WO2011000176A1

WO2011000176A1 - Coding and decoding method and codec of error correction code

Info

Publication number: WO2011000176A1
Application number: PCT/CN2009/073148
Authority: WO
Inventors: 杨宗杰
Original assignee: 慧帝科技(深圳)有限公司; 慧荣科技股份有限公司; 芯光飞株式会社
Priority date: 2009-07-01
Filing date: 2009-08-07
Publication date: 2011-01-06
Also published as: CN101938280B; KR101314232B1; TWI397811B; KR20130014484A; TW201102807A; WO2011000176A8; CN101938280A

Abstract

A coding and decoding method and a codec of an error correction code are provided. The method comprises the following steps: receiving original data; dividing the original data into a plurality of blocks of data; generating short parities of the blocks of data according to a first generator polynomial, respectively; attaching the short parities to the blocks of data from behind to respectively generate a plurality of short code words; combining the short code words to obtain coded data; generating a long parity of the coded data according to a second generator polynomial, wherein the first generator polynomial is a function of at least one minimal polynomials of the second generator polynomial; attaching the long parity to the coded data from behind to generate a long code word of the error correction code. The method reduces the time for correcting error codes, thus improving the efficiency of the decoder.

Description

Error correction code encoding and decoding method and codec

The present invention relates to the field of data communication technologies, and more particularly to a coding and decoding method for an error correction code and a codec. Background technique

The error correction code is used to correct data errors. The data transmitted by the communication system is often encoded as an error correction code (including data messages and check codes) before being transmitted on the transmission side. When the receiving end receives the error correction code data, even if the data is corrupted during transmission and a random error occurs, the correct data can be recovered by decoding the error correction code. Similarly, data storage systems often encode stored data as error correction codes before storing the data. When the data is corrupted during storage and a random error occurs, the correct error can be recovered by decoding the error correction code. Common error correction codes such as BCH, Ray-Chaudhuri, and Hocquenghem code and RS code (; Reed-Solomon code). The BCH code is often used for the storage of flash data, and the RS code is often used for the storage of optical data.

When the data storage system wants to take out the data stored by it, the extracted error correction code is taken, so the error correction code must be decoded before the data is used to be restored to the original data. 1 is a flow chart of a conventional decoding method 100 for error correction codes. First, the decoder receives an error correction code (step 102). Next, the decoder calculates a plurality of symptom codes based on the parity of the error correction code (syndrome X step 104). Next, the decoder checks if the symptom codes are all zero (step 106). If the symptom code is zero, there is no error in the error correction code, so no further correction is needed. Conversely, if one of the symptom codes is not zero, it indicates that an error correction code has occurred, so the error correction code must be corrected. First, the decoder calculates a plurality of coefficients of an error-location polynomial based on the symptom codes (step 108). Next, the decoder performs a Chien search to find the root of the error polynomial (step 110). Since the root of the error polynomial indicates the position of the bit in the error correction code where the error occurred, the decoder can follow the error polynomial The root corrects the error correction code (step 112), and obtains an error-free error correction code, that is, obtains the correct data.

However, when the decoder calculates the coefficients of the error polynomial in step 108, it takes a lot of time. Similarly, when the decoder performs a Qin search in step 110 to find the root of the error polynomial, it also takes a lot of time. In the conventional decoding method 100, as long as one of the plurality of symptom codes of the error correction code is not zero, it indicates that an error has occurred, so step 108 and step 110 must be performed in order to correct the error, thereby causing the decoding time of the system. delay. When the plurality of symptom codes of the error correction code are not zero, if the error correction code can be modified in other manners in some cases, the coefficient of the error polynomial is calculated in step 108 and the Qin search is performed in step 110. By the root of the error polynomial, the required decoding time can be greatly reduced, and the performance of the decoder is improved. Therefore, there is a need for an encoding and decoding method that reduces the decoding time of an erroneous correction code. Summary of the invention

The technical problem to be solved by the present invention is to provide a coding and decoding method for an error correction code and a codec for the above-mentioned drawbacks of the prior art.

One of the technical solutions adopted by the present invention to solve the technical problem is: constructing an encoding and decoding method for an error correction code, comprising the steps of: receiving a raw data; dividing the original data into a plurality of sector data; A first generator polynomial generates short parity codes of the segment data respectively; and the short check codes are appended to the segment data to respectively generate a plurality of short codewords (short codeword) Combining the short codewords to obtain an encoded data; generating a long parity of the encoded data according to a second generator polynomial, wherein the first generating polynomial is the second generating polynomial At least one minimum polynomial function; appending the long check code to the encoded data to generate a long codeword of the error correction code.

The method for encoding and decoding an error correction code according to the present invention, wherein the first generator polynomial is a least common multiple of at least one minimum polynomial of the second generator polynomial.

The method for encoding and decoding the error correction code according to the present invention further includes storing the long codeword in a storage medium. The method for encoding and decoding the error correction code according to the present invention further includes:

Reading the long codeword from a storage medium; extracting the short codewords contained therein from the long codeword; calculating a plurality of short symptoms of the short codewords according to the short check codes of the short codewords a code; checking whether the short symptom codes are all zero; and correcting the corresponding short codes by using the non-zero short symptom codes when one or more non-zero short symptom codes of the short symptom codes are not zero word.

The method for encoding and decoding the error correction code according to the present invention further includes:

After the short symptom code is calculated, calculating a long symptom code of the long codeword according to the long check code of the long codeword; checking whether the long symptom code is zero; when the long symptom code is not zero, Checking whether the non-zero short symptom codes can correctly correct the corresponding short code words; and when the non-zero short symptom codes can correctly correct the corresponding short code words, use the non-zero short symptoms The code corrects the long symptom code to get a correction and a long symptom code.

When the long symptom code is not zero, and the portion of the non-zero short symptom code cannot correctly correct the corresponding short code word, the short symptom word that cannot be correctly corrected is corrected by the long symptom code.

The method for encoding and decoding an error correction code according to the present invention, wherein the long codeword and the short codeword are BCH codes or RS codes.

The second technical solution adopted by the present invention to solve the technical problem is: constructing a codec of an error correction code, comprising an error correction code encoder and an error correction code decoder; the error correction code encoder receiving one Raw data, the original data is divided into a plurality of segment data, and short parity codes of the segment data are generated, and the short check codes are appended to the segment data to respectively generate a plurality of short codes. Short codeword, combining the short code words to obtain an encoded data, generating a long parity of the encoded data, and appending the long check code to the encoded data to generate a long codeword (long Codeword) for storing in a storage medium; the error correction code decoder reads the long codeword from the storage medium, and extracts the short codewords contained therein from the long codeword, according to the short codewords The short check codes calculate a plurality of short syndromes of the short code words, check if the short symptom codes are all zero, and when one of the short symptom codes is one to several non-zero short When the symptom code is not zero, the corresponding short code words are corrected by using the non-zero short symptom codes.

The codec of the error correction code according to the present invention, wherein the error correction code encoder is based on Generating a polynomial to generate the short check codes of the segment data, and generating a long check code of the encoded data according to a second generating polynomial, wherein the first generating polynomial is the second generating polynomial At least one function of the smallest polynomial.

The codec of the error correction code of the present invention, wherein the first generator polynomial is a least common multiple of at least one minimum polynomial of the second generator polynomial.

The codec of the error correction code of the present invention, wherein the error correction code encoder comprises: a short codeword encoder, according to the first generating polynomial to generate the short check codes of the segment data; a first adder, the short check code is appended to the segment data to respectively generate the short codewords; a long codeword encoder combining the short codewords to obtain the encoded data, and according to the first Generating a polynomial to generate the long check code of the encoded data; and a second adder appending the long check code to the encoded data to generate the long codeword.

The codec of the error correction code according to the present invention, wherein when the short symptom code is calculated, the error correction code decoder calculates a long symptom code of the long codeword according to the long check code of the long codeword , check whether the long symptom code is zero, when the long symptom code is not zero, check whether the non-zero short symptom code can correctly correct the corresponding short code words, when the non-zero short symptom code can be When the corresponding short code words are correctly corrected, the long symptom code is corrected by using the non-zero short symptom codes to obtain a corrected long symptom code.

The codec of the error correction code according to the present invention, wherein when the long symptom code is not zero, and the part of the non-zero short symptom code cannot correctly correct the corresponding short codeword, the error correction code is decoded. The long symptom code is used to correct the short code words that cannot be correctly corrected.

The codec of the error correction code of the present invention, wherein the error correction code decoder comprises: a symptom code calculation module, and calculating the short codes of the short code words according to the short check codes of the short code words a symptom code, and calculating the same symptom code of the long codeword according to the long check code of the long codeword; a control circuit, checking whether the short symptom codes are all zero, when the short symptom code is in the If the non-zero short symptom code is not zero, the non-zero short symptom code is used to correct the corresponding short code words, and it is checked whether the long symptom code is zero, and if the long symptom code is not zero, check whether the non-zero is The zero short symptom code can correct the corresponding short code words correctly, and correct the long symptom code by using the non-zero short symptom codes when the non-zero short symptom codes can correctly correct the corresponding short code words. . The codec of the error correction code according to the present invention, wherein the long codeword and the short codeword are

BCH code or RS code.

The third technical solution adopted by the present invention to solve the technical problem is: constructing a decoding method of the error correction code, comprising the steps of: receiving a long codeword of the error correction code, wherein the long codeword Include a plurality of short codewords and a long parity code, each of the short codewords including a short parity code; extracting the included code from the long codeword Short code words; calculating a plurality of short symptom codes of the short code words according to the short check codes of the short code words; checking whether the short symptom codes are all zero; when the short symptom codes are When one of the plurality of non-zero short symptom codes is not zero, the non-zero short symptom codes are used to correct the corresponding short code words; when the short symptom codes are calculated, according to the length of the long code words The check code calculates a long symptom code of the long code word; checks whether the long symptom code is zero; when the long symptom code is not zero, it is checked whether the non-zero short symptom code can be correctly corrected. The short code words; when the non-zero short symptom codes When corrects those of the corresponding short code word is correct, symptoms using short codes to correct such non-zero length of the symptom code, to obtain a post-correction code length symptoms.

The method for decoding the error correction code according to the present invention further includes:

The method for decoding an error correction code according to the present invention, wherein the short check codes of the short code words are generated according to a first generating polynomial, and the long check code of the long code words is generated according to a second generating polynomial And the first generating polynomial is a function of at least one minimum polynomial of the second generating polynomial.

The method for decoding an error correction code according to the present invention, wherein the first generator polynomial is a least common multiple of at least one minimum polynomial of the second generator polynomial.

The method for decoding an error correction code according to the present invention, wherein the long codeword and the short codeword are BCH codes or RS codes.

The technical solution of the present invention has the following beneficial effects: the decoding time of the error correction code is reduced, the probability of false positives is reduced, and the performance of the decoder is improved. DRAWINGS

The present invention will be further described below in conjunction with the accompanying drawings and embodiments, in which:

1 is a flow chart of a conventional decoding method of an error correction code;

Figure 2 is a block diagram of a data storage system of the present invention;

Figure 3A is a block diagram of an error correction code encoder of the present invention;

3B is a flowchart of a method of encoding an error correction code of the present invention;

Figure 4 is a schematic illustration of a long codeword produced by the present invention;

Figure 5 is a circuit diagram of an encoder of the present invention, which may be a short codeword encoder or a long codeword encoder of Figure 3A;

Figure 6 is a block diagram of the error correction code decoder of the present invention;

Figure 7 is a circuit diagram of a symptom code calculation module of the present invention;

Figure 8 is a flow chart showing a decoding method of the error correction code of the present invention.

In the figure, 202 is the host; 204 is the data storage device; 212 is the controller; 214 is the storage medium; 222 is the error correction code encoder; 224 is the error correction code decoder; 300 is the error correction code encoder; 302 is short Codeword encoder; 304 is the first adder;

306 is a long codeword encoder; 308 is a second adder; CL is a long codeword; C _S1 , C _S2

C _SN is a short code word; DD ₂ , ..., D _N is sector data; PS PS ₂ , ..., PS _N is a short check code; PL is a long check code; 500 is a short code word encoder or a long code word code 530, 511-51N is a buffer; 501-50N is an adder; 521-52N is a multiplier; 600 is an error correction code decoder; 602 is a symptom code calculation module; 604 is an error polynomial calculation module; Search module; 608 is the control circuit; 700 is the symptom code calculation module; 701, 702, ..., 70K are symptom code generators; 731-73K is the adder; 721-72K is the multiplier; 711-71K is the buffer Device. detailed description

2 is a block diagram of a data storage system 200 of the present invention. In one embodiment, the data storage system 200 includes a host 202 and a data storage device 204. The data storage device 204 includes a controller 212 and a storage medium 214. In an embodiment, the controller 212 includes an error correction. A code encoder 222 and an error correction code decoder 224. When the host 202 wants to store data into the data storage device 204, the error correction code encoder 222 of the controller 212 first encodes the data into the error correction code d, and the controller 212 stores the error correction code (^ in the storage medium 214. When the host 202 reads the data D ₂ from the data storage device 204, the controller 212 first reads the error correction code C ₂ containing the data D ₂ from the storage medium 214, and then corrects the error by the error correction code decoder 224 of the controller 212. The code _{2 is} decoded into the data D ₂ , and finally the controller 212 transmits the data 0 ₂ to the host 202. In an embodiment, the data storage device 204 is a memory card, the storage medium 214 is a flash memory, and the error correction code is C ₂ is a BCH code. In another embodiment, the data storage device 204 is an optical drive, the storage medium 214 is an optical disk, and the error correction code (^ and ^ is !^ code. Please note that the storage device and the error The type of correction code is not a limitation of the present invention, and those skilled in the art can apply it to any type of storage device and error correction code under the teachings of embodiments of the present invention.

Figure 3A is a block diagram of the error correction code encoder 300 of the present invention. In one embodiment, the error correction code encoder 300 includes a short codeword encoder 302, a first adder 304, a long codeword encoder 306, and a second adder 308. Fig. 3B is a flow chart of the encoding method 350 of the error correction code of the present invention. The error correction code encoder 300 of Fig. 3A encodes the original data D into a long code word CL of the error correction code in accordance with the encoding method 350 of Fig. 3B. First, the error correction code encoder 300 receives an original data I step 352). Next, the error correction code encoder 300 divides the original data D into a plurality of extent data (step 354). After the short codeword encoder 302 receives the segment data, the short codeword encoder 302 then generates a short parity Ps of the segment data according to a first generator polynomial (generator polynomial M order). Step 356).

Next, the first adder 304 appends the short check codes Ps to the segment data to generate a plurality of short code words (short code worc^Cs step 358). The long codeword encoder 306 then combines the short codewords Ps to obtain an encoded data (step 360), and generates a long parity PL of the encoded data according to a second generator polynomial. Step 362). Finally, the second appender 308 appends the long check code PL to the encoded data to generate a long codeword CL of the error correction code (step 364). The first generator polynomial of the short codeword encoder 302 is a function of at least one minimum polynomial of the second generator polynomial of the long codeword encoder 306. In an embodiment, the first generating polynomial is the second A least common multiple (LCM:) of at least one minimum polynomial of the polynomial is generated. For example, if a second long code word encoder 306 corresponding to a plurality of polynomials g ^ minimal polynomial _{Ψι (χ), ψ 2 (} χ), ..., v k (x) is the smallest common multiple {ψι ( Χ)Χψ ₂ (Χ) ^x .. . ^x Vk(X)}. In an embodiment, the first generator polynomial corresponding to the short codeword encoder 302 is a minimum polynomial _ψι ( _Χ :>. In another embodiment, the first generator polynomial g' corresponding to the short codeword encoder 302 (x) ) is the least common multiple of the minimum polynomial ΨΙ Ο and ψ ₂ 0 [ψι0 ^χ ψ ₂ 0 ].

Figure 4 is a schematic illustration of a long codeword CL produced by the present invention. The long codeword CL is composed of N short code words C _{S 1} , C _S2 , ..., C _SN and a long check code PL. Each of the short code words C _{S 1} , C _S2 , ..., C _SN includes a sector data and a short check code. For example, the short codeword C _{S 1 is} formed by the check code P _S1 following the corresponding segment data, and the short code word C _{S2 is} formed by the check code P _S2 following the corresponding segment data D ₂ . And the short codeword C _SN is connected to the corresponding sector data by the check code P _SN

D _N is formed afterwards. The original data is cut into a plurality of extent data DD ₂ D _N , and the original data is encoded by the error correction code encoder 300 of FIG. 3A to form the long codeword CL of FIG.

5 is a circuit diagram of an encoder 500 of the present invention, which may be a short codeword encoder 302 or a long codeword encoder 306 of FIG. 3A. Suppose encoder 500 according to a generating polynomial g (x) is converted into the data D _A check code P, generating polynomial ^ x) primary coefficient is _gl, quadratic coefficient g _2, ..., N order terms The coefficient is g _N . The encoder 500 includes an adder 540, multipliers 521 to 52N, adders 501 to 50N, and buffers 51 1 to 51N and 530. First, the bits of the data D _A are sequentially sent to the adder 540. The adder 540 sequentially adds the bit of the data D _A to the data bit D _DN stored in the buffer 51N to obtain the data D _B . The multipliers 521, 522, 52N then multiply the data 0 ₆ by the coefficients _gl , g ₂ , ..., g _{N of the} generator polynomial g(x) to obtain the data D _C1 , D _C2 , ..., D _{CN , respectively} . After the data D _B is stored in the buffer 530, the adders 501, 502, ..., 50N are sequentially added to the data D _C1 , D _C2 , ..., D _CN , respectively, to obtain the data D _DN . Finally, after the buffer 51N stores the data D _DN , the data D _{DN is} output as the check code P.

Figure 6 is a block diagram of the error correction code decoder 600 of the present invention. In one embodiment, the error correction code decoder 600 includes a symptom code calculation module 602, an error polynomial calculation module 604, a Qin search module 606, and a control circuit 608. When the error correction code decoder 600 receives a long codeword of the error correction code, the error correction code decoder 600 extracts a plurality of short codes contained therein from the long codeword. Word. First, the symptom code calculation module 602 calculates a plurality of short syndromes S _la , S _lb , S _{1N of the} short code words according to the short check codes of the short code words, and according to the long code words The long check code calculates a plurality of long syndromes S ₁ , S ₂ , S _{K of} the long codeword. The error polynomial calculation module 604 is configured to calculate the coefficient of the error location polynomial of the long codeword according to the long symptom code S _h S ₂ , S _K of the long codeword. The Qin search module 606 is used to find a plurality of roots of the error polynomial for correcting the long codeword of the error correction code. In addition, when the short symptom code s _la , s _lb , S _{1N of the} short code word is not 0, the error polynomial calculation module 604 also calculates the error polynomial of the short code word according to the short symptom code that is not zero, and is determined by Qin. The search module 606 performs a Qin search to find the root of the error polynomial of the short codeword to immediately correct the error that occurred in the short codeword. Similar to the conventional method 100 of FIG. 1, the control circuit 608 checks whether the long symptom code S _l5 S ₂ , S _K is zero, and stops the error polynomial calculation when the equal length symptom codes S _l5 S ₂ , S _K are all zero. Module 604 calculates the coefficients of the error polynomial and stops the Qin search module 606 from searching for the root of the error polynomial. However, control circuit 608 has other functions that reduce the time required to decode long codewords and improve the performance of error correction code decoder 600. This part of the function will be illustrated in Figure 8.

In an embodiment, since the first generator polynomial used to encode the short codeword is a function for encoding the smallest polynomial of the second generator polynomial of the long codeword, the same set of symptom code calculation module 602 can be used to calculate the long code. The symptom code of the word and the symptom code of the short code word. FIG. 7 is a circuit diagram of the symptom code calculation module 700 of the present invention. The symptom code calculation module 700 includes a plurality of symptom code generators 701, 702, ..., 70K, respectively, which generate long symptom codes S ₂ of long symptom codes, ... , S _K . Symptoms code generator 701 also generates a plurality of short code words symptoms short code _{_{S la, S lb, · ·}} ·, S 1No In one embodiment, the length codeword data bits are sequentially delivered to the D code generator 702 SYMPTOMS 70K, when the data bit D of the long code word is processed, the symptom code generator 702 70K generates the long symptom code S ₂ S of the long code word, and the data bit D of the short code word is also sequentially delivered to the symptom code generation. Device

701. Whenever the data bit D of a short codeword is processed, the symptom code generator 701 generates a short symptom code corresponding to the short codeword. For example, when the segment data and the short check code P _S1 are input to the symptom code generator 701, the symptom code generator 701 generates a short symptom code of the short code word C _S1 ; when the segment data D ₂ and the short check code P _{When S2} is input to the symptom code generator 701, the symptom code generator 701 generates a short symptom code of the short code word C _S2 . Since the long code word is composed of a plurality of short code words, when the symptom code generator 701 After processing the data bits D of the plurality of short code words included in the long codeword, the symptom code generator 701 generates the long symptom code S _{1 Q} of the long codeword.

Each symptom code generator 701, 702 70K in Fig. 7 includes an adder, a multiplier, and a buffer. For example, in the first symptom code generator 701, the buffer 71 1 stores data and outputs it. The adder 731 adds the data bit D of the long code word to the data output from the buffer 71 1 to obtain a first symptom code Si. The multiplier 721 multiplies the coefficient α by the symptom code Si to obtain data, and the newly obtained data is sent to the buffer 71 1 for storage. The coefficient α of the symptom code generator 701 is a common root of the generator polynomial of the long codeword encoder and the generator polynomial of the short codeword encoder, and the coefficients of the other symptom code generators 702, ..., 70Κ are α ² , ..., respectively. α and α, α ² , ..., α ^κ are the roots of the generator polynomial of the long codeword encoder.

8 is a flow chart of a method 800 of decoding an error correction code of the present invention. The error correction code decoder 600 of FIG. 6 performs decoding of the error correction code in accordance with the method 800. First, the error correction code decoder 600 receives a long codeword (step 802). Next, the symptom code calculation module 602 sequentially calculates a short symptom code of a short code word in the long code word (step 804). For example, the error correction code decoder 600 firstly compares the first short code word C _S1 in the long code word CL. Calculation. At this time, the control circuit 608 checks if the calculated short symptom code is zero (step 806). When the short symptom code is zero, indicating that the short codeword is correct, the symptom code calculation module 602 continues to calculate the short symptom code of the other short codewords in the long codeword (step 804), for example, then calculating the second short The code word C _S2 , the third short code word C _S3 ... until all short code words in the long code word are processed (step 812). When the short symptom code is not zero, indicating that the short code word has an error, the control circuit 608 corrects the short code word with a non-zero short symptom code and records the corrected result (step 808), and continues to calculate the symptom code calculation module 602. The short symptom code of the short codeword in the long codeword (step 804) until all short codewords in the long codeword have been processed (step 810).

Next, symptom code calculation module 602 calculates a long symptom code for the long codeword (step 814). If the long symptom code is zero (step 816), indicating that the long codeword is correct, the decoding of the long codeword ends. If the long symptom code is not zero (step 816), it indicates that the long code word has an error. Control circuit 608 now continues to check if all non-zero short symptom codes correctly correct the short codeword (step 818). If all of the non-zero short symptom codes correctly correct the short codeword (step 818), then control circuit 608 corrects the long symptom code using a non-zero short symptom code (step 820), for example, if the fourth short codeword is ^ ₄ If the short symptom code is not all zero, then use the non-zero short The symptom code is to correct the corresponding position in the non-zero long symptom code. If corrected, the symptom code is zero (step

822), indicating that the errors have been corrected by the short symptom code, the correction result using the short code word correction can be replied to the host, and the long symptom code can be corrected without using the long symptom code, which can save time. . If the corrected long-term symptom code is not zero (step 822), or part of the non-zero short symptom code fails to correct the short codeword correctly (step 818), then control circuit 608 utilizes the original long symptom code for a short codeword that cannot be correctly corrected. A correction is made (step 824) to obtain the correct long codeword, and the decoding of the long codeword ends.

If all the short symptom codes are considered to be correct when all the short symptom codes are zero, misjudgment may occur. Because the correction ability of the short symptom code is low, there may be only one or two bits of correction ability, and when the error of the short code word exceeds the correction ability of the short symptom code, for example, an error of 8 bits occurs. Short symptom codes may also be calculated as zero. Therefore, it is necessary to re-test with a long symptom code with stronger correction ability. The long symptom code has a higher correction ability and may have a correction ability of 24 bits. Therefore, if there is an 8 bit error in a short codeword, it can still be found through the long symptom code and make subsequent corrections. The chance of a false positive can be reduced.

Although the present invention has been disclosed in the above preferred embodiments, it is not intended to limit the invention, and it is possible to make some modifications and refinements without departing from the spirit and scope of the invention. The scope of the invention is defined by the scope of the appended claims.

Claims

Rights request

A method for encoding and decoding an error correction code, comprising the steps of: receiving a raw data;

Dividing the raw data into a plurality of segment data;

Generating a short check code for the segment data according to a first generating polynomial;

Adding the short check codes to the segment data to respectively generate a plurality of short code words; combining the short code words to obtain an encoded data;

Generating a long check code of the encoded data according to a second generating polynomial, wherein the first generating polynomial is a function of at least one minimum polynomial of the second generating polynomial;

The long check code is appended to the encoded data to generate a long codeword of the error correction code.

2. The method of encoding and decoding an error correction code according to claim 1, wherein the first generator polynomial is a least common multiple of at least one minimum polynomial of the second generator polynomial.

3. The method of encoding and decoding an error correction code according to claim 1, further comprising storing the long codeword in a storage medium.

The method for encoding and decoding an error correction code according to claim 1, further comprising:

Reading the long codeword from a storage medium;

Extracting the short code words contained therein from the long codeword;

Calculating a plurality of short symptom codes of the short code words according to the short check codes of the short code words; checking whether the short symptom codes are all zero;

When one or more non-zero short symptom codes of the short symptom codes are not zero, the corresponding short code words are corrected by the non-zero short symptom codes.

The method for encoding and decoding an error correction code according to claim 4, further comprising:

After the short symptom code is calculated, calculating a long symptom code of the long codeword according to the long check code of the long codeword; Check if the long symptom code is zero;

When the long symptom code is not zero, it is checked whether the non-zero short symptom codes can correctly correct the corresponding short code words;

When the non-zero short symptom codes can correctly correct the corresponding short code words, the long symptom code is corrected by using the non-zero short symptom codes to obtain a corrected long symptom code.

The method for encoding and decoding an error correction code according to claim 5, further comprising:

The method for encoding and decoding an error correction code according to claim 1, wherein the long codeword and the short codeword are BCH codes or RS codes.

8. A codec for error correction code, comprising:

An error correction code encoder receives a raw data, divides the original data into a plurality of segment data, generates a short check code of the segment data, and adds the short check codes to the segment data to respectively Generating a plurality of short codewords, combining the short codewords to obtain an encoded data, generating a long check code of the encoded data, and appending the long check code to the encoded data to generate a long codeword for storage in a Storage medium;

An error correction code decoder, reading the long codeword from the storage medium, taking out the short codewords included in the long codeword, and calculating the short codes according to the short check codes of the short codewords a plurality of short symptom codes of the code word, checking whether the short symptom codes are all zero, and when one or several non-zero short symptom codes of the short symptom codes are not zero, using the non-zero short symptom codes Correct the corresponding short code words.

The codec of the error correction code according to claim 8, wherein the error correction code encoder generates the short check codes of the segment data according to a first generation polynomial, and according to A second generating polynomial to generate the long check code of the encoded data, wherein the first generating polynomial is a function of at least one minimum polynomial of the second generating polynomial.

10. The codec of the error correction code according to claim 9, wherein the first generator polynomial is a least common multiple of at least one minimum polynomial of the second generator polynomial.

The codec of the error correction code according to claim 9, wherein the error correction code encoder comprises:

a short codeword encoder, based on the first generating polynomial to generate the short check codes of the segment data;

a first adder, the short check codes are appended to the segment data to respectively generate the short code words;

a long codeword encoder combining the short codewords to obtain the encoded data, and generating the long check code of the encoded data according to the second generated polynomial;

A second adder appends the long check code to the encoded data to generate the long codeword.

The codec of the error correction code according to claim 8, wherein, after the short symptom code is calculated, the error correction code decoder calculates the length according to the long check code of the long codeword A long symptom code of the long code word, check whether the long symptom code is zero, and when the long symptom code is not zero, check whether the non-zero short symptom code can correctly correct the corresponding short code word, when When the non-zero short symptom code can correctly correct the corresponding short code words, the long symptom code is corrected by using the non-zero short symptom code to obtain a corrected long symptom code.

13. The codec of the error correction code according to claim 8, wherein when the long symptom code is not zero, and the portion of the non-zero short symptom code cannot correctly correct the corresponding short code When the word is used, the error correction code decoder uses the long symptom code to correct the short code words that cannot be correctly corrected.

The codec of the error correction code according to claim 12, wherein the error correction code decoder comprises:

a symptom code calculation module, calculating the short symptom codes of the short code words according to the short check codes of the short code words, and calculating the long code words according to the long check code of the long code words a long symptom code; a control circuit, checking whether the short symptom codes are zero, and correcting the non-zero short symptom code when the short symptom code among the short symptom codes is not zero Wait for a short codeword to check if the long symptom code is zero. When the long symptom code is not zero, check if the non-zero short symptom code can correctly correct the corresponding short codeword, and when the non-zero The short symptom code can correctly correct the corresponding short code words and correct the long symptom code by using the non-zero short symptom codes.

The codec of the error correction code according to claim 8, wherein the long codeword and the short codeword are BCH codes or RS codes.

A method for decoding an error correction code, comprising the steps of: receiving a long codeword of the error correction code, wherein the long codeword comprises a plurality of short codewords and a long check code, each of the The short code words include a short check code;

Extracting the short code words contained therein from the long codeword;

When one or more non-zero short symptom codes of the short symptom codes are not zero, the corresponding short code words are corrected by using the non-zero short symptom codes;

After the short symptom code is calculated, calculating a long symptom code of the long codeword according to the long check code of the long codeword;

Check if the long symptom code is zero;

The method for decoding an error correction code according to claim 16, further comprising: when the long symptom code is not zero, and the portion of the non-zero short symptom code cannot correctly correct the corresponding short When the code word is used, the long symptom code that cannot be correctly corrected is corrected by the long symptom code.

The method for decoding an error correction code according to claim 16, wherein the short check codes of the short code words are generated according to a first generating polynomial, and the long check code of the long code words Generating according to a second generator polynomial, wherein the first generator polynomial is a function of at least one minimum polynomial of the second generator polynomial.

The method of decoding an error correction code according to claim 16, wherein the first generating polynomial is a least common multiple of at least one minimum polynomial of the second generating polynomial.

The method for decoding an error correction code according to claim 16, wherein the long codeword and the short codeword are BCH codes or RS codes.