JP3252515B2 - Error correction device - 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 apparatus for decoding an error correction code by obtaining a determinant on a Galois extended field.

[0002]

2. Description of the Related Art In recent years, for example, a so-called "1", "1", "compact disk" for recording a signal by the length of a pit or a land, and a digital VTR for recording a signal by a difference in the direction of magnetization given to a magnetic tape. A device that records and reproduces a signal with a digital signal of "0" has been commercialized. In these devices, a digital signal of "1" and "0" recorded on a recording medium is read by a head to reproduce the recorded signal. However, dust adhering to the medium and defects occurring on the medium are reproduced. When playing back and decoding the recorded signal due to dropout etc.
A signal coded to “1” is erroneously decoded to “0”, and a signal coded to “0” is erroneously decoded to “1”.

In order to correct such decoding errors, in the above-described devices, when a signal is recorded, an error correction code is added to the information signal as redundant bits and recorded. Is decoded by an error correction circuit provided in the reproduction block, so that a signal that matches the encoded and recorded information signal can be decoded.

Hereinafter, such a conventionally used error correction device (for example, see "Multiple byte error correction system" disclosed in Japanese Patent Publication No. 4-55556) will be described with reference to the drawings.

FIG. 3 is a block diagram of an error correction apparatus for a (N, N-6, 7) Reed-Solomon code on GF (2 ^m ) (m is a positive integer). In FIG. 3, 1 is a syndrome calculator, 2 is an error position coefficient calculator, 3 is an error pattern coefficient calculator, 4 is an error position and error pattern calculator, and 5 is a delay unit.

[0006] The error position coefficient calculator 2 of the error correction device configured as described above generates an error from the syndromes S ₀ , S ₁ , S ₂ , S ₃ , S ₄ , and S ₅ calculated by the syndrome calculator 1. The position coefficients Δ ₀ , Δ ₁ , Δ ₂ , and Δ ₃ are obtained, and the values of Δ ₀ , Δ ₁ , Δ ₂ , and Δ ₃ are three when the number of errors determined to have occurred is three.

[0007]

(Equation 1)

[0008]

(Equation 2)

[0009]

(Equation 3)

[0010]

(Equation 4)

[0011] When it is 2, Δ ₀ = S ₁ · S ₃ + S ₂ · S ₂ , Δ ₁ = S ₀ ·
When S ₃ + S ₁ · S ₂ and Δ ₂ = S ₁ · S ₁ + S ₀ · S ₂ , 1, Δ ₀ = S ₁ ,
Δ ₁ = S ₀ (· is multiplication over GF (2 ^m ), + is GF
(2 ^m ) indicates addition. The same applies hereinafter.)

FIG. 4 is a block diagram of the error position coefficient calculator 2. In FIG. 4, reference numeral 11 denotes a multiplier on GF (2 ^m ), and reference numeral 12 denotes an adder on GF (2 ^m ).

The calculation of Δ ₀ , Δ ₁ , Δ ₂ , Δ ₃ is exactly the formula. Therefore, for example, G that can correct four errors
When the configuration of the error correction device for the (N, N-8, 9) Reed-Solomon code on F (2 ^m ) (m is a positive integer) is similarly given, the syndrome calculated by the syndrome calculator 1 is given.
From S ₀ , S ₁ , S ₂ , S ₃ , S ₄ , S ₅ , S ₆ , S ₇ , the error location coefficients Δ ₀ , Δ ₁ ,
Δ ₂ , Δ ₃ , Δ ₄ are obtained, and the values of Δ ₀ , Δ ₁ , Δ ₂ , Δ ₃ , Δ ₄ are (N, N) when the number of errors determined to have occurred is 3 or less. N-6, 7) Same as in the case of Reed-Solomon code, and when it is 4,

[0014]

(Equation 5)

[0015]

(Equation 6)

[0016]

(Equation 7)

[0017]

(Equation 8)

[0018]

(Equation 9)

## EQU1 ## Therefore, Δ₀Is (Equation 10), and a =
S₁, b = S_Two, c = S_Three, d = S_Four, e = S_Five, f = S₆, g = S₇And Δ_FourIs
In (Equation 10), a = S₀, b = S₁, c = S_Two, d = S_Three, e = S_Four, f = S_Five,
g = S₆And Δ _TwoIs (Equation 11), and a = S₀, b = S₁, c = S_Two, d
= S_Three, e = S_Four, f = S_Five, g = S₆, h = S₇As each official
Can be obtained.

[0020]

(Equation 10)

[0021]

[Equation 11]

[0022]

However, in the above configuration, in order to obtain the value of the determinant, multiplication is performed nine times in each of (Equation 1), (Equation 2), (Equation 3), and (Equation 4). , Addition 5 times, (Equation 5), (Equation 7), and (Equation 9) require 28 multiplications and 17 additions, respectively. If the circuit is realized as hardware, the operation clock becomes high or the execution time of the operation becomes long. Alternatively, there has been a problem that the scale of hardware becomes very large.

The present invention solves such a problem and obtains the value of the determinant with a smaller number of executions of the operation than in the past, thereby performing error correction with a low operation clock or a short operation execution time. No, calculations are performed by hardware
It is an object of the present invention to provide an error correction device capable of reducing its size when implemented.

[0024]

According to the present invention, there is provided an error correction apparatus for decoding an error correction code added to an information signal and recorded and reproduced on a record carrier. A syndrome calculator that calculates a syndrome based on the input codeword; and, based on the syndrome, determines the number of errors in the input codeword and outputs an error number determination signal. And the error locator polynomial X ⁿ + σ _n-1 · X ^n-1 + σ _n-2 · X ^{n -2} +… + σ ₁ · X + σ
An error locator polynomial coefficient calculator for calculating a coefficient σ _{i of 0} (i = n-1, n-2,..., 1, 0), and a coefficient σ obtained by this calculation
_{Using i} , the error locator polynomial ^Xn + σn _- 1Xn ^-1 + σn _- 2X
^n-2 +... + σ ₁ · X + σ _{0 is set} to 0, a root X is obtained, an error position calculator for obtaining the error position based on the root X, the obtained error position and the syndrome And an error pattern calculation circuit for generating an error pattern based on the number-of-errors determination signal, and a delay unit for delaying an input code word by a time required until the error pattern is generated from the input signal code word And a corrector that generates a codeword corrected by using the output of the delay unit and the error pattern.

The error locator polynomial coefficient calculator decodes an error correction code on an extended field GF (2 ^m ) (m is a positive integer) of the Galois field GF (2) based on the input syndrome. When performing a determinant operation for determining the number of occurring errors and a determinant operation for obtaining coefficients of an error locator polynomial, after performing a low-order determinant operation, A plurality of higher-order determinant operations that require the result of the determinant operation are performed in parallel.

[0026]

According to the present invention, when calculating the coefficients of the polynomial in the error locator polynomial coefficient calculator, the determinant must be calculated after performing a low-order determinant operation, and then the results must be commonly used. By performing high-order determinant operations in parallel, determinant calculations can be realized in a short execution time, and thereby error correction can be speeded up. Further, when these operations are realized by a hardware circuit, the circuit scale can be reduced.

[0027]

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS An embodiment of the error correction device of the present invention will be described.

FIG. 1 is a block diagram showing an embodiment of an error correction apparatus according to the present invention. In FIG. 1, 21 is a syndrome calculator, 22 is an error locator polynomial coefficient calculator, 23 is an error position calculator, 24 is an error pattern calculator, 25 is a delay unit, 26
Is a corrector. Reference numeral 27 denotes a syndrome calculator 21, an error locator polynomial coefficient calculator 22, an error locator calculator 23, and an error pattern calculator 24, and is hereinafter referred to as a calculation block. Hereinafter, a description will be given assuming that the (N, N-8, 9) Reed-Solomon code on GF (2 ^m ) is quadrupled.

First, a reception sequence R = (r
_{N-1, r N-2} , ..., r 1, r 0) is inputted to the syndrome calculator 21, syndrome calculator 21 is the syndrome _{S = (S 0, S 1} ,
S ₂ , S ₃ , S ₄ , S ₅ , S ₆ , S ₇ ) are calculated. The received sequence R is also input to the delay unit 25, and the delay unit 25 delays the received sequence R while performing a later-described calculation required for error correction in the error correction calculation block 27. Syndrome S
Is calculated based on (Equation 12).

[0030]

(Equation 12)

Here, the transmitted code sequence is represented by C =
(C _N−1 , c _N−2 ,..., C ₁ , c ₀ ), an error sequence between the code sequence C and the reception sequence R is E = (e _N−1 , e _N−2). ,…, E ₁ ,
e ₀ ) holds the relational expression of (Equation 13). Error sequence E
Is a series in which an element in which an error has occurred is an error pattern and an element in which no error has occurred is 0 among N elements. Therefore, since (Equation 12) can be replaced with (Equation 14) and encoding is performed so as to satisfy (Equation 15), (Equation 16) holds. In the present invention, the error position of the (N−j) th (j = 0, 1,..., N−2, N−1) digit from the head is given by α ^j .

[0032]

(Equation 13)

[0033]

[Equation 14]

[0034]

(Equation 15)

[0035]

(Equation 16)

If there is no error in the reception sequence R, that is, E =
(0,0, ..., 0,0), the syndrome S =
(0,0,0,0,0,0,0,0).

The error locator polynomial calculator 22 calculates the coefficients of the error locator polynomial based on the syndrome S described above. This calculation will be described later in detail. Note that the number of errors is v (v = 1, 2, 3, 4), and the error position is X _k (k = 1,.
If v), the error locator polynomial is represented by (Equation 17). Based on the coefficient σ _j (j = 0,..., V-1) calculated by the error locator polynomial calculator 22, the error locator polynomial is set to zero, and the root error position is determined by the error locator calculator 23. calculate. Here, when the value obtained as the root is inappropriate as an error position (in the case of a double root, when the root = 0, when the error position exceeds the range of the code word, etc.), or no root is obtained. In this case, a detection signal is added assuming that five or more errors have occurred.

[0038]

[Equation 17]

Next, using the syndrome S and the obtained error position X _k (k = 1,..., V), the corresponding error pattern Y
_k (k = 1,..., v) is calculated by the error pattern calculator 24.
(Equation 16) Clearly, when v = 1, S ₀ = Y ₁ , v = 2
(Equation 18) when v = 3, (Equation 19) when v = 3, and (Equation 20) when v = 4. These relations are
A v source primary simultaneous equations of Y _k, can be determined easily an error pattern Y _k.

[0040]

(Equation 18)

[0041]

[Equation 19]

[0042]

(Equation 20)

While performing the above calculations, the received sequence R
Is delayed by a delay unit 25, and based on (Equation 13), an exclusive OR of the delayed sequence and the obtained error sequence is obtained by a corrector 26, whereby error correction is performed. Complete.

Next, the error locator polynomial coefficient calculator 22 in the error correction device of the present embodiment will be described in detail. FIG. 2 is a block diagram of the error locator polynomial coefficient calculator 22.
In FIG. 2, 31 is a 0 error determiner, 32 is a 1 error determiner,
33 is a two-error decision unit, 34 is a three-error decision unit, 35 is a one-error decision coefficient calculator, 36 is a two-error decision coefficient calculator, 37 is a three-error decision coefficient calculator, and 38 is a first-order position polynomial coefficient calculator. , 39 is 2
A fourth-order position polynomial coefficient calculator, 40 is a third-order position polynomial coefficient calculator, 41 is a fourth-order position polynomial coefficient calculator, and 42 is a selector.

First, the syndromes S ₀ , S ₁ , S ₂ , S ₃ , S ₄ , S ₅ , S ₆ , and S ₇ calculated by the syndrome calculator 21 are calculated by the 0 error determiner 31 and the 1 error determination coefficient calculator. Unit 35, 2 error judgment coefficient calculator
36, input to the 3 error judgment coefficient calculator 37. Hereinafter, description will be given according to the calculated sequence.

(1) The 0 error determiner 31 calculates S ₀ = S ₁ = S ₂ = S ₃
If = S ₄ = S ₅ = S ₆ = S ₇ = 0, it is determined that there are 0 errors, and a determination signal indicating that the number of errors is 0 is output. The 0 error determiner 31 can be constituted by, for example, a logic circuit that outputs a high-level signal only when S _{0 to} S ₇ are all 0.

(2) One error determination coefficient calculator 35 receives the input
Syndrome S₀, S₁, S_Two, S_Three, S_Four, S _Five, S₆, S₇From, (number
21) 1 error determination coefficient A02, A1 given by (Equation 26)
Find 3, A24, A35, A46, A57.

[0048]

(Equation 21)

[0049]

(Equation 22)

[0050]

(Equation 23)

[0051]

(Equation 24)

[0052]

(Equation 25)

[0053]

(Equation 26)

1 The error determiner 32 calculates A02 = A13 = A24 = A35 =
If A46 = A57 = 0, it is determined that there is one error, and a determination signal indicating that the number of errors is one is output. This one error determiner 32 is, for example, A02, A13, A24, A35, A46, A57.
Can be constituted by a logic circuit that outputs a high-level signal only when all are zero. At this time, σ ₁₀ = S ₁ / S ₀ (1) is obtained by the first-order position polynomial coefficient calculator 38, and σ ₀ = σ ₁₀ , σ ₁ = undefined, σ ₂ = undefined, σ ₃ is obtained by the selector 42. = Output undefined.

(3) The two error judgment coefficient calculator 36 receives the input
Syndrome S₀, S₁, S_Two, S_Three, S_Four, S _Five, S₆, S₇From
A04 = S₀・ S_Four + S_Two ^Two … (2) A15 = S₁・ S_Five + S_Three ^Two … (3) A26 = S_Two・ S₆ + S_Four ^Two … (4) A37 = S_Three・ S₇ + S_Five ^Two .. (5) are obtained, and then 2 errors given by (Equation 27) to (Equation 30) are obtained.
Judgment coefficient A₀₂₄, A₁₃₅, A_{Two 46}, A₃₅₇Ask for.

[0056]

[Equation 27]

[0057]

[Equation 28]

[0058]

(Equation 29)

[0059]

[Equation 30]

The two error determiner 33 calculates A024 = A135 = A246 = A3
If 57 = 0, it is determined that there are two errors, and a determination signal indicating that the number of errors is two is output. The two-error determiner 33 can be composed of, for example, a logic circuit that outputs a high-level signal only when A ₀₂₄ , A ₁₃₅ , A ₂₄₆ , and A ₃₅₇ are all 0. At this time, the second-order position polynomial coefficient calculator 39 calculates σ ₂₁ = (S ₀ · S ₃ + S ₁ · S ₂ ) / A02 (6) σ ₂₀ = A13 / A02 (7) At 42, σ ₀ = σ ₂₀ , σ ₁ = σ ₂₁ , σ ₂ = undefined, and σ ₃ = undefined.

According to (Equation 27) to (Equation 30), A024, A13
Determining 5, A246, A357 is equivalent to expanding the determinant (Equation 31) on GF (2 ^m ) as in (Equation 32) and obtaining the value of the determinant. This is, for example, the syndromes S ₀ , S ₁ , S ₂ , S ₃ , S used for calculation in (Equation 27).
_It is easy to understand that 4 corresponds to A, B, C, D, and E in the determinant shown in (Equation 32).

[0062]

(Equation 31)

[0063]

(Equation 32)

According to (Equation 32), the calculation of this determinant requires six multiplications, five additions, and three square operations, but C · E + D ² , A · If E + C ² and A · C + B ² are calculated in advance, the calculation can be performed only by three multiplications and two additions.
In the above-described calculation, the number of determinants is four, and originally, 24 multiplications, 20 additions, and 12 squares are required. In the present embodiment, A04, A15, A26, and A37 need to be calculated in this step, but A02, A13, A24, A35, A46, and A57
Can be calculated by only 16 multiplications, 12 additions, and 4 squaring operations since 1 has already been calculated by the error determination coefficient calculator 35, and the determinant calculation is simplified. it can.

(4) The three error judgment coefficient calculator 37 receives the input
Syndrome S₀, S₁, S_Two, S_Three, S_Four, S _Five, S₆, S₇First, A06 = S₀・ S₆ + S_Three ^Two … (8) A17 = S₁・ S₇ + S_Four ^Two ... (9) is obtained, and then 3 errors given by (Equation 33) and (Equation 34)
Judgment coefficient A₀₂₄₆, A1₃₅₇Ask for.

[0066]

[Equation 33]

[0067]

(Equation 34)

If A0246 = A1357 = 0, the three error determiner 34 determines that there are three errors, and outputs a determination signal indicating that there are three errors. The three-error determiner 34 can be formed of, for example, a logic circuit that outputs a high-level signal only when A0246 and A1357 are both 0.

According to (Equation 33) and (Equation 34), A0246, A135
Finding 7 is GF (2^m) Above the determinant (Equation 35)
To obtain the value of the determinant by expanding as in (Equation 36)
Equivalent to. This is, for example, the calculation in (Equation 33)
Syndrome S used₀, S ₁, S_Two, S_Three, S_Four, S_Five, S₆To the (number
A, B, C, D, E, F, G in the determinant shown in 36)
It is easy to understand if you make it correspond.

[0070]

(Equation 35)

[0071]

[Equation 36]

According to (Equation 36), the calculation of this determinant requires nine multiplications, eight additions, and six square operations, but A · C + B ² , E · G + F ² , A ・ E + C ² , C ・ G + E ² , A ・ G + D ² , C ・ E + D ²
Is calculated in advance, the calculation can be performed only by three multiplications and two additions. In the above-described operation, the number of determinants is two, and originally 18 multiplications, 16 additions, 12
Times square operation is required. In this embodiment, A06, A17
Need to be calculated in this step, but A02, A13, A24, A3
5, A46 and A57 are 1 error decision coefficient calculators 35, A04, A15, A26 and A
Since 37 has already been calculated by the 2 error determination coefficient calculator 36, the determinant can be calculated by only eight multiplications, six additions, and two square operations, which makes the determinant operation simple. Can be

(5) If the three error determination coefficient calculator 37 determines that there are three errors, the third-order position polynomial coefficient calculator 40 calculates σ ₃₂ = A025 / A024 (10) σ ₃₁ = A035 / A024 (11) σ ₃₀ = A135 / A024 (12) is obtained, and the selector 42 obtains σ ₀ = σ ₃₀ , σ ₁ = σ ₃₁ , and σ ₂ = σ
₃₂ , σ ₃ = output undefined. However, A025 and A035 are given by (Equation 37) and (Equation 38), respectively.

[0074]

(37)

[0075]

(38)

A025, A035 according to the equations (37) and (38)
Is equivalent to expanding the determinant (Equation 39) on GF (2 ^m ) as in (Equation 40) to obtain the value of the determinant. This means, for example, that the syndromes S ₀ , S ₁ , S ₂ , S ₃ , S ₄ , and S ₅ used in the calculation in (Equation 37) are represented by (Equation 4)
It is easy to understand when considering them in correspondence with A, B, C, D, E and F in the determinant shown in (0).

[0077]

[Equation 39]

[0078]

(Equation 40)

According to equation (40), the calculation of this determinant requires six multiplications, five additions, and three squaring operations, but C · E + D ² , A · If E + C ² and A · C + B ² are calculated in advance, the calculation can be performed only by three multiplications and two additions.
In the above operation, the number of determinants is two, and originally one
Two multiplications, ten additions, and six squaring operations are required. In this embodiment, since A02, A13, A24, and A35 have already been calculated by the one error determination coefficient calculator 35 and A04 and A15 have already been calculated by the two error determination coefficient calculator 36, six multiplications and four times The determinant can be calculated only by the addition, and the determinant operation can be simplified.

(6) When it is determined that the number of errors is greater than three, first, the fourth-order position polynomial coefficient calculator 41 first calculates the number of errors as in A025 and A035 described above.

[0081]

[Equation 41]

[0082]

(Equation 42)

Then, σ ₄₃ = A0247 / A0246 (13) σ ₄₂ = A0257 / A0246 (14) σ ₄₁ = A0357 / A0246 (15) σ ₄₀ = A1357 / A0246 (16) In the selector 42, σ ₀ = σ ₄₀ , σ ₁ = σ ₄₁ , σ ₂ = σ
₄₂ and σ ₃ = σ ₄₃ are output. However, A0247, A0257, and A0357 are given by (Equation 43), (Equation 44), and (Equation 45), respectively.

[0084]

[Equation 43]

[0085]

[Equation 44]

[0086]

[Equation 45]

For A0247 and A0357, A247 and A257 are calculated in this step, but A24, A35, A46, and A57 are 1 error determination coefficient calculators 35, and A26, A37, A024, A135, A246, and A357 are calculated. (2) In the error determination coefficient calculator 36, A025 and A035 have already been obtained in the third-order position polynomial coefficient calculator 40, so that the determinant can be calculated by only 14 multiplications and 10 additions,
Determinants can be simplified.

Calculating A0257 by (Equation 44)
GF (2^mThe above determinant (Equation 46) is expressed as (Equation 47)
It is equivalent to expanding to find the value of the determinant. this is,
For example, the syndrome used for calculation in (Equation 44)
Room S₀, S₁, S_Two, S_Three, S_Four, S_Five, S₆, S ₇Is shown in (Equation 47).
Corresponding to A, B, C, D, E, F, G, H in the determinant
It is easy to understand when you think about it.

[0089]

[Equation 46]

[0090]

[Equation 47]

According to (Equation 47), the calculation of this determinant requires 18 multiplications, 17 additions, and 6 squaring operations, but A · C + B ² , F · H + G ² , A ・ E + C ² , D ・ H + F ² , A ・ G + D ² , D ・ F
+ E ² , B ・ D + C ² , E ・ G + F ² , B ・ F + D ² , C ・ G + E ² , B ・ H + E ² , C ・ E + D ² In this case, the operation can be performed only by six multiplications and five additions.

In this embodiment, A02, A13, A24, A35, A46, A57
Is the one error determination coefficient calculator 35, A04, A15, A26, and A37 are the two error determination coefficient calculators 36, and A06 and A07 are the three error determination coefficient calculators 37. This determinant can be calculated only by multiplication and five additions, and the determinant operation can be simplified.

As is clear from the above description, the quadruple error correction can be performed by (Equation 21) to (Equation 30), (Equation 33), and (Equation 3).
4), (Formula 37), (Formula 38), (Formula 43) to (Formula 4)
As shown in 5), six second-order determinants and six third-order determinants are used.
It is necessary to find five determinants and four determinants, and the expansion formulas of these determinants have many common terms.
Using the results of (Equation 26), (Equation 27) to (Equation 3)
0), (Equation 33), (Equation 34), (Equation 37), (Equation 3)
The calculation of 8) can be simplified. Similarly, by using the results of (Equation 21) to (Equation 26), the calculation of (Equation 44) can be simplified. Further, (Equation 27) to (Equation 30), (Equation 37),
Using the result of (Equation 38), the calculation of (Equation 43) and (Equation 45) can be simplified, and the intermediate values of Expressions (2) to (5) can be used.
If Equations (8) and (9) are obtained, Equation 27 is obtained.
(Equation 30), (Equation 33), (Equation 34), (Equation 37) (Equation 3)
8) The calculation of (Equation 44) can be simplified.

The calculation order based on the above context is shown in (Table 5), (Table 6), and (Table 7). The calculation means used here is P + Q · R or P ² within one operation period.
It is assumed that + QR can be calculated, and that either one of the calculations can be arbitrarily selected. There can also be P = 0. The above calculation is based on P + Q · R or P ² + Q · R
Is explained using a calculator that can select and calculate
If there is at least one multiplier and one adder,
By combining them as appropriate and configuring the calculator,
These calculations can be performed similarly.

[0095]

[Table 5]

[0096]

[Table 6]

[0097]

[Table 7]

Similarly, (N, N-6, 7) on GF (2 ^m )
(Table 8) shows the calculation order of the same purpose as described above when performing triple error correction using the Reed-Solomon code. Here with is calculation means, as in the case of quadruple error correction described above, 1 can be calculated a P + Q · R or P ² + Q · R in the operation period, and that this one of the calculation can be arbitrarily selected Is assumed. Also, P = 0
It is possible. In addition, the above calculation is P + Q · R or P ²
It is explained using a calculator that can calculate by selecting + Q ・ R
But at least one multiplier and one adder
If appropriate, combine them to form a calculator
, These calculations can be performed similarly.

[0099]

[Table 8]

As described above, in the embodiment of the error correction apparatus according to the present invention, since the calculation order is set so as not to repeatedly calculate the result necessary for realizing error correction, the shortest The required value of the determinant can be obtained in the execution time of (1), thereby realizing code error correction in a short processing time.

In order to actually perform the calculation in such an order, a circuit (in the case of hardware) or a region (in the case of software) that holds the value of the previously calculated low-order determinant is required. If they are missing, it may be necessary to calculate the same value more than once.
However, if a part of the above calculation results can be used in common, the execution time can be shortened.

[0102] In this embodiment, GF (2 ^m) on the (N,
N-8, 9) Reed-Solomon code or (N, N-
6, 7) Although the Reed-Solomon code is handled, a systematic calculation can be similarly performed for an arbitrary code length, an arbitrary number of information symbols, and an arbitrary Reed-Solomon code on a body. Although the quadruple correction is performed, this calculation method can be applied as long as the number of corrections does not exceed the capability of the code. In addition, the present invention is applicable to any calculation means, and the calculation order is as shown in Table 5.
(Table 6) Other than those shown in (Table 7) or (Table 8) may be used.

[0103]

As is apparent from the above description, the present invention provides a method of calculating the determinant of a polynomial in an error locator polynomial coefficient calculator after performing a low-order determinant operation. By performing a higher-order determinant operation that requires those results in common, the determinant calculation can be simplified. Therefore, when error correction is implemented as a software program, the number of program steps can be reduced, and when implemented as hardware, the operation clock can be slowed down or the execution time shortened and the circuit scale can be reduced. However, its practical effects are great.

[Brief description of the drawings]

FIG. 1 is a block diagram showing an embodiment of an error correction apparatus according to the present invention;

FIG. 2 is a block diagram of an error locator polynomial coefficient calculator according to the present invention;

FIG. 3 is a block diagram of a conventional error correction device.

FIG. 4 is a block diagram of an error position coefficient calculator of a conventional error correction device.

[Description of Code] 21 Syndrome Calculator 22 Error Locator Polynomial Coefficient Calculator 23 Error Location Calculator 24 Error Pattern Calculator 25 Delay Unit 26 Corrector 27 Calculation Block 31 0 Error Judge 32 1 Error Judge 33 2 Error Judge 34 3 error judgment unit 35 1 error judgment coefficient calculator 36 2 error judgment coefficient calculator 37 3 error judgment coefficient calculator 38 1st position polynomial coefficient calculator 39 2nd position polynomial coefficient calculator 40 3rd order position polynomial coefficient calculator 41 Fourth-order position polynomial coefficient calculator 42 Selector

Claims (3)

(57) [Claims] 1. A syndrome calculator for inputting an error correction codeword recorded and reproduced on a record carrier by adding a check signal to an information signal and calculating a syndrome based on the codeword, and a syndrome calculator based on the syndrome. In addition to determining the number of errors in the input codeword and outputting an error number determination signal,
Error locator polynomial X ⁿ + σ _n-1 × X based on the syndrome
ⁿ⁻¹ + σ _n-2 · X ^n-2 +… + σ ₁ · X + σ ₀ coefficient σ _i (i = n-1, n-2,
..., and a error position polynomial coefficient calculator for calculating a 1,0)
The error locator polynomial coefficient calculator comprises:
Based on the algorithm, the extended field GF (2 ^m ) of the Galois field GF (2 )
When decoding the error correction code (m is a positive integer),
Determinant operation to determine the number of errors that have occurred, and
Determinant operation to find the coefficients of the error locator polynomial
Is performed, after performing a low-order determinant operation,
Multiple higher-order types that require the result of a lower-order determinant operation
An error correction device characterized by performing the determinant operations in parallel . 2. An input codeword is composed of an (N, N-8,9) Reed-Solomon code on an extended field GF (2 ^m ) (m is a positive integer) of a Galois field GF (2). The error locator polynomial coefficient calculator is a calculator that can arbitrarily select and calculate P + Q · R or P ² + Q · R when quadruple correcting the Reed-Solomon code based on the input syndrome. (· Indicates multiplication on GF (2 ^m ), + indicates addition on GF (2 ^m )), and performs determinant operations based on the order shown in (Table 1), (Table 2), and (Table 3). no rows, the error location polynomial _{^{X n + σ n-1 ·}} X n-1 + σ
_n− X ⁿ⁻² +… + σ ₁ × X + σ ₀ coefficient σ _i (i = n−1, n−2,…, 1,
0) error correction device according to claim 1, wherein calculating a. [Table 1] [Table 2] [Table 3] 3. An input codeword is composed of an (N, N-6,7) Reed-Solomon code on an extended field GF (2 ^m ) (m is a positive integer) of a Galois field GF (2). The error locator polynomial coefficient calculator is a calculator that can arbitrarily select and calculate P + Q · R or P ² + Q · R when the Reed-Solomon code is triple-corrected based on the input syndrome. (· Indicates multiplication on GF (2 ^m ), + indicates addition on GF (2 ^m )), and performs a determinant operation based on the order of (Table 4) to obtain an error locator polynomial X ⁿ + σ _n-1・ X ^n-1 + σ _n-2・ X ^n-2 +… + σ ₁・ X + σ ₀
Coefficients _{σ i (i = n-1} , n-2, ..., 1,0) error correction device according to claim 1, wherein the calculating of. [Table 4]