CN117116329A - Self-adaptive error correction method, device and system suitable for optical storage - Google Patents
Self-adaptive error correction method, device and system suitable for optical storage Download PDFInfo
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Abstract
The invention discloses a self-adaptive error correction method, equipment and a system suitable for optical storage, which belong to the technical field of optical storage, and the coding stage comprises the following steps: using RS (n) 0 The k) codes encode each row of the m rows and k columns of data blocks B to be encoded to obtain m check symbol sequences, and after the check symbol sequences are attached to the corresponding rows, m symbol sequences are obtainedForm symbol block B 0 The method comprises the steps of carrying out a first treatment on the surface of the Then, the steps are performed: (S1) initializing j=1; (S2) Using RS (n) j ，k j ) For symbol block B j‑1 M rows of symbol sequences in (a)Respectively coding, and adding the obtained check symbol sequences to the corresponding rows to obtain m symbol sequencesForm symbol block B j ；k j ＝n j‑1 The method comprises the steps of carrying out a first treatment on the surface of the (S3) adding 1 to j, and if j is less than or equal to S, switching to (S2); otherwise, RS encoding is carried out on the same order check symbol sequence of all rows, and the obtained check symbol sequence is uniformly added to B 0 After that, the process is performed. The invention can obviously improve the error correction capability of the optical storage system under the condition of not obviously increasing the occupation of redundant space.
Description
Technical Field
The invention belongs to the technical field of optical storage, and in particular relates to a self-adaptive error correction method, device and system suitable for optical storage.
Background
The optical storage technology is widely applied to mass cold data storage with the advantages of long storage life, non-contact read-write, high safety, easy disc replacement, low production cost, convenient copying and issuing and the like. Conventional optical storage techniques are based on laser interactions with the medium, resulting in changes in the properties of the medium to store information. With the advent of the digital age, information storage needs have grown, and it is predicted that the total amount of data generated globally by 2025 is expected to reach 175 gigabytes (ZB), and in order to meet the increasing storage needs, it is of great importance to increase the storage capacity of optical storage devices.
Conventional optical storage techniques increase the storage capacity of optical storage devices by shrinking the focused laser spot and the size of the recorder on the medium, but are limited by the optical diffraction limit, and it is increasingly difficult to increase the capacity of optical discs using conventional optical storage techniques.
In the conventional optical storage technology, in order to ensure reliable signal readout, reed-solomon error correction codes (Reed-solomon codes) are widely used, but with the development of multi-order optical storage technology, the existing error correction code scheme cannot meet the error correction capability required by the new technology, and if the existing error correction code scheme is required to meet the required error correction capability, a lot of redundant space is occupied, so that the storage capacity is reduced. Therefore, the existing optical storage error correction code technology cannot achieve both error correction capability and occupation of redundant space, and has certain limitation in practical application.
Disclosure of Invention
Aiming at the defects and improvement demands of the prior art, the invention provides a self-adaptive error correction method, equipment and a system suitable for optical storage, and aims to remarkably improve the error correction capability of an optical storage system under the condition of not obviously increasing the occupation of redundant space.
To achieve the above object, according to one aspect of the present invention, there is provided an adaptive error correction method suitable for optical storage, including an encoding stage; the encoding stage comprises:
an initial encoding step: using RS (n) 0 The k) codes encode each row of m rows and k columns of data blocks B to be encoded to obtain m pieces of data blocks with the length of n 0 -k check symbol sequences, appended to the corresponding row, resulting in m symbol sequencesForm m rows n 0 Symbol block B of column 0 ；
A higher order code step comprising:
(S1) initializing j=1;
(S2) Using RS (n) j ，k j ) For symbol block B j-1 M rows of symbol sequences in (a)Respectively coding to obtain m pieces of n-length j -k j J-order check symbol sequence r 1_j (x)～r m_j (x) After appending to the corresponding row, m symbol sequences are obtained +.>Form m rows n j Symbol block B of column j ；k j ＝n j-1 ；
(S3) adding 1 to the value of j, and if j is less than or equal to S, turning to the step (S2); otherwise, transferring to a cascade check coding step; s is a preset positive integer;
the cascade check coding step comprises the following steps: for first order check symbol sequence r 1_1 (x)、r 2_1 (x)、…r m_1 (x) RS encoding is carried out on the formed symbol sequence to obtain a cascade check symbol sequence R 1 (x) The method comprises the steps of carrying out a first treatment on the surface of the For second order check symbol sequence r 1_2 (x)、r 2_2 (x)、…r m_2 (x) RS encoding is carried out on the formed symbol sequence to obtain a cascade check symbol sequence R 2 (x) The method comprises the steps of carrying out a first treatment on the surface of the … …; for S-order check symbol sequence r 1_S (x)、r 2_S (x)、…r m_S (x) RS encoding is carried out on the formed symbol sequence to obtain a cascade check symbol sequence R S (x)；
The coding block construction step: will concatenate the check symbol sequence R 1 (x)、R 2 (x)…R S (x) The symbols in (a) are uniformly added to the symbol block B 0 Then, the coding block corresponding to the data block B is obtainedThe encoding is ended.
Further, the adaptive error correction method suitable for optical storage provided by the invention further comprises a decoding stage; the decoding stage comprises:
and (3) independent decoding: from the coded block to be decodedExtracting the first n in each row of (2) 0 The symbols are m, the length of which is n 0 Symbol sequence of->Using RS (n) 0 K) code is respectively for symbol sequence +.>Decoding to obtain m rows of symbol sequences +.>If there is a row with decoding failureTaking the row with the decoding failure as a target row, and triggering a high-order decoding step; otherwise, triggering a data block construction step;
the high-order decoding step includes:
(T1) initializing j=1;
(T2) slave code blockExtracting cascade check symbol sequence R j (x) Corresponding symbol sequence R' j (x) By means of RS (n j ，k j ) Code is respectively for m rows of symbol sequences->Encoding to generate m pieces of length n j -k j Is a j-order check symbol sequence r' 1_j (x)～r' m_j (x) R 'is paired by RS code' 1_j (x)～r' m_j (x) R 'and R' j (x) Decoding the constructed symbol sequence, adding the decoded first-order check symbol sequence to the corresponding row to obtain m pieces of code sequences with length of n j Is a sequence of symbols of (2)
(T3) from the symbol sequenceExtracting the symbol sequence of the target row and using RS (n j ，k j ) The code is decoded by the symbol sequence +.>The symbol sequences which do not contain the target line in the sequence and the symbol sequences obtained by this decoding together form m-line symbol sequences +.>
(T4) if there is a decoding failure line in the step (T3), taking the current decoding failure line as a target line and transferring to the step (T5); otherwise, triggering a data block construction step;
(T5) adding 1 to the value of j, and if j is less than or equal to S, turning to the step (T2); otherwise, the decoding fails;
and a data block construction step: and extracting information symbols from the successfully decoded rows, organizing the information symbols into data blocks according to the rows, and ending the decoding.
Further, the independent decoding step further includes: in the case of RS (n) 0 K) code is respectively applied to symbol sequencesWhile decoding, calculating a sign (i) of each row, wherein the sign (i) is used for recording the order of the i-th row needing high-order decoding, i=1, 2 and … m;
in step (T3), the symbol sequence in which any one of the target rows L is located isUsing RS (n) j ，k j ) The code is decoded, specifically:
acquiring the line number L of the target line L and the marking bit sign (L) thereof, if j<sign (l), the symbol sequence is directly followedAs a decoding result; otherwise, using RS (n j ，k j ) Code pair symbol sequence->Decoding is performed.
According to yet another aspect of the present invention, there is provided an adaptive error correction device adapted for optical storage, comprising: a computer readable storage medium storing a computer program;
and a processor for reading the computer program stored in the computer readable storage medium and executing the adaptive error correction method suitable for optical storage.
According to yet another aspect of the present invention, there is provided an optical storage system comprising: comprising an optical storage medium and an adaptive error correction device suitable for optical storage provided by the invention.
In general, through the above technical solutions conceived by the present invention, the following beneficial effects can be obtained:
(1) The invention further carries out higher-order coding on the basis of the RS coding step, and can effectively improve the error correction capability, thereby improving the reliability of the optical storage system; meanwhile, the high-order check symbol generated by the high-order code is coded to obtain a cascade check symbol, and finally, the cascade check symbol is stored without storing the high-order check symbol, and because the high-order check symbol can be recovered through the cascade check symbol and the data size of the cascade check symbol is reduced compared with that of the high-order check symbol, the invention can greatly reduce the occupancy rate of the redundant space on the basis of not influencing the improvement of the error correction capability brought by the high-order check code, and therefore, the invention can obviously improve the error correction capability of the optical storage system under the condition of not obviously increasing the occupancy of the redundant space.
(2) In the preferred scheme of the invention, the sign (i) of each line is calculated while independent decoding is carried out, so as to record the order of each line which needs to be subjected to high-order decoding, and when the high-order decoding is carried out, if the current decoding order does not reach the high-order decoding order which needs to be carried out of the target line, the decoding process is not carried out after the current high-order check symbol is restored, thereby avoiding invalid decoding calculation, reducing the calculated amount and improving the decoding efficiency.
Drawings
FIG. 1 is a schematic diagram of an adaptive error correction method suitable for optical storage according to an embodiment of the present invention;
FIG. 2 is a graph showing average overhead of performing secondary decoding with and without flag bits according to an embodiment of the present invention;
FIG. 3 is a diagram showing the error correction capability of the embodiment of the present invention using different schemes;
FIG. 4 is a schematic diagram of encoding concatenated check symbols according to an embodiment of the present invention;
FIG. 5 is a schematic diagram of not encoding concatenated check symbols according to an embodiment of the present invention;
FIG. 6 is a schematic diagram of a data block to be encoded according to an embodiment of the present invention;
FIG. 7 is a schematic diagram of a symbol block after an initial encoding step according to an embodiment of the present invention;
fig. 8 is a schematic diagram of a coding block obtained after coding according to an embodiment of the present invention.
Detailed Description
The present invention will be described in further detail with reference to the drawings and examples, in order to make the objects, technical solutions and advantages of the present invention more apparent. It should be understood that the specific embodiments described herein are for purposes of illustration only and are not intended to limit the scope of the invention. In addition, the technical features of the embodiments of the present invention described below may be combined with each other as long as they do not collide with each other.
In the present invention, the terms "first," "second," and the like in the description and in the drawings, if any, are used for distinguishing between similar objects and not necessarily for describing a particular sequential or chronological order.
In order to make the technical scheme provided by the invention clearer and more detailed, the related principle of the Reed-solomon error correcting code (Reed-solomon code) is briefly described as follows:
the RS code is a linear error correction code with very strong error correction performance, and can correct random errors and burst errors. The RS code is calculated in a galois field GF (2 m ) There are 2 in the representation domain m Elements, each element can be alpha 0 、α 0 、…α 0 Is represented by the sum of (a). The basic idea of RS codes is to select a suitable generator polynomial g (x) and to compute the codeword polynomials for each information field to be a multiple of g (x). If the remainder of the received codeword polynomial divided by the generator polynomial is not 0, then it is known that an error exists in the received codeword.
At GF (2) m ) In the domain, the meaning of each symbol of RS (n, k) is as follows:
m represents that each symbol consists of an m-bit binary number;
n represents a codeword having n symbols in total;
k represents that there are k information symbols in one codeword;
r=n-k=2t indicates that there are r check symbols in one code block;
t represents the number of symbols that can be corrected.
In RS codes, symbols may also be referred to as symbols, and accordingly, one codeword is a symbol sequence consisting of information symbols and check symbols generated by encoding.
The decoding process is as follows: and substituting Galois field elements used by the generator polynomial into the code element polynomial to obtain n-k syndromes, calculating error position polynomials by using the syndromes, and respectively obtaining error positions and error values by using a Qian search algorithm and a Forney algorithm.
Since in the RS code, in order to correct one information symbol, 2 additional check symbols are required to be stored, and the redundant space occupancy is high. In optical storage applications, the error rate is often higher, and in order to ensure the storage reliability, if the conventional RS code is adopted to complete encoding and decoding, more redundant check symbols need to be stored, which seriously affects the storage capacity of the optical storage system. In order to solve the problem, the invention provides a self-adaptive error correction method, device and system suitable for optical storage, and the whole thought is as follows: on the basis of the traditional RS code coding, higher-order coding is performed, but a higher-order check symbol sequence generated by the higher-order coding is not directly stored, but a symbol sequence formed by the higher-order check symbol sequence is coded again to generate cascade check symbols, and finally the cascade check symbols are stored, so that under the condition of ensuring the same error correction capability, the storage of a large number of higher-order check symbols is avoided, and the purpose of remarkably improving the error correction capability of an optical storage system under the condition of not obviously changing the occupation of redundant space is achieved.
The following are examples.
Example 1:
an adaptive error correction method suitable for optical storage, as shown in fig. 1, comprises an encoding stage; the encoding stage comprises: an initial encoding step, a high-order encoding step, a cascade check encoding step, and an encoding block construction step.
The initial encoding step encodes the data block to be encoded by conventional RS encoding, and specifically includes: using RS (n) 0 The k) codes encode each row of m rows and k columns of data blocks B to be encoded to obtain m pieces of data blocks with the length of n 0 -k check symbol sequences, appended to the corresponding row, resulting in m symbol sequencesForm m rows n 0 Symbol block B of column 0 。
After the initial encoding step, the number of error symbols that can be corrected for each row of symbol sequence is t=r/2, where r=n 0 -k. In order to further improve the error correction capability and ensure the storage reliability, the present embodiment further performs a higher-order encoding step on each row of symbol sequence based on the initial encoding step to generate more check symbols, in practical application, the higher-order encoding order S may be set according to specific error correction requirements, and then sequentially performs a first-order higher-order encoding, a second-order higher-order encoding, a … … S-order higher-order encoding, and the first-order higher-order encoding encodes the symbol block B generated by the initial encoding 0 Each row of symbol sequence of the code sequence is an information symbol, and the symbol sequence generated by the previous higher-order code of each other higher-order code is an information symbol; each higher order code uses a different generator polynomial, in turn denoted g 1 (x),g 2 (x),…,g s (x) A. The invention relates to a method for producing a fibre-reinforced plastic composite Specifically, the higher-order encoding step includes:
(S1) initializing j=1;
(S2) Using RS (n) j ，k j ) For symbol block B j-1 M rows of symbol sequences in (a)Respectively coding to obtain m pieces of n-length j -k j J-order check symbol sequence r 1_j (x)～r m_j (x) After being attached to the corresponding row, m symbol sequences are obtainedForm m rows n j Symbol block B of column j ；k j ＝n j-1 ；
(S3) after adding 1 to the value of j, if j is less than or equal to S, indicating that the high-order coding is not finished, turning to the step (S2) to perform the next-order high-order coding; otherwise, it indicates that the high-order encoding ends, because each high-order encoding generates additional check symbols, if the check symbols are directly stored, the redundancy space occupancy rate is too high, and the storage capacity of the optical storage system is seriously affected.
In this embodiment, since each higher-order code is executed after the previous higher-order code is finished, when the check symbols generated by the higher-order check code are encoded, all the check symbols generated by the same higher-order code are formed into an information symbol sequence to be encoded, so as to generate a corresponding concatenated check symbol sequence. Specifically, the cascade check coding step includes: for first order check symbol sequence r 1_1 (x)、r 2_1 (x)、…r m_1 (x) RS encoding is carried out on the formed symbol sequence to obtain a cascade check symbol sequence R 1 (x) The method comprises the steps of carrying out a first treatment on the surface of the For second order check symbol sequence r 1_2 (x)、r 2_2 (x)、…r m_2 (x) RS encoding is carried out on the formed symbol sequence to obtain a cascade check symbol sequence R 2 (x) The method comprises the steps of carrying out a first treatment on the surface of the … …; for S-order check symbol sequence r 1_S (x)、r 2_S (x)、…r m_S (x) RS encoding is carried out on the formed symbol sequence to obtain a cascade check symbol sequence R S (x)。
The data size of the concatenated check symbol is greatly reduced compared with the high-order check symbol, and therefore, the present embodiment appends the concatenated check symbol to the symbol block B through the encoding block construction step 0 Thereafter, instead of the storage of high-order check symbols, in particular, the encoding block construction stepThe method comprises the following steps: will concatenate the check symbol sequence R 1 (x)、R 2 (x)…R S (x) The symbols in (a) are uniformly added to the symbol block B 0 Then, the coding block corresponding to the data block B is obtainedThe encoding is ended.
Based on symbol block B in subsequent decoding process 0 The information in the code sequence and the cascade check symbol can restore each higher-order code symbol sequence, so the embodiment greatly reduces the occupation amount of redundant space on the basis of ensuring the error correction capability of higher-order check codes.
Corresponding to the above-mentioned encoding stage, the adaptive error correction method applicable to optical storage provided in this embodiment further includes a decoding stage;
the decoding stage comprises: an independent decoding step, a high-order decoding step, and a data block construction step.
The independent decoding step corrects a small amount of errors in the coding block to be decoded through RS coding; a high-order decoding step, namely decoding the rows which cannot be successfully decoded in the independent decoding step, wherein in the decoding process, the high-order check symbols of each row are recovered according to the stored cascade check symbols, and then decoding is carried out by a decoding method corresponding to the high-order check codes; and the data block construction step is used for extracting the original information symbol after the decoding is successful.
The independent decoding step specifically comprises the following steps: from the coded block to be decodedExtracting the first n in each row of (2) 0 The symbols are m, the length of which is n 0 Symbol sequence of->Using RS (n) 0 K) code is respectively for symbol sequence +.>Decoding to obtain m rowsSymbol sequence->If the decoding failure line exists, taking the decoding failure line as a target line, and triggering a high-order decoding step; otherwise, triggering the data block construction step.
The high-order decoding step includes:
(T1) initializing j=1;
(T2) slave code blockExtracting cascade check symbol sequence R j (x) Corresponding symbol sequence R' j (x) By means of RS (n j ，k j ) Code is respectively for m rows of symbol sequences->Encoding to generate m pieces of length n j -k j Is a j-order check symbol sequence r' 1_j (x)～r' m_j (x) R 'is paired by RS code' 1_j (x)～r' m_j (x) R 'and R' j (x) Decoding the constructed symbol sequence, adding the decoded first-order check symbol sequence to the corresponding row to obtain m pieces of code sequences with length of n j Is a sequence of symbols of (2)
(T3) from the symbol sequenceExtracting the symbol sequence of the target row and using RS (n j ，k j ) The code is decoded by the symbol sequence +.>The symbol sequences which do not contain the target line in the sequence and the symbol sequences obtained by this decoding together form m-line symbol sequences +.>
(T4) if there is a decoding failure line in the step (T3), taking the current decoding failure line as a target line and transferring to the step (T5); otherwise, triggering a data block construction step;
(T5) adding 1 to the value of j, and if j is less than or equal to S, turning to the step (T2); otherwise, the decoding fails;
and a data block construction step: and extracting information symbols from the successfully decoded rows, organizing the information symbols into data blocks according to the rows, and ending the decoding.
In the independent decoding step, the number of error symbols in each row can be calculated in the process of independently decoding each row, and since the number of error symbols which can be corrected by the RS code used in the initial encoding and the higher order check encoding of each step is known, whether the higher order decoding is needed for each row or not, and the order of specifically performing the higher order decoding can be directly calculated after the order of the independent decoding step. Based on this, in order to reduce the amount of computation in the high-order decoding step, in this embodiment, the independent decoding step further includes: in the case of RS (n) 0 K) code is respectively applied to symbol sequencesWhile decoding, calculating a sign (i) of each row, wherein the sign (i) is used for recording the order of the i-th row needing high-order decoding, i=1, 2 and … m;
in step (T3), the symbol sequence in which any one of the target rows L is located isUsing RS (n) j ，k j ) The code is decoded, specifically:
acquiring the line number L of the target line L and the marking bit sign (L) thereof, if j<sign (l), the symbol sequence is directly followedAs a decoding result; otherwise, using RS (n j ，k j ) Code pair symbol sequence->Decoding is performed.
Based on the optimization, if the current decoding order does not reach the higher-order decoding order needed by the target row, the decoding process is not executed after the higher-order check symbol is recovered, so that invalid decoding calculation can be avoided, the calculated amount is reduced, and the decoding efficiency is improved. As shown in fig. 2, in order to compare the time overhead of decoding the same data block with the flag bit and without the flag bit, it is known from the result shown in fig. 2 that the flag bit needs to be initialized for the first decoding, and the time overhead of the flag bit and the flag bit has no difference, but as the symbol error rate increases before decoding, the effect of the flag bit is more and more significant, so that the time overhead of decoding can be effectively reduced, and the decoding efficiency is improved.
In general, the embodiment further performs higher-order encoding based on the RS encoding step, so that the error correction capability can be effectively improved, thereby improving the reliability of the optical storage system; meanwhile, the high-order check symbol generated by the high-order code is coded to obtain a cascade check symbol, and finally, the cascade check symbol is stored without storing the high-order check symbol. That is, the present embodiment can significantly improve the error correction capability of the optical storage system without significantly increasing the redundant space occupation.
It should be noted that, in practical application, the initial encoding and the capability of each order of high-order check encoding determine the number of symbol errors that can be corrected finally, and can be set correspondingly according to practical application. The error correction capability of the cascade check codes provides guarantee for the recovery of the higher-order check symbols and determines the final redundant space occupancy rate, so that the setting needs to be comprehensively considered.
In theory, the cascade check symbol is encoded again, so that the reliability of data storage can be further improved, but under the condition of fixed storage space, the storage space of the cascade check symbol can be compressed for storing the check symbol generated by recoding, and experimental comparison analysis shows that the embodiment only stores cascade check codes but not codes the cascade check codes, so that higher error correction performance can be obtained under the same storage space. The error correction capability of the above two methods is shown in fig. 3, where scheme 1 represents a scheme of encoding the concatenated check symbol, and scheme 2 represents a scheme of not encoding the concatenated check symbol, that is, a scheme adopted in the present embodiment. As can be seen from fig. 3, when the symbol error rate before decoding is high, the error correction performance is the same because the high-order decoding of both methods fails due to the large number of errors, but the scheme adopted in the embodiment shows better error correction performance with the decrease of the symbol error rate before decoding.
The results of one comparison are as follows:
fig. 4 is a schematic diagram of encoding cascade check symbols after encoding data blocks of 155 rows (corresponding to n=155 in fig. 3) and 214 columns. In the data block, the original information symbol of each row (d in the corresponding diagram i ) The number is 214, and the low-order check symbols (in the corresponding diagram) The number is 32. Using a 6-order higher order check (corresponding to m=7 in the figure), each order check containing 2 higher order check symbols (corresponding to each +.>2 symbols) i.e. at most 6 extra error correction capabilities are provided. Check symbols (p in the corresponding diagram) of these 6-order higher order check symbols j j) The numbers are 104,68,44,28,20,16 respectively. These p' s j ' one more time protection, check symbol (p in the corresponding diagram * ) The number is 30.
Fig. 5 is a schematic diagram of encoding data blocks of 155 rows (corresponding to n=155 in fig. 3) and 214 columns, where after cascade check encoding is performed to obtain cascade check symbols, the cascade check symbols are not encoded any more. In the data block, the original information symbols of each row (corresponding mapD in (d) i ) The number is 214, and the low-order check symbol (p in the corresponding diagram i ) The number is 32. Using 11 higher order parity (corresponding to m=11 in the figure), each parity having 2 higher order parity symbols (corresponding to S in the figure 2t+1 →S 2t+2m A total of 22 higher order syndromes), i.e., up to 11 extra error correction capabilities are provided. The check symbols of these 11-order higher order check symbols (p in the corresponding diagram j ') number is 104,68,44,28,20,16,12,8,4,4,2, and the sum of the number of check symbols generated by the added fourth-order high-order check codes is exactly 30.
As can be seen from comparing fig. 4 and fig. 5, the present embodiment obtains and stores the concatenated check symbols, which can obtain better benefits in terms of storage space and error correction performance. Meanwhile, the calculation of encoding for the concatenated check symbol is omitted.
In order to make the technical solution of the present embodiment clearer and more detailed, the encoding stage and decoding stage of the adaptive error correction method for optical storage provided in the present embodiment are further explained below in conjunction with a specific application example.
Now, assume that there is a 30 row 215 column block of information data, each element of which is 8bit in length and belongs to the galois field GF (2 8 ) As shown in fig. 6.
For this data block, the encoding process is as follows:
an initial encoding step is first performed. For each row 215 of the information data block, encoding using an RS (245,215) code to obtain 30 check symbols, wherein the encoding uses a generator polynomial of
g(x)＝(x-α)(x-α 2 )…(x-α 30 )
The check symbols obtained in each row are added at the back of the row to form a symbol block of 30 rows and 245 columns together, as shown in fig. 6, in each row, the first 215 symbols are information symbols, and the last 30 symbols are check symbols; the RS code based mechanism is known that each row of the data block can correct up to 15 symbol errors.
Then a higher order encoding step is performed. Specifically, two times of high-order coding are performed, the first order high-order coding adopts RS (247,245) codes, and the used generator polynomial is as follows:
g 1 (x)＝(x-α 31 )(x-α 32 )
after first-order high-order check coding, generating 2 first-order high-order check symbols in each row, and increasing the number of error correction symbols in each row to 16;
the second-order higher-order coding adopts RS (249,247) codes, and the used generator polynomials are as follows:
g 2 (x)＝(x-α 33 )(x-α 34 )
generating 2 second-order first-order check symbols after second-order high-order check coding, and increasing the number of error correction symbols of each row to 17;
after the higher-order coding is finished, the total number of the first-order higher-order check symbols and the second-order higher-order check symbols is 120.
A concatenated check coding step is then performed. The data block elements in fig. 6 are represented by new markers T for each row of symbols T i_1 ,…,T i_245 The symbol sequences formed by the first-order high-order check symbol and the second-order high-order check symbol are respectively marked as r i_1 (x) And r i_2 (x)。
Higher order check symbol r corresponding to 30 rows of symbols i_1 (x) Combining the two information sequences into one information sequence and performing RS (90,60) coding to obtain a cascade check code R 1 (x) Higher order check symbol r corresponding to 30 rows of symbols i_2 (x) Combining the two information sequences into one information sequence and performing RS (90,60) coding to obtain a cascade check symbol R 2 (x)，R 1 (x) And R is 2 (x) Each contains 30 check symbols and 60 cascade check symbols, and compared with the high-order check symbols, the data volume is greatly reduced.
And finally, executing the coding block construction step. The 60 concatenated check symbols are appended to the right of the data block shown in fig. 7, combined into 30 rows 247 column data blocks as shown in fig. 8. Wherein R1-1 and R1-2 … … R1-30 respectively represent cascade check codes R 1 (x) Wherein, R2-1, R2-2 … … R2-30 respectively represent cascade check symbol R 2 (x) Is a symbol of 30 of the three symbols.
Now assume that the original symbol T of each row of the data block in FIG. 8 i_1 ,…,T i_245 The number of symbol errors is 15 or less, the number of symbol errors is different, the number of symbol errors is 16 in the 1 st row, the number of symbol errors is 17 in the 2 nd row, and the number of symbol errors in the 3 rd to 30 th rows is 15 or less. The decoding phase for that data block is as follows.
First, an independent decoding step is performed. T for each row by using traditional Reed-Solomon decoding algorithm i_1 ,…,T i_245 A total of 245 symbols are subjected to low-order verification: respectively alpha is 1 ,α 2 ,…,α 30 Substituting the symbol polynomials to calculate the syndrome S 1 ,S 2 ,…,S 30 And then calculating an error position polynomial and an error value polynomial through a syndrome, respectively calculating an error position and a corresponding error value through a chien search algorithm and a Forney algorithm, and finally correcting the corresponding position of the code element, recalculating the syndrome and judging whether the decoding is correct.
Due to T i_1 ,…,T i_245 The maximum error correction capability of the code is 15 symbol errors obtained by using RS (245,215) codes, so that decoding failure occurs in lines 1 and 2, and decoding succeeds in lines 3-30. And taking the 1 st line and the 2 nd line as target lines, and triggering a high-order decoding step.
The high-order decoding steps are performed as follows:
first order high order decoding is performed: symbol T of each row i_1 ,…,T i_245 Encoding with RS (247,245) to obtain first-order check code r' i_1 (x) Each first order check code contains 2 check symbols, which is due to T 1_1 ,…,T 1_245 And T 2_1 ,…,T 2_245 Contains uncorrected errors, so that it calculates the first-order check code r' 1_1 (x) And r' 2_1 (x) Is incorrect, and the first order check code calculated in lines 3-30 is correct. First order check code r 'corresponding to 30 lines of code elements' i_1 (x) Is combined into an information sequence and is connected with a cascade check code R 1 (x) Spliced together into a code element, and then the correct first-order check code r 'is restored by using an RS (90,60) decoding algorithm' 1_1 (x) And r' 2_1 (x) A. The invention relates to a method for producing a fibre-reinforced plastic composite By first-order check code r' 1_1 (x) Can be the first1 line calculates higher order companion S 31 And S is 32 Will first order syndrome S 31 、S 32 And original companion S 1 ,S 2 ,…,S 30 The combination can achieve the capability of correcting 16 symbol errors, and the subsequent decoding algorithm flow is the same as the traditional decoding algorithm flow. So 16 symbol errors on line 1 can be corrected but 17 symbol errors on line 2 cannot be corrected, and then the second-order higher-order decoding needs to be performed:
symbol T of each row i_1 ,…,T i_245 Encoding with RS (249,247) to obtain second order check code r' i_2 (x) Each second order check code contains 2 check symbols, due to T 2_1 ,…,T 2_245 Contains uncorrected errors, so that it calculates the second order check code r' 2_2 (x) Is erroneous and the second order check code calculated for the other rows is correct. Second order check code r 'corresponding to 30 lines of code elements' i_2 (x) Is combined into an information sequence and is connected with a cascade check code R 2 (x) Spliced together into a code element, and then the correct second-order check code r 'is restored by using an RS (90,60) decoding algorithm' 2_2 (x) A. The invention relates to a method for producing a fibre-reinforced plastic composite By a second order check code r' 2_2 (x) Second order syndromes S can be calculated for line 2 33 And S is 34 Will be second order syndrome S 33 、S 34 First order concomitant S 31 、S 32 And original companion S 1 ,S 2 ,…,S 30 The combination can achieve the capability of correcting 17 symbol errors, and the subsequent decoding algorithm flow is the same as the traditional decoding algorithm flow. So 17 symbol errors of row 2 can be corrected.
Example 2:
an adaptive error correction device adapted for optical storage, comprising: a computer readable storage medium storing a computer program;
and a processor configured to read a computer program stored in a computer-readable storage medium, and execute the adaptive error correction method applicable to optical storage provided in the above embodiment 1.
In this embodiment, the specific implementation of each module may refer to the description in embodiment 1 above, and will not be repeated here.
Example 3:
an optical storage system comprising: comprising an optical storage medium and an adaptive error correction device adapted for optical storage as provided in the above-described embodiment 2.
It will be readily appreciated by those skilled in the art that the foregoing description is merely a preferred embodiment of the invention and is not intended to limit the invention, but any modifications, equivalents, improvements or alternatives falling within the spirit and principles of the invention are intended to be included within the scope of the invention.
Claims (5)
1. An adaptive error correction method suitable for optical storage, comprising an encoding stage; the encoding stage comprises:
an initial encoding step: using RS (n) 0 The k) codes encode each row of m rows and k columns of data blocks B to be encoded to obtain m pieces of data blocks with the length of n 0 -k check symbol sequences, appended to the corresponding row, resulting in m symbol sequencesForm m rows n 0 Symbol block B of column 0 ；
A higher order code step comprising:
(S1) initializing j=1;
(S2) Using RS (n) j ，k j ) For symbol block B j-1 M rows of symbol sequences in (a)Respectively coding to obtain m pieces of n-length j -k j J-order check symbol sequence r 1_j (x)～r m_j (x) After being attached to the corresponding row, m symbol sequences are obtainedForm m rows n j Symbol block B of column j ；k j ＝n j-1 ；
(S3) adding 1 to the value of j, and if j is less than or equal to S, turning to the step (S2); otherwise, transferring to a cascade check coding step; s is a preset positive integer;
the cascade check coding step comprises the following steps: for first order check symbol sequence r 1_1 (x)、r 2_1 (x)、…r m_1 (x) RS encoding is carried out on the formed symbol sequence to obtain a cascade check symbol sequence R 1 (x) The method comprises the steps of carrying out a first treatment on the surface of the For second order check symbol sequence r 1_2 (x)、r 2_2 (x)、…r m_2 (x) RS encoding is carried out on the formed symbol sequence to obtain a cascade check symbol sequence R 2 (x) The method comprises the steps of carrying out a first treatment on the surface of the … …; for S-order check symbol sequence r 1_S (x)、r 2_S (x)、…r m_S (x) RS encoding is carried out on the formed symbol sequence to obtain a cascade check symbol sequence R S (x)；
The coding block construction step: will concatenate the check symbol sequence R 1 (x)、R 2 (x)…R S (x) The symbols in (a) are uniformly added to the symbol block B 0 Then, the coding block corresponding to the data block B is obtainedThe encoding is ended.
2. The adaptive error correction method for optical storage of claim 1, further comprising a decoding stage; the coding stage includes:
and (3) independent decoding: from the coded block to be decodedExtracting the first n in each row of (2) 0 The symbols are m, the length of which is n 0 Symbol sequence of->Using RS (n) 0 K) code is respectively for symbol sequence +.>Decoding to obtain m-line symbol sequenceIf the decoding failure line exists, taking the decoding failure line as a target line, and triggering a high-order decoding step; otherwise, triggering a data block construction step;
the high-order coding step includes:
(T1) initializing j=1;
(T2) slave code blockExtracting cascade check symbol sequence R j (x) Corresponding symbol sequence R' j (x) By means of RS (n j ，k j ) Code is respectively for m rows of symbol sequences->Encoding to generate m pieces of length n j -k j Is a j-order check symbol sequence r' 1_j (x)～r' m_j (x) R 'is paired by RS code' 1_j (x)～r' m_j (x) R 'and R' j (x) Decoding the constructed symbol sequence, adding the decoded first-order check symbol sequence to the corresponding row to obtain m pieces of code sequences with length of n j Symbol sequence of->
(T3) from the symbol sequenceExtracting the symbol sequence of the target row and using RS (n j ，k j ) The code is decoded by the symbol sequence +.>The symbol sequences which do not contain the target line in the sequence and the symbol sequences obtained by this decoding together form m-line symbol sequences +.>
(T4) if there is a decoding failure line in the step (T3), taking the current decoding failure line as a target line and transferring to the step (T5); otherwise, triggering a data block construction step;
(T5) adding 1 to the value of j, and if j is less than or equal to S, turning to the step (T2); otherwise, the decoding fails;
the data block construction step: and extracting information symbols from the successfully decoded rows, organizing the information symbols into data blocks according to the rows, and ending the decoding.
3. The adaptive error correction method for optical storage of claim 2, wherein said independent decoding step further comprises: in the case of RS (n) 0 K) code is respectively applied to symbol sequencesWhile decoding, calculating a sign (i) of each row, wherein the sign (i) is used for recording the order of the i-th row needing high-order decoding, i=1, 2 and … m;
in the step (T3), the symbol sequence in which any one of the target lines L is located isUsing RS (n) j ，k j ) The code is decoded, specifically:
acquiring the line number L of the target line L and the marking bit sign (L) thereof, if j<sign (l), the symbol sequence is directly followedAs a decoding result; otherwise, using RS (n j ，k j ) Code pair symbol sequence->Decoding is performed.
4. An adaptive error correction device adapted for optical storage, comprising: a computer readable storage medium storing a computer program;
and a processor for reading a computer program stored in said computer readable storage medium, performing the adaptive error correction device of any one of claims 1-3 adapted for optical storage.
5. An optical storage system, comprising: comprising an optical storage medium and an adaptive error correction device adapted for optical storage as claimed in claim 4.
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