JP2606647B2 - Error correction method - Google Patents

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to an error correction method applied to a digital image recording apparatus and the like, and more particularly to an error correction method for performing erasure correction on a product code of a Reed-Solomon code using a Euclidean algorithm and a Chen algorithm.

[0002]

2. Description of the Related Art In a digital image recording apparatus for recording and reproducing a digital video signal, a product code obtained by doubly encoding a Reed-Solomon code is used in order to efficiently correct a generated burst error or random error. I have.

As shown in FIG. 7, a product code is a two-dimensional array of digital data, an error correction code (referred to as an outer code) is added to horizontal data, and vertical data and An error correcting code (referred to as an inner code) is added to the outer code to form a double coding.

In general, when decoding a digital video signal recorded by such a product code, first, an error correction is performed on the inner code to perform a decoding process, and then the data corrected by the inner code is further processed. The error is corrected by the outer code and decoded. Also, an error flag indicating that an error exceeding the correction capability has occurred at the time of error correction of the inner code is added for each inner code sequence, and erasure correction is performed using the error flag information at the time of error correction by the outer code. I have.

FIG. 5 is a flowchart showing an example of a conventional inner code error correction process. Here, a case is shown in which the minimum inter-code distance d ₁ in the inner code of the Reed-Solomon product code is 9 and the maximum number of correctable error symbols t ₁ is 4. Generally, t ₁ = (d ₁ −
1) / 2.

First, the syndromes S ₁₀ , S
_11, ..., to calculate the S _17, respectively (Step 50
1). If the syndromes S ₁₀ , S ₁₁ ,..., S ₁₇ are all 0 (step 502), the mode shifts to the no error mode, the error flag F is set to “0”, and the process ends (step 510). Also, syndromes S ₁₀ , S ₁₁ ,
..., when not in all S ₁₇ 0 transitions to the error correction mode, determine the error value polynomial and the error locator polynomial from the syndrome by Euclid algorithm, further error location from the error value polynomial and the error locator polynomial by the algorithm of Chen And an error pattern are calculated (step 503).

The Euclidean algorithm and Chen's algorithm are described in, for example, Imai et al.
Key points of error correction coding technology (Electronics Essentials No. 20), Japan Industrial Technology Center, Showa 6
It is described in the first edition of March 2013, pp. 298-307.

Next, the number of error symbols is estimated from the calculation result in step 503, and the processing flow branches (step 504). Here, when the estimated error symbol number is larger than the maximum correctable error symbol number t ₁ (t ₁ = 4), it is determined that the error cannot be corrected, the error flag F is set to “1”, and the process ends (step 509). . Also,
If the estimated number of error symbols is 1, 2, 3, or 4, the respective error corrections are performed, the error flag F is set to "0", and the process is terminated (steps 505, 506, and 50).
7,508).

FIG. 6 is a flowchart showing an example of a conventional outer code error correction process. Here, a case is shown in which the minimum inter-code distance d ₂ in the outer code is 9, the maximum number of correctable error symbols t ₂ is 4, and the maximum number of correctable erasure symbols p is 8. In general, t ₂ = (d ₂ −1) / 2 and p = 2t ₂ .

First, the syndromes S ₂₀ , S
_21, ..., to calculate the S ₂₇ (step 601). If the syndromes S ₂₀ , S ₂₁ ,..., S ₂₇ are all 0 (step 602), the mode shifts to the no error mode, the error flag F is set to “0”, and the process is terminated (step 60).
9). If all the syndromes S ₂₀ , S ₂₁ ,..., S ₂₇ do not become 0, the number of symbols in which the error flag F is set to “1” in the inner code error correction process is counted. If it is 2t ₂ (2t ₂ = 8) or more, it is determined that correction is impossible, and if the count value is less than 7, the mode shifts to the error erasure correction mode (step 603). When it is determined that the correction is impossible, "1" is set to the error flag F, and the process is terminated (step 608).

Further, an erasure is set according to the counting result of step 603, an error numerical polynomial and an error position polynomial are obtained by the Euclidean algorithm, and the error position and error are obtained from the error position polynomial and the error numerical polynomial by the Chen algorithm. A pattern is calculated (step 604).

Next, it is determined whether or not correction is possible based on the number of erasure symbols in the counting result in step 603 and the estimated number of error symbols in the calculation result in step 604 (step 605). Here, when the number of estimated error symbols is 4, when the number of estimated error symbols is 3 and the number of erasure symbols is 0 to 2, when the number of estimated error symbols is 2 and the number of erasure symbols is 0 to 4, Number of estimated error symbols is 1 and number of erasure symbols is 0 to 6
At this time, if the number of erasure symbols corresponds to any one of 1 to 7, the corresponding error correction is performed, the error flag F is set to "0", and the process ends (step 607).

On the other hand, if none of the above applies, it is determined that correction is impossible, and "1" is set in the error flag F, and the process is terminated (step 606).

[0014]

In the above-mentioned conventional error correction method, when the error cannot be corrected in the inner code error correction processing, the error flag F of each inner code sequence is set to "1" and the outer code of the outer code is set. In the error correction process, the number of the error flags F set to "1" is counted, and the number of erasure symbols is obtained to correct the error. However, in the error correction processing of the inner code, even when the error correction of the maximum correctable error symbol number with a high possibility of erroneous correction is performed, or when it is determined that there is no error with a low possibility of the erroneous correction. In any case, the error flag F is set to “0”. Therefore, there is a problem that the reliability of the error flag is low.

In the outer code error correction process, the error is corrected by an error flag having low reliability. When the number of erasure symbols is equal to or more than the maximum number of erasable symbols, it is determined that the error cannot be corrected. There is a problem that the correction ability is not sufficient because of the judgment.

An object of the present invention is to improve the reliability of error correction by utilizing the fact that the number of divisions in the Euclidean algorithm is equal to the number of error symbols and that the error position is not larger than the code length. An object of the present invention is to provide an error correction method capable of maximizing the error correction capability of a Solomon product code.

[0017]

According to the present invention, there is provided an error correction method for performing an outer code error correction process after an inner code error correction process on a product code of a Reed-Solomon code, the method comprising: When the number of symbols is t ₁ (t ₁ is a positive integer), the inner code error correction process calculates a syndrome of the input data to obtain a first syndrome. In this case, it is determined that there is no error, and when all are not 0, the first error position and error pattern are calculated based on the first syndrome by the Euclidean algorithm and the Chen algorithm, and the first number of divisions and the first error are calculated. estimating errors calculated the number of symbols, the first when the estimated error symbol number is greater than t ₁ is determined to uncorrectable, t ₁ following field Comparing the first estimated number of error symbols with the first number of divisions, if they do not match, determines that correction is impossible, and if they match, compares the first error position with the code length. If the first error position is larger than the code length, it is determined that the first error position cannot be corrected.
Error correction according to the first estimated number of error symbols is performed on the data symbols other than those determined as no error or uncorrectable, and error correction is performed on the data symbols after the error correction processing.
3-bit error flags F ₀ , F ₁ ,
Against F _2, the error is when it is determined that no error
Error flag F ₀ , F ₁ , F ₂ is set to “0”
When the number of first estimated error symbols is 1 or more, t ₁ −
In the case of 1 or less to "1" only on the error flag F ₀
If the first number of estimated error symbols is t ₁ ,
In this case, “1” is set to the error flags F ₀ and F ₁ respectively.
If it is determined that correction is impossible, the error
The lags F ₀ , F ₁ , and F ₂ are all set to “1” .

[0018]

In the error correction method for the outer code in the error correction method according to the present invention, the syndrome of the input data is calculated when the maximum correctable error symbol number of the outer code is t ₂ (t ₂ is a positive integer). To obtain a second syndrome. If all the second syndromes are 0, it is determined that no error has occurred.
_1, the number of error correction in said error correction processing of the code based on F ₂ is counting the number of symbols is determined as the symbol rate and uncorrectable was t _1, the count result is 2t ₂
If it is larger than 2t ₂ , it is determined that correction is impossible, and if it is within 2t ₂ , an erasure flag is set according to the error flags F ₁ and F _2, and the _second Euclidean algorithm and the Chen algorithm are used based on the syndrome. The error position and error pattern are calculated and the second
Is obtained, the number of second estimated error symbols and the number of erasure symbols are determined, and it is determined whether or not correction is impossible based on the second estimated error symbol number and the number of erasure symbols. In this case, the second estimated number of error symbols is compared with the second number of divisions, and if they do not match, it is determined that correction is impossible. If they do, the second error position and the code length are determined. And comparing the second
If there is an error position whose error position is larger than the code length, it is determined that the error cannot be corrected, and then error correction is performed according to the second estimated number of error symbols except for those determined to be no error or uncorrectable. Error correction reliability
1-bit error flag F that represents
Is set to "0" or "1" .

Also, the erasure flag is set.
Value is the case the error flag F ₁ is the number that is the "1" is 2t ₂ -1 or less, Se the value of the error flag F ₁
Tsu collected by said When the error flag F ₂ is the number that is the "1" is 2t ₂ -1 or less, the value of the error flag F ₂
Set, the number of error flags F _1, F ₂ are both "1" is the case of 2t _2, the error flag F ₁
It is configured to set a value .

Further, the determination as to whether or not the correction is impossible based on the second estimated error symbol number and the erasure symbol number is performed by setting the second estimated error symbol number to u (u is a positive integer). If the Ja number of symbols v and (v is a positive integer), the when the error flag F ₁ is the number that is the "1" is 2t ₂ -1 or less, when _{u = t 2, u = t} 2 −
When i (i is i = 1, 2,..., t ₂ −1) and v = 0 to v = 2i, u = 0 and v = 1 to v = 2t ₂ −
When the 1, also determines that uncorrectable when not correspond to any, the When the error flag F ₂ is the number that is the "1" is 2t ₂ -1 or less, when u = t _2, u = t ₂ -i
And v = 0 to v = 2i (i is i = 1, 2,..., T ₂
-1), u = 0 and v = 1 to v = 2t ₂ −1
Is determined to be uncorrectable when none of the above applies, and when the number of the error flags F ₁ and F ₂ both being “1” is 2t ₂ , the correction is impossible when v = 2t ₂ is not satisfied. Is determined.

Still further, the reliability of the error correction of the outer code.
The value to be set in the error flag F of 1 bit representing the will, when subjected to and the error correction when no error "0"
And set the error flag in the erasure flag.
Sets the value of the error flag F ₀ when the value of F ₁ is determined to uncorrectable is set, the erasure
Value of the flag error flag F ₂ is configured to <br/> sets the value of the error flag F ₁ when it is determined that the uncorrectable is set.

[0023]

DESCRIPTION OF THE PREFERRED EMBODIMENTS Next, the present invention will be described with reference to the drawings.

FIG. 1 is a flowchart showing one embodiment of the error correction processing of the present invention for the inner code of a Reed-Solomon product code. Here, the minimum distance d ₁ between codes of the inner code
Is set to 9, and the maximum number of correctable error symbols t _{1 is set} to 4. Also, as the error flag code words are provided three bits <br/> error flag F ₀ of, F _1, F _2, respectively.

First, the syndromes S ₁₀ , S
_11, ..., to calculate the S _17, respectively (Step 10
1). If the syndromes S ₁₀ , S ₁₁ ,..., S ₁₇ are all 0 (step 102), the processing shifts to the no error mode, and all the error flags F ₀ , F ₁ , F ₂ are set to “0” and the processing is performed. The process ends (step 115). If all of the syndromes S ₁₀ , S ₁₁ ,..., S ₁₇ do not become 0, the mode shifts to the error correction mode, and an error numerical polynomial and an error position polynomial are obtained based on the syndromes by the Euclidean mutual algorithm. The error position and error pattern are calculated based on the error numerical polynomial and the error position polynomial (step 10).
3).

Next, the number of error symbols is estimated from the calculation result in step 103, and the processing flow is determined according to the estimated number of error symbols (step 104). That is, when the estimated number of error symbols is greater than the maximum number of correctable error symbols t ₁ (t ₁ = 4), it is determined that correction is impossible. Further, it is determined if the estimated error symbol number 1, when to estimate the error symbol number 2 or 3, the process route in accordance with the respective time estimated error symbol number of the maximum correctable error symbol number t _1.

Thereafter, it is checked whether or not the estimated number of error symbols matches the number of divisions in the Euclidean algorithm, and if they do not match, it is determined that correction is impossible (steps 105, 106, 107). At the same time, if the error position calculated in step 103 is larger than the code length, it is determined that correction is impossible (steps 108 and 10).
9, 110). If it is determined that the correction is impossible, "1" is set to all of the error flags F ₀ , F ₁ , and F ₂ , and the process ends (step 114).

On the other hand, when the estimated number of error symbols is 1 and it is not determined that correction is impossible, the error flag F ₀
To "1", "0" to F _1, is set respectively to "0" to F ₂ ends the error correction to the process (Step 11
1). If the estimated number of error symbols is two or three and it is not determined that correction is impossible, the error flag F
"1" to _0, "0" to F _1, is set respectively to "0" to F ₂ ends the error correction to the process (Step 11
2). Further, when the estimated number of error symbols is 4 and it is not determined that the error cannot be corrected, the error flag F _{0 is set} to “1”, F _{1 is set} to “1”, and F ₂ is set to “0”. Correct and end the process (step 11
3). Thus, the 3- bit error flags F ₀ , F ₁ ,
F ₂ is a parameter indicating the reliability of the error correction. FIG. 3 is a block diagram of a circuit for realizing the above-described inner code error correction processing. Here, the syndrome calculation unit 3
1 indicates that the syndromes S ₁₀ , S ₁₁ ,...
To calculate the S _17. The Euclidean calculation unit 32 calculates an error numerical polynomial and an error locator polynomial based on the syndrome by the Euclidean algorithm and sends a signal indicating the number of divisions k. The Chien calculator 33 calculates the error position E1 and the error pattern Ep based on the error numerical polynomial and the error locator polynomial according to the Chen algorithm.
And sends a signal indicating the estimated number m of error symbols. The comparing section 34 compares the estimated error symbol number m with the number of divisions k and sends out a comparison result. Comparison unit 35
Receives and compares the signal indicating the error position E1 and the predetermined code length n, and sends out a comparison result. Correcting unit 36, the syndrome _{S 10, S 1 1, ......} , S 1 7 and the error position E1 and the error pattern Ep and the estimated error symbol number m a comparison unit 34,
The error correction is performed by receiving each of the 35 comparison results,
At the same time, error flags F ₀ , F ₁ , and F ₂ are set according to the determination conditions.

Next, the error correction processing flow for the outer code will be described with reference to FIG.

Here, the minimum distance d ₂ between codes of the outer code is 9, the maximum number of error symbols t ₂ that can be corrected is 4, and
The maximum correctable erasure symbol number p is set to eight.
Further, a 1- bit error flag F is provided. In general, t ₂ = (d ₂ −1) / 2 and p = 2t ₂ .

First, the syndromes S ₂₀ , S
_21, ..., to calculate the S _27, respectively (Step 20
1). If the syndromes S ₂₀ , S ₂₁ ,..., S ₂₇ are all 0 (step 202), the mode shifts to the no error mode, the error flag F is set to “0”, and the process ends (step 221). Also, syndromes S ₂₀ , S ₂₁ ,
..., if not to all S ₂₇ 0 and goes to the error erasure correction mode, the error correction processing of the inner code error flag F _1, F ₂ is counting the number of symbols is set to "1" process Determine the flow. Here, when the number of symbols for which the error flag F ₁ is set to “1” (hereinafter, described as F ₁ = “1”) is 7 or less, that is, when 2t ₂ −1 or less (step 203) ), When the number of symbols of the error flag F ₂ = "1" is 7 or less (step 204), the error flag F ₁ = "1" or F ₂ =
For symbol number are both 8 of "1" is determined, that is, equal to the maximum correctable erasure symbol number 2t ₂ in (step 205), either. If none of the above cases applies, it is determined that correction is impossible. After that, the erasure flag is set according to the determination condition based on the error flags F ₁ and F ₂ . That is, the error flag F
₁ = Erajaf when the number of symbols of "1" is 7 or less
It sets the value of the error flag F ₁ to lag, error flag
When the number of symbols of F ₂ = “1” is 7 or less, the erasure
The value of the error flag F ₂ is set in the flag , and F ₁ =
If the number of “1” or F ₂ = “1” is 8, the erasure
It sets the value of the error flag F ₁ in the flag. And
An error numerical polynomial and an error locator polynomial are obtained by using the Euclidean algorithm, and an error position and an error pattern are calculated by the Chen algorithm (step 206).

Next, determination is made based on the number of erasure symbols in step 203 and the estimated number of error symbols in step 206. That is, the error flag F ₁ =
The number of symbols of “1” is 7 or less and the error flag F ₂ =
In the case where the number of symbols of “1” is 7 or less, when the number of estimated error symbols is 4, the number of estimated error symbols is 3
When the number of erasure symbols is 0 to 2, when the number of estimated error symbols is 2 and the number of erasure symbols is 0 to 4, when the number of estimated error symbols is 1 and the number of erasure symbols is 0 to 6, , It is determined whether the number of erasure symbols is 1 to 7 (step 2).
07, 208). Also, F ₁ = “1” or F ₂ =
If the number of “1” is 8, it is determined whether or not the number of erasure symbols is 8 (step 209).

The conditions that are not determined to be uncorrectable in steps 207, 208, and 209 are generally expressed as follows. Here, the number of estimated error symbols is u (u is a positive integer), and the number of erasure symbols is v (v
Is a positive integer).

When the number of error flags F ₁ = “1” is 2t ₂ −1 or less, when u = t ₂ , u = t ₂
-I (i is i = 1, 2,..., T ₂ −1) and v = 0 to v = 2i, u = 0 and v = 1 to v = 2t ₂
When -1.

When the number of error flags F _{2 set} to “1” is 2t ₂ −1 or less, when u = t ₂ , u = t ₂
−i and v = 0 to v = 2i (i is i = 1, 2,...,
When t ₂ −1), u = 0 and v = 1 to v = 2t ₂
When -1.

When the number of the error flags F ₁ and F ₂ both set to “1” is 2t ₂ , v = 2t ₂ .

If it is not determined in Steps 207, 208, and 209 that the correction is impossible, it is checked whether the estimated number of error symbols matches the number of divisions by the Euclidean algorithm. If they do not match, it cannot be corrected (steps 210, 211, 212).
If they match, the error position calculated in step 206 is compared with the code length, and if the error position is larger than a predetermined code length, it is determined that correction is impossible (step 213, step 213).
214, 215).

After passing through these steps, error correction corresponding to each determination condition is performed, and an error flag F is set as follows, and the process is terminated.

When there is no error (the syndromes are all 0) or when error correction is performed, the error flag F =
"0" (steps 217, 219, 220, 22)
1). Error flag F ₁ in the error correction processing of the inner code
= “1” and it is determined that correction is impossible, the error flag F is set to the same flag as F ₀ (hereinafter, F =
"F _0" hereinafter) is set to (step 216), also the error flag F ₂ = "1" have been set when it is determined that uncorrectable, an error flag F = a "F _1" ( Step 218).

FIG. 4 is a block diagram of a circuit for realizing the above-described outer code error correction processing.

Here, the syndrome calculating section 41 calculates syndromes S ₂₀ , S ₂₁ ,..., S ₂₇ from the input data. The error flag counting section 42 outputs the error flags F ₀ , F ₁ , F ₂ from the inner code error correction processing circuit shown in FIG.
In response to this, the number of symbols for which the error flags F ₁ and F ₂ are set to “1” is counted and a count value c is transmitted. The Euclidean calculator 43 calculates the syndromes S ₂₀ , S ₂₁ ,..., S by the Euclidean algorithm according to the count value c.
_An error numerical polynomial and an error position polynomial are calculated from ₂₇ and a signal indicating the number of divisions k is transmitted. The Chien calculation unit 44 calculates the error position E1 and the error pattern Ep from the error numerical value polynomial and the error position polynomial by the algorithm of Chen, and sends out a signal indicating the number m of error symbols. The comparison unit 45 compares the number m of error symbols with the number k of divisions and sends out a comparison result. Comparison section 46
Receives and compares the signal indicating the error position E1 and the code length n, and sends out a comparison result. The correction unit 47 includes syndromes S ₂₀ , S ₂₁ ,..., S ₂₇ and error flags F ₀ , F ₁ , F
₂ , the error position E1, the error pattern Ep, the number m of error symbols, and the comparison results of the comparison units 45 and 46, respectively, to execute error correction, and at the same time, set the error flag F.

[0042]

As described above, according to the present invention, in the error correction processing of the inner code of the Reed-Solomon product code,
Each codeword is provided with a 3-bit error flag indicating the reliability of error correction, and it is determined whether correction is impossible based on the number of error symbols, the number of divisions, the error position, and the like obtained by the Euclidean algorithm and Chen's algorithm. after setting the predetermined value to the 3-bit error flag with error correction according to the conditions, in the error correction processing of the outer code, the algorithm of the Euclidean <br/> de mutual division algorithm and Chen based on the error flag of 3 bits error The number of symbols, the number of erasure symbols, the number of divisions,
Error correction is determined based on the error position, etc., and error correction is performed according to each determination condition, thereby improving the reliability of error correction and maximizing the error correction capability of Reed-Solomon product codes. Have.

[Brief description of the drawings]

FIG. 1 is a flowchart of an inner code error correction process according to an embodiment of the present invention.

FIG. 2 is a flowchart of an outer code error correction process according to an embodiment of the present invention.

FIG. 3 is a block diagram of a circuit that realizes an error correction process of the inner code shown in FIG.

FIG. 4 is a block diagram of a circuit that realizes an outer code error correction process shown in FIG. 2;

FIG. 5 is a flowchart illustrating an example of a conventional inner code error correction process.

FIG. 6 is a flowchart illustrating an example of a conventional outer code error correction process.

FIG. 7 is a diagram illustrating a configuration of a product code.

[Description of Codes] 31, 41 Syndrome calculation unit 32, 43 Euclidean calculation unit 33, 44 Chien calculation unit 34, 35, 45, 46 Comparison unit 36, 47 Correction unit 42 Error flag counting unit 101-115 Error correction of inner code Processing steps 201 to 221 Outer code error correction processing steps

Claims (5)

(57) [Claims] 1. An error correction method for performing error correction of an outer code after error correction of an inner code for a product code of a Reed-Solomon code, wherein the maximum number of error-correctable error symbols of the inner code is t ₁ (t ₁ Is a positive integer), the inner code error correction process calculates a syndrome of the input data to obtain a first syndrome, and when all the first syndromes are 0, determines that there is no error;
If not all 0, the first error position and error pattern are calculated by the Euclidean algorithm and Chen algorithm based on the first syndrome, and the first number of divisions and the first number of estimated error symbols are obtained. If the first estimated error symbol number is greater than t ₁ , it is determined that correction is impossible. If the first estimated error symbol number is less than t _1, the first estimated error symbol number is compared with the first division number to obtain one. If they do not match, it is determined that correction is impossible, and if they match, the first error position is compared with the code length, and if there is one whose first error position is larger than the code length, it is determined that correction is impossible. After that, error correction according to the first estimated number of error symbols is performed on the data other than those determined as no error or uncorrectable, and the data after the error correction processing is performed.
For the 3-bit error flags F ₀ , F ₁ , and F ₂ representing the reliability of error correction for data symbols,
Are determined, the error flags F ₀ , F ₁ , F
₂ is set to “0”, and the first estimated error
If the number of symbols is 1 or more and t ₁ -1 or less, the above error occurs.
Only the flag F ₀ is set to “1”, and the first estimation error is set.
The error flag if error symbol number of t ₁
Set “1” to F ₀ and F ₁ respectively, and determine that
Wherein if it is a constant error flag F _0, the F _1, F ₂
An error correction method characterized by setting "1" to all . 2. The error correction process for the outer code in the case where the maximum number of error-correctable error symbols of the outer code is t ₂ (t ₂ is a positive integer), calculates a syndrome of the input data, A syndrome is obtained. If all the second syndromes are 0, it is determined that there is no error. If not all the errors are 0, the number of error corrections in the error correction processing of the inner code is t ₁ based on the error flags F ₁ and F _2. And the number of symbols determined to be uncorrectable are counted. If the counted result is greater than 2t ₂ , it is determined that correction is impossible. If the counted result is within 2t _{2, the} error flags F ₁ and F ₂ are determined. Calculating the second error position and error pattern by the Euclidean algorithm and Chen's algorithm based on the syndrome by setting the erasure flag according to Both the second number of divisions and the second
The number of estimated error symbols and the number of erasure symbols are determined, and it is determined whether or not correction is impossible based on the second estimated number of error symbols and the number of erasure symbols. The second number of estimated error symbols is compared with the second number of divisions. If they do not match, it is determined that correction is impossible. If they do match, the second error position is compared with the code length to compare the second error position with the code length. If the error position of No. 2 is larger than the code length, it is determined that the error cannot be corrected, and then error correction is performed according to the second estimated number of error symbols except for the one determined to be no error or uncorrectable. 2. The error correction method according to claim 1, wherein "0" or "1" is set to a one-bit error flag F representing the reliability of error correction of the code in accordance with a determination condition. (3)Value to be set in the erasure flag
Is  The error flag F₁2t is "1"_Two
-1 or less, the error flag F₁ Set the value of
And the error flag F_Two2t is "1"_Two
-1 or less, the error flag F_Two Set the value of
IThe error flag F₁, F_TwoAre both "1"
Number is 2t_TwoThe error flag F₁ Set the value of
Claims characterized by2Error correction method described. 4. A determination as to whether correction is impossible based on the second estimated error symbol number and the erasure symbol number is performed by setting the second estimated error symbol number to u (u is a positive integer). Assuming that the number of jasymbols is v (v is a positive integer), the number of times that the error flag F ₁ is “1” is 2t ₂
−1 or less, when u = t ₂ , u = t ₂ −i (i is i = 1, 2,..., T ₂ −1) and v = 0 to v = 2i
, When u = 0 and v = 1 to v = 2t ₂ −1, it is determined that correction is impossible when none of the above applies, and the number of times when the error flag F ₂ is “1” is 2t _Two
−1 or less, when u = t ₂ , u = t ₂ −i and v
= 0 to v = 2i (i is i = 1, 2,..., T ₂ -1)
When u = 0 and v = 1 to v = 2t ₂ −1, it is determined that correction is impossible when none of the above applies, and both the error flags F ₁ and F ₂ become “1”. 4. The error correction method according to claim 3 , wherein when the number of the bits is 2t ₂ , it is determined that the correction is not possible when v = 2t ₂ is not satisfied. 5. A 1 representing the reliability of error correction of the outer code.
The value to be set in the bit error flag F is set to “0” when there is no error and when error correction is performed, and the value of the error flag F ₁ is set in the erasure flag.
There is set the value of the error flag F ₀ when it is determined that the uncorrectable is set, the erasure flag
Error correction method of claim 4, wherein the setting the value of the error flag F ₁ when the value of the error flag F ₂ is determined to uncorrectable is set.