JP2694794B2 - Error correction processing 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 processing method, and more particularly to an error correction processing method applicable to the decoding of codes including Reed Solomon codes.

[0002]

2. Description of the Related Art A conventional error correction processing method will be described with reference to the drawings.

FIGS. 5 and 6 are flowcharts of the Euclidean algorithm showing the first and second conventional examples, respectively.

First, the Euclidean algorithm at the time of error correction of the first conventional example shown in FIG. 5 will be described.

Here, B ₀ (X) is the error locator polynomial that has just been calculated, B _-1 (X) is the error locator polynomial that has been calculated in the previous operation, and B _i (X) is i times. The error locator polynomial obtained by the later operation is shown. R ₀ (X) is the error number polynomial that is currently obtained, R _-1 (X) is the error number polynomial obtained by the previous operation, and Ri is the number of times i. The error numerical polynomial obtained by the following calculation is shown. B _{-1 in} step 51 as initial setting
_{0 for} (X), 1 for B ₀ (X), X for R _-1 (X)
Substitute ² ( ^t ) with S (X) for R ₀ (X). Here, t is the maximum error correction capability number, and S (X) is a syndrome polynomial.

When i = 1, step 52 and step 53
Where R _i-1 (X) / R _i-1 (X) = Q _i (X), R
_i-2 (X) -Ri _-1 (X) _.Qi (X) = _Ri (X),
The calculation of B _i-2 (X) -B _i-1 (X) · Q _i (X) is performed to obtain the quotient Q ₁ (X), and then R ₁ (X), B
Calculate ₁ (X). Then, in step 54, R ₁
The order of (X) and t are compared. As a result, R
If the degree of ₁ (X) is lower than t, step 56.
Where B ₁ (X) is the error locator polynomial σ (X) and R ₁ (X)
Is the error numerical polynomial η (X). If the order of R ₁ (X) is higher than t, 1 is added to i in step 55 to obtain 2, and the operations in steps 52 and 53 are performed again to obtain R
Repeat until the order of _i (X) becomes lower than t. At the time when it becomes lower, B _i (X) is the error locator polynomial σ (X)
Then, R _i (X) becomes the error numerical polynomial η (X).

By using σ (X) and η (X), the error location and the error pattern can be obtained and correction can be performed.

Next, the Euclidean algorithm when the error correction and erasure correction are mixed in the second conventional example shown in FIG. 6 will be described.

As an initial setting, in step 61, B _-1 (X)
To 0, B ₀ (X) to 1, R _-1 (X) to X ^2t , R
Substitute [σ _K (X) · S (X)] modX ^2t for ₀ (X). Here, t is the maximum error correction capability number, σ _K (X) is the erasure location polynomial, and S (X) is the syndrome polynomial.

When i = 1, in steps 62 and 63, R _i-1 (X) / R _i-1 (X) = Q _i (X), R
_i-2 (X) -Ri _-1 (X) _.Qi (X) = _Ri (X),
B _i−2 (X) −B _i−1 (X) · Q _i (X) is calculated, and in step 64, the order of R ₁ (X) and u =
A comparison with “(d−1 + k) / 2” is performed. Here, d is the correctable minimum distance between codes between the received code and the transmitted code, and k is the number of erasures. As a result, the order of R ₁ (X) is u
If so, B ₁ (X) is the error locator polynomial σ (X) and R ₁ (X) is the error numerical polynomial η in step 66.
(X). If the order of R ₁ (X) is higher than u, 1 is added to i in step 65 to make 2 and step 6 is performed again.
The calculation of 2, 63 is repeated and repeated until the order of R ₁ (X) becomes lower than u. When it becomes low, B _i (X)
Is the error locator polynomial σ (X), and R ₁ (X) is the error numerical polynomial η (X).

Even in erasure correction, this σ
By using (X) and η (X), error location,
The error pattern can be obtained and can be corrected.

[0012]

In the error correction processing method of the first conventional example, the syndrome polynomial S (X) given at the time of initialization is not all "0" for all codes,
That is, if there is an error and all of the codes of the upper t places are "0", that is, if the order is lower than t from the initial stage, if an attempt is made to give 1 to i as it is, an erroneous B ₁ (X) , R ₁ (X) are obtained, resulting in error correction.

Further, in the error correction processing method of the second conventional example, u = which is a judgment condition for erasure correction.
In "(d-1 + k) / 2", there is no setting for the case where the order of R ₀ (X) is lower than u from the time of initial setting before giving i = 1. If the calculation is done, there is a problem that incorrect B _i (X) and R _i (X) are calculated for the originally correctable data string and the error is corrected.

[0014]

According to the error correction processing method of the present invention, an error locator polynomial for calculating an error position of an input signal composed of a plurality of digital code strings and an error value polynomial for calculating an error value can be obtained. A first Euclidean algorithm is provided, and a syndrome polynomial operation of a predetermined maximum error correction capability number t (integer of t ≧ 1) is performed on the input signal, and all the syndrome code strings of the operation results of the syndrome polynomial are The first whether it is not "0"
If the syndrome code sequence is all "0", the input signal is judged to be error-free, and if all of the syndrome code sequences are not "0", the syndrome code is determined. The first Euclidean algorithm is applied to the syndrome code sequence only when it is determined that all of the upper t ranks of the sequence are not “0” and all the second determination results are not “0”. The error locator polynomial and the error numerical polynomial are calculated according to

Further, the error correction processing method of the present invention performs an erasure correction on an input signal composed of a plurality of digital code strings by an erasure location polynomial to calculate an error position of the input signal. A second Euclidean algorithm capable of obtaining an error numerical value polynomial for calculating a numerical value is provided, and a syndrome polynomial operation of a predetermined maximum error correction capability number t (integer of t ≧ 1) is performed on the input signal, A first judgment is made as to whether all the syndrome code strings of the calculation result of this syndrome polynomial are not "0". If the first judgment result is that all the syndrome code strings are "0", the input signal is erroneous. None, and all the syndrome code strings are “0”
If not, a second determination is made as to whether all of the higher order t of the syndrome code sequence are not "0", and the syndrome code sequence is determined only when it is determined that all are not "0" as a result of the second determination. Then, the erasure location polynomial, the error locator polynomial, and the error numerical polynomial are calculated by the second Euclidean algorithm.

In this configuration, the second Euclidean algorithm determines that the syndrome code string of the syndrome code string is not all “0” up to the upper t-th place of the syndrome code string as a result of the second judgment. Let X be the code, S (X) be the polynomial of the syndrome code string, B ₀ (X) and R ₀ (X) be the error locator polynomial and the error value polynomial that have just been obtained, respectively, and be obtained by the previous operation. The error locator polynomial and the error numerical polynomial are B
₋₁ (X) and R ₋₁ (X), the error locator polynomial and the error value polynomial obtained by the operation after i times (i ≧ 0) are B _i (X) and R _i (X), and error correction, respectively. Let t be the number of capabilities, d be the minimum distance between codes, k be the number of erasures (t, d, and k are integers greater than or equal to 1), and the predetermined erasure polynomial of the _k erasure be σ _k (X), and B _-1 (X) is 0
, B ₀ (X) to 1, R _-1 (X) to X ^2t , R
₀ (X) by substituting [sigma _K (X) · S (X)] MODx ^2t calculation result of the initial setting, whether polynomial R ₀ (X) satisfies a predetermined degree determination conditions How about the third
If, as a result of the third determination, the order determination condition is satisfied in the initial setting, B ₀ (X) is set as an error locator polynomial σ (X) and R ₀ (X) is set as an error. If a numerical polynomial η (X) is used and the order determination conditions are not satisfied in the initial setting, i = 1 to i times of R
_i-2 (X) / R _i-1 (X) = Q _i (X), and R _i-2 (X) −R _i-1 (X) · Q _i (X) = R _i ( X) B _i-2 (X) -B _i-1 (X) · Q _i (X) = B _i (X) are sequentially performed, and the i-th operation result satisfies the order determination condition. And B _i (X) = σ (X), R
Let _i (X) = η (X).

[0017]

Next, the present invention will be described with reference to the drawings.

FIG. 1 is a flow chart showing an algorithm of a first embodiment of the present invention, FIG. 2 is a block diagram of a syndrome arithmetic circuit in the first embodiment, and FIG. 3 is a full "symbol code" in the first embodiment. This is a determination circuit for determining “0” and all “0” s of the syndrome codes of the upper 8th place.

In FIG. 2, the syndrome arithmetic circuit according to the first embodiment is composed of 16 arithmetic circuits from 0th place to 15th place, each of which is an 8-bit input.
0 to 15) adder circuit 111 _i for adding the current input 8 bits and the previous operation result 8 bits,
Multiplier 1 for multiplying the result of the adder 111 _{i by} a constant α ⁱ
12 _i and the result of the multiplication circuit 112 _i are added to the addition circuit 111 _i.
And a register (D) 113 _i for feedback to

In FIG. 3, the decision circuit in the first embodiment is arranged such that NOR 114 _i and NOR 114 _{0 to} NOR 114 ₁₅ for the input 8 bits of the i-th place (i = 1 to 15).
“0” of the syndrome code as the logical product of each output of
To detect and AND115, NOR from NOR114 ₉
AND 116 for detecting all "0" s of the syndrome codes up to the upper 8th place by taking the logical product of the respective outputs up to 114 ₁₅ .

In this embodiment, the minimum distance between codes d = 17,
The processing procedure will be described assuming that the maximum error correction capability number t = 8.

First, in step 11, the syndrome code for the input signal is calculated by the syndrome arithmetic circuit shown in FIG. 2, and this syndrome code is used as the syndrome polynomial S.
(X) = S ₁₅ X ¹⁵ + S ₁₄ X ¹⁴ + ... + S ₂ X ² + S ₁ X +
Represented as S ₀ . In this staple 11, if all the signs of each digit are not “0”, that is, S (X) ≠ 0 from the output signal of the AND 115 of the determination circuit shown in FIG.
8 from the output signal of AND 116 of the judgment circuit shown in FIG.
If it is determined that all of the higher-order codes higher than the order are not "0", the operation by the first Euclidean algorithm is performed.

Here, the error locator polynomial thus obtained is B ₀ (X), the error numerical polynomial is R ₀ (X), and the error locator polynomial obtained by the previous operation is B _-1 (X), an error value polynomial and R _-1 (X), an error position polynomial calculated by the calculation after i times B _i (X), an error value polynomial R _i (X)
It expresses.

In the syndrome polynomial S (X) given at the initialization of step 11, if the order is lower than t from the initial stage, S (X) is calculated by the syndrome, S (X) = S ₁₅ X ¹⁵ + S ₁₄ X ¹⁴ + S ₁₃ X ¹³ ... +
It is given by the formula S ₂ X ² + S ₁ X + S ₀ . X ^2t is t =
Since it is 8, it is X ¹⁶ . Here, in Step 15, R _-1 (X) is X ¹⁶ and R ₀ (X) is S ₁₅ X ¹⁵ + S _14.
X ¹⁴ + S ₁₃ X ¹³ + ... + S ₂ X ² + S ₁ X + S ₀ is substituted, and i = 1, R is set in steps 16 and 17.
_i-2 (X) / R _i-1 = Q _i (X), R _i-2 (X) -R
_i-1 (X) · Q _i (X), B _i-2 (X) -B _i-1 (X)
-Calculate Q _i (X) to obtain R _-1 (X) / R ₀ (X)
The quotient Q ₁ (X), and R ₁ (X) and B ₁ (X) are calculated. Since the order of the dividend is 16 and the order of the divisor is 15, the quotient is the first order when division is performed,
The remainder is expressed by a 14th degree polynomial. In this case, the order of the remainder polynomial R ₁ (X) is 14th order, and as a result of the order determination in step 18, the order is higher than t, which is 8th order, so 1 is added to i in step 19 to be 2, Subsequently, in steps 16 and 17, the quotient Q ₂ (X) of R ₀ (X) / R ₁ (X) and R ₂ (X) and B ₂ (X) are calculated, and the degree of the remainder polynomial is calculated. Is repeated until becomes lower than t. And when it becomes low, step 2
At 0, B ₁ (X) becomes the error locator polynomial σ (X), and R 1
₁ (X) becomes the error numerical polynomial η (X).

[0025] Next S at step 11 (X) is a S ₁₅ to S ₉ is "0" from the initial time, at least not S ₈ is "0" S (X) = S 8 X 8 + S 7 X 7 + S ₆ X ⁶ ＋ …… ＋
The case of S ₂ X ² + S ₁ X + S ₀ will be described. In this case, in the calculation of R ₋₁ (X) / R ₀ (X), the dividend is 16th order,
Since the divisor is the 8th degree, the quotient is expressed by the 8th degree and the remainder is expressed by the 7th degree polynomial. As a result, the order of the remainder polynomial R ₁ (X) becomes 7th order, which is lower than the 8th order t = 8. Therefore, the determination condition is satisfied, and B ₁ (X) is the error locator polynomial σ.
In (X), R ₁ (X) becomes an error numerical polynomial η (X).

Next, S (X) is S (X) in which S _{15 to} S ₈ are “0” since the initial stage and at least S ₇ is not “0”.
^{_{= S 7 X 7 + S 6}} X 6 + ...... + S 2 X 2 + S 1 X + S 0
The case will be described. In this case R _-1 (X) / R
The operation of ₀ (X) has a 16th-order dividend and a 7th-order divisor, so the quotient is expressed by a 9th-order polynomial and the remainder is expressed by a 6th-order polynomial. As a result, the remainder polynomial becomes 6th order and satisfies the judgment condition. However, since R ₀ (X) is 7th order from the initial stage, it is considered that the judgment condition is also satisfied, so it is necessary to perform gradual division. Whether it is correctable data or not, try to use another way of thinking.

Next, the first embodiment will be described with reference to the atomic polynomial f (X).
= X ₈ + X ₄ + X ₂ + X + 1, the polynomial of the code of the input signal will be described as the information polynomial W = (X−α ¹⁵ ). This information polynomial W (X) means that S ₁₅ = W (α ¹⁵ ) = α ¹⁵ −α ¹⁵ = 0. The product of W (X) and an arbitrary polynomial T (X) can be considered as an information polynomial. W (α
^{Since 15} ) = 0, W (X) · T (X) = 0.
Therefore, it is considered that the term of S ₁₅ becomes “0” in any polynomial including (X−α ¹⁵ ).

Using this idea further, W (X) is given by (X-α
¹⁵ ) (X-α ¹⁴ ), both S ₁₅ and S ₁₄ are “0”. Therefore, by using the sign of the term of the syndrome to be set to “0” in W (X) = (X−α ⁿ ) (X−α ^n-1 ) ..., an arbitrary number of upper terms of the syndrome polynomial are “ It is possible to set it to 0 ". S ₁₅ = S ₁₄ = S ₁₃ = S
₁₂ = S ₁₁ = S ₁₀ = S ₉ = S ₈ = 0 means W
(X) is (X-α ¹⁵ ) (X-α ¹⁴ ) (X-α ¹³ ) (X-
α ¹² ) (X-α ¹¹ ) (X-α ¹⁰ ) (X-α ⁹ ) (X-α
⁸ ) can be said to include.

Here, assuming that T (X) = 0, W (X)
* T (X) = (X- (alpha) ¹⁵ ) (X- (alpha) ¹⁴ ) (X- (alpha) ¹³ )
^{(X-α 12) (X} -α 11) (X-α 10) (X-α 9)
(X-α ⁸ ) = X ⁸ + α ¹⁸³ X ⁷ + α ²⁵⁴ X ⁶ + α ²³²
X ⁵ + α ²⁶ X ⁴ + α ⁰ X ³ + α ⁴⁵ X ² + α ²⁵² X + α ⁹²
Becomes Representing this with a data string of code length N,
(0, 0 ... 0, 0, α ⁰ , α ¹⁸³ , α ²⁵⁴ , α ²³² ,
It can be regarded as data of α ²⁶ , α ⁰ , α ⁴⁵ , α ²⁵² , α ⁹² ).

By the way, a code word of "0" having a code length N (0, 0, 0, 0, ..., 0, 0, 0, 0) is used as a transmission word, and (0, 0, ..., 0, 0, α ⁰ , α ¹⁸³ , α ²⁵⁴ ,
When α ²³² , α ²⁶ , α ⁰ , α ⁴⁵ , α ²⁵² , and α ⁹² ) are the received words, it can be seen that this is 9 errors because there are 9 terms other than “0”. At this time, the syndrome is S ₁₅ =
S ₁₄ = ... = S ₉ = S ₈ = 0, S ₇ = α ⁷⁵ , S ₆ = α
¹⁶² , S ₅ = α ¹²⁵ , S ₄ = α ¹³⁹ , S ₃ = α ¹⁵⁸ , S
₂ = α ¹¹¹ , S ₁ = α ¹³⁶ , S ₀ = α ⁴⁹ , and the higher t
The symbol is in the state of "0". Therefore, from this fact, the upper t symbol of the syndrome polynomial is “0”.
In the case of, it can be judged that there is an error exceeding the correction capability. In such a case, in order to prevent an error correction by performing division, it is determined that the correction is impossible and the correction is not performed.

[0031] _{Next, S = 15 = S 14 =} S 13 = S 12 = S 11 =
A case where S ₁₀ = S ₉ = 0 will be described. T (X) = 0
Then, W (X) · T (X) = (X−α ¹⁵ ) (X−α
¹⁴ ) (X-α ¹³ ) (X-α ¹² ) (X-α ¹¹ ) (X-
α ¹⁰ ) (X−α ⁹ ) = X ⁷ + α ⁹⁶ X ⁶ + α ²⁴⁷ X ⁵ + α
It becomes ¹⁷³ X ⁴ + α ¹⁸⁵ X ³ + α ²⁸ X ² + α ¹⁵⁶ X + α ⁸⁴ . Representing this with a data string of code length N, (0,
0, ..., 0, 0, α ⁰ , α ⁹⁶ , α ²⁴⁷ , α ¹⁷³ ,
It can be regarded as the data α ¹⁸⁵ , α ²⁸ , α ¹⁵⁶ , α ⁸⁴ ). This is similar to the above, the code word of the code length N is “0” (0, 0, 0, 0, ..., 0, 0, 0,
0) as a transmission word, and (0, 0, ..., 0, 0, α ⁰ ,
α ⁹⁶ , α ²⁴⁷ , α ¹⁷³ , α ¹⁸⁵ , α ²⁸ , α ¹⁵⁶ , α ⁸⁴ )
It can be seen that there are 8 errors when is the received word. At this time, the syndrome is S ₁₅ = S ₁₄ = ... S ₉ = 0,
S ₈ = α ¹³⁰ , S ₇ = α ⁴³ , S ₆ = α ¹⁰⁶ , S ₅ = α
¹⁵² , S ₄ = α ³⁵ , S ₃ = α ¹⁷ , S ₂ = α ¹⁷³ , S ₁ =
Since α ²³ and S ₀ = α ¹⁰⁴ , the code at the higher-order t−1th place is “0”. Therefore, from this, it can be determined that the correction is possible when the code up to the higher-order t−1 th position of the syndrome polynomial is “0”.

That is, in the 11 steps shown in FIG.
It is determined whether all codes of the syndrome polynomial are all “0”. When all the codes are “0”, it is determined that there is no error in 12 steps. If not all “0”, it is determined in step 13 whether the higher-order t-th code of the syndrome polynomial is “0”. If it is “0”, it is determined that the correction cannot be performed in step 14 and no correction is performed. By outputting and leaving it to the processing of the next stage, it becomes possible to take an appropriate response to a data string that was conventionally erroneously determined and erroneously corrected, suppressing the error correction probability, and more It becomes possible to improve reliability.

FIG. 4 is a flow chart showing the algorithm of the second embodiment of the present invention.

The algorithm of this embodiment will be described for the case where the minimum inter-code distance d = 9, the number of error correction capabilities t = 4, and the number of erasures = K, and steps 31 to 34 are step 11 in the first embodiment. From step 1
The description of the second Euclidean algorithm from step 35 to step 40 in the case of mixed error correction and erasure correction of the input signal will be described below because it is the same as that of step 4.

In step 35, [σ _k (X) · S (X)] mod is added to S (X) obtained up to step 33.
The calculation of X ^2t is performed and is substituted into R ₀ (X). Where σ _k
(X) is an erasure location polynomial. Or later,
The basic flow takes the same algorithm as in FIG. 1 and will be described accordingly.

R ₀ (X) is [σ _k (x) · S (X)] m
S ₇ X ⁷ + S ₆ X ⁶ + obtained by calculation of odX ^2t
S ₅ X ⁵ + ... + S ₂ X ² + S ₁ X + S ₀ is given and X ^2t is X ^{8 because} t = 4. R _-1 (X) has X ⁸ and R ₀ (X) has S ₇ X ⁷ + S ₆ X ⁶ + S ₅ X ⁵ +
... + S ₂ X ² + S ₁ X + S 0 is substituted, and when i = 1, the quotient Q ₁ (X) of the division of R ₋₁ (X) / R ₀ (X) and R ₁ (X), B ₁ (X ) Is calculated.

Here, since the order of the dividend is the 8th order and the order of the divisor is the 7th order, when the division is performed, the quotient is represented by the 1st order and the remainder is expressed by the 6th order polynomial. In this case, the remainder polynomial R
The order of ₁ (X) is 6th order, and in step 36, the order is compared with the order determination condition u = “(d−1 + k) / 2”. Here, "(d-1 + k) / 2" means N + 1> (d-1 + k) /
2 ≧ N, N: “(d−1 + k) / 2” = N when integer
Represents If it is 0 erasure, u = “(9-1 + 0) /
2 "= 4, 7 If erasure, u =" (9-1 + 7)
/ 2 "= 7, and u is compared with the order of R ₁ (X).

When u = 4, R ₁ (X) which is 6th order
Is higher than u, which is the fourth order, so 1 is added to i to be 2, and this time division of R ₀ (X) / R ₁ (X), and R
₂ (X) and B ₂ (X) are calculated and repeated until the order of the remainder polynomial becomes lower than u. Also, u =
If it is 7, R ₁ (X), which is 6th order, is lower than u, which is 7th order. Therefore, at this point, the determination condition is satisfied, and B ₁ (X) is added to the error locator polynomial σ (X) by R
₁ (X) becomes the error numerical polynomial η (X).

Here, for example, an 8-erasure will be described as a special case.

Since u = “(9-1 + 8) / 2”,
R ₋₁ (X) [σ _k (X) · S (X)] modX ^2t
Takes modX ⁸ , the order is 7th or less from the initial stage, which means that the order determination condition is satisfied. That is,
An algorithm is required when R ₋₁ (X) satisfies the order determination condition from the initial stage before giving 1 to i.

For example, the 0 error 8 erasure will be described. Since u = 8, R ₋₁ (X) is 7 from the beginning.
Since it is less than or equal to the next degree, the order determination condition is satisfied. Therefore, B
₀ (X) is the error locator polynomial σ (X), and R ₀ (X) is the error numerical polynomial η (X). At this time, B ₀ (X) is 1 and R ₀ (X) is [σ _k (x) · S (X)] modX ^2t.
Becomes The error locator polynomial is 1, and no error position is shown, but since the number of errors is 0 and the number of erasures is 8,
There is no problem that the error locator polynomial is 1. Actually, after this, the calculation of σ (X) · σ _k (X) is performed to obtain the error position, so that the erasure position represented by σ _k (X) can be obtained correctly at this time.

If it is not judged from the initial stage whether or not the order judgment condition is satisfied, taking the 0 error 8 erasure as an example, the judgment condition is satisfied after the division is performed meaninglessly once. B ₁ (X) at that time is set as an error locator polynomial. In this case, an erroneous error locator polynomial is found for an originally error-free data string, and error correction is performed.

Therefore, in step 35, B
After initializing ₋₁ (X), B ₀ (X), R ₋₁ (X), and R ₀ (X), set i = 0 and at step 36, whether the order determination condition is satisfied from the initial state. Find out. If so, in step 40, B ₀ (X)
Is the error locator polynomial σ (X), and R ₀ (X) is the error numerical polynomial η (X). If not, step 3
In step 7, i is incremented by 1 to be 1, and steps 38 and 3 are performed.
In 9 R _i-2 (X) / R _i-1 (X) = Q _i (X), R _i-2
(X) -R _i-1 (X) · Q _i (X), B _i-2 (X) -B
_i-1 (X) · Q _i (X) is calculated to obtain R _-1 (X) /
The quotient of division of R ₀ (X), Q ₁ (X), and B ₁ (X), R
₁ (X) is calculated, and the order is determined again in step 36. If they are satisfied, the error locator polynomial and the error value polynomial are obtained, and if they are not satisfied, the error locator polynomial and the error value polynomial can be obtained by repeating division until they are satisfied. As a result, it is possible to take an appropriate action and correct the data string that has been corrected in the past but was erroneously determined and error-corrected.

Also, as in the first embodiment, step 3
In step 1, it is judged whether all the codes of the syndrome polynomial are all “0”, and if all “0”, step 3
It is judged that there is no error in 2. When all are not "0", it is determined in step 33 whether the upper t code of the syndrome polynomial is "0". If it is "0", it is determined that the correction is impossible in step 34 and no correction is performed, and the flag is set. By outputting and letting it be processed in the next stage,
It becomes possible to take an appropriate response to the data string that has been erroneously determined and error-corrected, and it is possible to suppress the error-correction probability and further improve the reliability.

[0045]

As described above, according to the present invention, at the initial stage of setting a syndrome polynomial having the maximum error correction capability number t as a divisor polynomial, it is determined whether all codes of the syndrome polynomial are all "0" and all " When it is "0", it is judged as no error, and when it is not all "0", it is judged whether the upper t-order codes are all 0s. When it is all 0s, it is judged as uncorrectable and correction is not executed and a flag is output. By leaving it to the processing in the next stage, there is an effect that the reliability of error correction can be improved as compared with the conventional case.

If the order determination condition is satisfied from the initial stage of erasure correction, the error locator polynomial and the error value polynomial are obtained at that time, and if they are not satisfied, the division is repeatedly performed until the order determination condition is satisfied. By obtaining it, it becomes possible to correct the data string that was conventionally erroneously calculated and error-corrected, or the data string that could be corrected but was erroneously judged and error-corrected. Moreover, there is an effect that error correction can be suppressed.

[Brief description of the drawings]

FIG. 1 is a flowchart showing an algorithm of a first exemplary embodiment of the present invention.

FIG. 2 shows an example of a syndrome arithmetic circuit in the first embodiment.

FIG. 3 shows an example of a judgment circuit for judging all “0” s of the syndrome code and all “0s” of the syndrome codes up to the 8th highest rank in the first embodiment.

FIG. 4 is a flowchart showing an algorithm of the second exemplary embodiment of the present invention.

FIG. 5 is a flowchart showing an algorithm of a first conventional example.

FIG. 6 is a flowchart showing an algorithm of a second conventional example.

[Explanation of symbols]

111 ₀ , ... 111 ₁₅ Adder circuit 112 ₀ , ... 112 ₁₅ Multiplier circuit 113 ₀ , ... 113 ₁₅ Register (D) 114 ₀ , ... 114 ₁₅ NOR 115, 116 AND

Claims (3)

(57) [Claims] 1. A first Euclidean algorithm capable of obtaining an error locator polynomial for calculating an error position of an input signal composed of a plurality of digital code strings and an error value polynomial for calculating an error value, wherein: Then, a syndrome polynomial operation of a predetermined maximum error correction capability number t (integer of t ≧ 1) is performed, and a first determination is made whether all the syndrome code strings of the operation results of this syndrome polynomial are “0”, As a result of this first determination, all the syndrome code strings are “0”.
In the case of, the input signal is assumed to be error-free, and when all of the syndrome code sequences are not "0", a second determination is made as to whether all of the higher order t of the syndrome code sequence are not "0". An error characterized in that the error locator polynomial and the error value polynomial are calculated by the first Euclidean algorithm for the syndrome code string only when it is determined that all are not “0” as a second determination result. Correction processing method. 2. An error position polynomial for calculating an error position of the input signal and an error value polynomial for calculating an error value are obtained by performing erasure correction on an input signal composed of a plurality of digital code sequences with an erasure location polynomial. A second Euclidean algorithm capable of performing a syndrome polynomial operation of a predetermined maximum error correction capability number t (integer of t ≧ 1) on the input signal, and a syndrome code of the operation result of the syndrome polynomial. A first judgment is made as to whether or not all the strings are "0", and as a result of this first judgment, all the syndrome code strings are "0".
In the case of, the input signal is assumed to be error-free, and when all of the syndrome code sequences are not "0", a second determination is made as to whether all of the higher order t of the syndrome code sequence are not "0". Only when it is determined that all are not “0” as a result of the second determination, the erasure location polynomial, the error locator polynomial, and the error value polynomial are calculated by the second Euclidean algorithm for the syndrome code string. An error correction processing method characterized by the above. 3. The second Euclidean algorithm, when the second determination result is that all of the upper t places of the syndrome code string are not “0”,
Let X be the code of the syndrome code string, S (X) be the polynomial of the syndrome code string, and B ₀ (X) and R ₀ (X) be the error locator polynomial and the error value polynomial that have been obtained, respectively. The error locator polynomial and the error value polynomial obtained by the calculation of B are calculated as B ₋₁ (X) and R, respectively.
₋₁ (X), B _i (X) and R _i (X) are the error locator polynomial and the error value polynomial obtained by the operation after i times (integer of i ≧ 0), t is the error correction capability number, and The minimum distance is represented by d, the number of erasures is represented by k (t, d, and k are all integers of 1 or more), and a predetermined erasure polynomial of the _k erasure is represented by σ _k (X), and B _-1 (X) is represented by 0. And B ₀ (X)
To 1, R _-1 (X) to X ^2t , and R ₀ (X) to [σ
The calculation result of _K (X) · S (X)] modX ^2t is substituted for initialization, and a third judgment is made as to whether or not the polynomial of R ₀ (X) satisfies a predetermined order judgment condition. Done,
As a result of the third determination, if the order determination condition is satisfied in the initial setting, B ₀ (X) is set to the error locator polynomial σ.
(X) and R ₀ (X) is an error numerical polynomial η
(X), and if the order determination condition is not satisfied in the initial setting, i = 1 to i times of R _i-2 (X) / R _i-1 (X) = Q
_i (X), R _i-2 (X) -R _i-1 (X) .Q _i (X) = R _i (X) B _i-2 (X) -B _i-1 (X ) .Q _i (X) = B _i (X) is sequentially performed, and when the i-th operation result satisfies the order determination condition, B _i (X) = σ (X), R
3. The error correction processing method according to claim 2, wherein _i (X) = [eta] (X).