method is based on the syndrome in the Chang Jishu matrix A
Determining a first divided circuit and a second divided circuit corresponding to the Chang Jishu matrix a by using a preset calculation tool according to a preset equivalent circuit splitting method, wherein the method comprises the following steps:
respectively calculating in the Chang Jishu matrix A by using a preset calculation tool
Chang Jishu multipliers with coefficients in the galois field;
method pair for dividing by using preset equivalent circuit
And performing equivalent division on the constant coefficient multipliers to determine a first divided circuit and a second divided circuit corresponding to the Chang Jishu matrix A.
8. A syndrome calculation apparatus in RS decoding, comprising:
a polynomial determining module, configured to utilize a preset multiplication strategy to deform a syndrome polynomial determined based on the received codeword polynomial r to obtain an iterative syndrome polynomial s;
the expression determining module is used for determining an adjoint expression S = Ar + bs by using a preset periodic iteration formula based on a preset parallelism p and the iteration adjoint polynomial S; wherein A is a constant coefficient matrix of (n-k) rows and p columns, b is a constant coefficient matrix of (n-k) rows and 1 column, n represents that one code block in the received code element information corresponds to n code elements, and k represents that k information code elements exist in the n code elements in the code element information;
a circuit splitting module for determining Chang Jishu matrix A by using a preset calculation tool according to a preset equivalent circuit splitting method
Number of coefficients corresponds to->
(ii) a calculated value; wherein each of the n-k rows corresponds to 2p calculated values;
a data segmentation module for iteratively segmenting the data by using a preset data iterative segmentation method
Carrying out array segmentation on the numerical values, determining a calculation value corresponding to each group of data based on a preset exclusive-or algorithm until (n-k) calculation values corresponding to the Chang Jishu matrix A are determined, and then determining a simplified expression of the Chang Jishu matrix A based on the (n-k) calculation values;
a syndrome determining module, configured to determine a syndrome by using the simplified expression, the iterative syndrome polynomial, and the syndrome expression, so as to complete RS decoding error correction by using the syndrome;
wherein the preset multiplication strategy is a Hornor criterion; the preset equivalent circuit splitting method splits each coefficient and performs two-division input by combining the m value of a Galois field; the preset data iteration segmentation method comprises the following steps: dividing the 2*p calculated values corresponding to each line in n-k lines by a preset division number, and if the calculated values cannot be completely divided, filling zero to obtain w groups of data, wherein each preset division number m bits is a group, each bit of each m bit is subjected to bit exclusive OR logic, each bit is input of the preset division number bits, and circuit initial values are obtained through calculation.
9. An electronic device comprising a processor and a memory; wherein the processor implements the syndrome calculating method in the RS decoding according to any one of claims 1 to 7 when executing the computer program stored in the memory.
10. A computer-readable storage medium for storing a computer program; wherein the computer program, when executed by a processor, implements a syndrome calculation method in RS decoding according to any one of claims 1 to 7.
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