JPH1028059A - Method and device for euclid algorithm - Google Patents

Abstract

PROBLEM TO BE SOLVED: To reduce the operation quantity of a method and device for Euclid algorithm used for an error correction system, such as the BCH error correction system, Reed-Solomon error correction system, etc., for Galois field operation so that the processing speed can be increased. SOLUTION: Since the operating quantity of Galois field operation is reduced when polynominals B(z)=Sk-1 z<k-1> +Sk-2 z<k-2> +...S0 and M(z)=1 are initialized from a syndrome equation S(z)=Sk-1 z<k-1> +Sk-2 z<k-2> +...+S0 (where k is an integer of >0 and Sk-1 to S0 are elements on a Galois field) and polynominals A(z)= Sk-2 z<k-1> +Sk-3 z<k-2> +...+S0 z and L(z)=z are initialized by using the coefficient of the syndrome equation S(z), the processing speed of a method and device for Euclid algorithm can be increased.

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a method and an apparatus for Euclidean mutual exclusion used in error correction systems such as a BCH error correction system and a Reed-Solomon error correction system.

[0002]

2. Description of the Related Art In various fields such as recording media such as optical disks and digital transmission systems such as digital satellite broadcasting, error correction methods such as a BCH error correction method and a Reed-Solomon error correction method are used as error correction methods.

In an error correction method such as a BCH error correction method or a Reed-Solomon error correction method, first, a syndrome equation S (z) = S _K−1 z based on a received signal is received on the receiving side.
_{^{K-1 + S K-2}} z K-2 + ... + seek the S _0.

If there is no error in the signal, the coefficients S _{K-1 to} S _{0 of} the syndrome equation S (z) are given by S _K-1 = S _K-2 =
.. = S ₀ = 0, that is, the syndrome equation S (z) = 0
Becomes If there is an error in the signal, the syndrome equation S (z) ≠ 0.

When an error exists in the received signal and the syndrome equation S (z) ≠ 0, an error locator polynomial σ (z) is obtained from the syndrome equation S (z), and the error locator polynomial σ (z) is obtained. ) To correct the error.

In general, an Euclidean algorithm is used to obtain an error locator polynomial σ (z) from the syndrome equation S (z). Conventionally, the Euclidean mutual exchange method is described in Computer Architecture, 67-3 (September 16, 1987) "Error Correction Method and LS for Optical Disk Devices"
Described in "Development of I."

[0007] The following description is based on the Reed-Solomon error correction method based on the report of the Digital Broadcasting System Committee of the Telecommunications Technology Council. That is, the code generator polynomial: g (Z)
= (Z + α ⁰ ) (Z + α ¹ ) (Z + α ² )… (Z + α ¹⁵ ), (α = 02h), field generating polynomial: X ⁸ + X ⁴ + X ³ + X ² +1 , Packet length: 204 bytes,
The number of information bytes in the packet length is 188 bytes, and the number of error corrections is 8 bytes.

[0008] The above Reed-Solomon error-correcting Yuke
In the lid mutual exchange method, Reed-Solomon encoding is used.
Syndrome equation S (z) = S based on the obtained signal_Fifteenz^Fifteen
+ S ₁₄z^K14+ ... + S₀(S_Fifteen~ S₀Is the Galois body GF
(2⁸), The polynomials A (z), B (z), L
Initialize (z) and M (z) and perform Galois field arithmetic
To find the error locator polynomial σ (z). Galois body
About the algorithm of, edited by IEICE, Hideki Imai
It is described in Chapter 3 of "Coding Theory".

Hereinafter, a conventional Euclidean mutual division method will be described with reference to the drawings. FIG. 15 is a flowchart showing an initial setting method of a conventional Euclidean mutual exclusion method. FIG. 16 is a flowchart showing a general Euclidean mutual exchange method after initialization.

In a conventional Euclidean mutual exchange method,
Is a read solo model according to the initial setting method shown in FIG.
Syndrome equation S based on an encoded signal
(Z) = S _Fifteenz^Fifteen+ S₁₄z^K14+ ... + S₀(S_Fifteen~ S₀Is
Galois body GF (2⁸)) The polynomials A (z), B
(Z), L (z) and M (z) are initialized, and FIG.
General Euclidean mutual exchange method after initial setting shown in Fig. 6
Therefore, a Galois field operation is performed, and the error locator polynomial σ
Find (z). In Galois field arithmetic, the polynomials A (z),
A process for reducing the order of B (z) is performed. Polynomial A
If any of the orders of (z) and B (z) becomes 7th order or less
The process ends.

An example of the operation of the conventional Euclidean algorithm shown in FIGS. 15 and 16 will be described below.

(Equation 1) shows a first operation example of the conventional Euclidean algorithm. This calculation example is a case where coefficients S _{15 to} S ₈ ≠ 0 of the syndrome equation S (z). In this calculation example, an error locator polynomial σ (z) is obtained as a result of six Galois field calculations.

[0013]

(Equation 1)

(Equation 2) shows a second operation example of the conventional Euclidean algorithm. This calculation example is a case where the coefficient S ₁₅ ≠ 0 of the syndrome equation S (z) and at least one of S _{14 to} S ₈ is 0. In this calculation example, an error locator polynomial σ (z) is obtained as a result of four Galois field calculations.

[0015]

(Equation 2)

(Equation 3) shows a third operation example of the conventional Euclidean algorithm. This calculation example is a case where the coefficients S _{15 to} S _n = 0 and S _n-1 ≠ 0 of the syndrome equation S (z) (n ≦ 15; n is an integer). In this calculation example, an error locator polynomial σ (z) is obtained as a result of four Galois field calculations.

[0017]

(Equation 3)

As described above, the conventional Euclidean algorithm requires a large number of Galois field operations. This has hindered an increase in processing speed.

[0019]

As described above, the conventional Euclidean mutual division method requires a large number of Galois field operations, which hinders an increase in processing speed.

An object of the present invention is to solve the above-mentioned problems and to provide a method and an apparatus for Euclidean mutual exclusion which reduce the amount of Galois field operation and which can cope with an increase in processing speed.

[0021]

SUMMARY OF THE INVENTION The present invention in order to solve this problem, the syndrome equations S (z) = S k- 1 z k -1
+ S _k−2 z ^k−2 +... + S ₀ (k is an integer of k> 0, S _{k−1 to} S
₀ is an element on the Galois field) from the polynomials A (z), B (z),
Initialization of L (z) and M (z) is performed, Galois field operation is performed, and an Euclidean mutual division method for obtaining an error locator polynomial is performed.
S _k-1 z ^k-1 + S _k-2 z ^k-2 +... + S ₀ , M (z) = 1, and the polynomial A (z) = S _k-2 z by the coefficient of the syndrome equation S (z). _{^{k-1 + S k-3}} z k-2 + ... + S 0 z, L
This is a Euclidean algorithm in which (z) = z.

Further, the present invention uses the syndrome equation S
(Z) = S_k-1z^k-1+ S_k-2z^k-2+ ... + S₀And enter
And a polynomial storage device A, B, L, M, and a Galois field arithmetic unit.
And a polynomial storage device based on the syndrome equations
Initialization of A, B, L, M, and polynomial storage
Galois field using A, B, L, M and Galois field arithmetic unit
Euclidean algorithm that performs the operation and finds the error locator polynomial
At the initial setting, the polynomial storage device B
Polynomial B (z) = S_k-1z^k-1+ S_k-2z^k-2+ ... + S
₀And the polynomial M (z) = 1 in the polynomial storage device M
And the coefficient of the syndrome equation S (z)
The polynomial A (z) = S_k-2z^k-1+ S
_k-3z^k-2+ ... + S₀z is stored in a polynomial storage device L as a polynomial
Euclid, characterized by storing L (z) = z
It is a mutual exchange device.

Accordingly, the Euclidean mutual division method and apparatus according to the present invention can cope with an increase in processing speed because the amount of Galois field operation is reduced.

[0024]

First invention of the embodiment of the present invention is the syndrome equations S (z) = S k- 1 z k-1 + S k-2 z k -2 + ... + S
₀ , (k is an integer of k> 0, and S _{k-1 to} S ₀ are elements on the Galois field) from the polynomials A (z), B (z), L (z), M
Initialize (z), perform Galois field arithmetic,
In the Euclidean mutual division method for finding an error locator polynomial, the initial setting method is the polynomial B (z) = S _{k−1
^{z k-1 + S k-}} 2 z k-2 + ... + S 0, and M (z) = 1, the coefficient of the syndrome equations S (z), the polynomial _{A (z) = S k-} 2 z k- ¹ + S _k-3 z ^k-2 + ... + S ₀ z, L
This is a Euclidean mutual division method in which (z) = z is set, and the Euclidean mutual division can be executed by using the coefficient of the syndrome equation S (z). The number of Galois field operations required for performing the Euclidean mutual division is Since it is reduced, there is an effect that the processing speed can be increased.

According to a second aspect of the present invention, in the first aspect,
The initial setting method is the coefficient S of the syndrome equation S (z).
When _k-1 ~S _n = 0 and _{S n-1 ≠ 0 (n} ≦ k-1; n is an integer), the polynomial _{A (z) = S n-} 2 z k-1 + S n-3 z k- ² + ... +
S ₀ z ^{k−n + 1} , L (z) = z ^{k− n + 1} , and the Euclidean algorithm is used. The execution of the Euclidean algorithm is performed regardless of the coefficient of the syndrome equation S (z). This is possible, and the number of Galois field operations required for performing Euclidean mutual division is reduced, so that the processing speed can be increased.

According to a third aspect of the present invention, in the first aspect,
The initial setting method is the coefficient S of the syndrome equation S (z).
_{When k-1} = 0, the polynomial A (z) = z ^k , L (z) = 1
The Euclidean mutual exchange method is characterized in that Euclidean mutual exchange can be executed regardless of the coefficient of the syndrome equation S (z), and the Euclidean mutual execution can be performed by using the coefficient of the syndrome equation S (z). Since the number of required Galois field operations is reduced, the processing speed can be increased.

Further, the fourth invention provides a syndrome equation S
(Z) = S _k−1 z ^k−1 + S _k−2 z ^k−2 +... + S ₀ , and have polynomial storage units A, B, L, M and Galois field arithmetic unit, and syndrome equations Performs the initial setting of the polynomial storage devices A, B, L, and M, performs the Galois field operation using the polynomial storage devices A, B, L, and M and the Galois field arithmetic device, and obtains the Euclidean mutual multiplexing device for obtaining the error locator polynomial. At the time of initialization, the polynomial storage device B
Polynomial _{B (z) = S k-} 1 z k-1 + S k-2 z k-2 + ... + S 0,
The polynomial storage device M stores the polynomial expression M (z) = 1, and the polynomial storage device A stores the polynomial expression A (z) = S _k−2 z ^k−1 + S _k− by the coefficient of the syndrome equation S (z). ₃ z ^k-2 + ...
+ S ₀ z, a polynomial storage device L, which stores a polynomial L (z) = z. The Euclidean mutual elimination device is characterized in that Euclidean mutual exclusion can be performed by using a coefficient of a syndrome equation S (z). In addition, since the number of Galois field operations required to execute Euclidean mutual division is reduced, an effect is provided that the processing speed can be increased.

According to a fifth aspect of the present invention, in the fourth aspect,
At initialization, the coefficient S of the syndrome equation S (z)
_k-1 ~S _n = 0 and when _{S n-1 ≠ 0 (n} ≦ k-1; k is an integer), the polynomial storage device A, polynomial _{A (z) = S n-} 2 z
_{^{k-1 + S n-3}} z k-2 + ... + S 0 z kn +1, polynomial storage device L
In which the polynomial L (z) = z ^{k−n + 1} is stored, and the Euclidean algorithm can be executed regardless of the coefficients of the syndrome equation S (z). Since the number of Galois field operations required to execute Euclidean mutual division is reduced, the processing speed can be increased.

According to a sixth aspect of the present invention, in the fourth aspect,
At the time of initialization, at least the syndrome equation S
When the coefficient S _k−1 ≠ 0 of (z), the polynomial A (z) = z ^{k in} the polynomial storage device A, the polynomial L in the polynomial storage device L
(Z) = 1 is stored, and a syndrome equation S (z) is stored.
Irrespective of the coefficient of the Euclidean algorithm, the number of Galois field operations required for the execution of the Euclidean algorithm is reduced by the coefficient of the syndrome equation S (z), so that the processing speed can be increased. Have.

According to a seventh aspect of the present invention, in the fifth aspect,
The polynomial storage device A includes a register a_{k- 1}~ A₀With polynomial
The formula storage device B includes a register b_k-1~ B₀And the register dB
And a polynomial storage device L_i-1~ L₀(I is
i> 0), and the polynomial storage device M
m_j-1~ M₀(J> 0; j is an integer), and the register b
_k-1Monitor the register b_k-1Data stored in
A thin signal that outputs 0 as a monitoring signal if it is 0 and 1 if it is not 0
A drome monitoring device is provided.
_k-1~ A₀And the coefficients and constants of the syndrome equation S (z)
｛S_k-2, S_k-3, ..., S₀, 0} in register b_k-1~ B
₀To the coefficient ｛S of the syndrome equation S (z)_k-1,
S_k-2, ..., S₀、 Into the register l_v~ L_v-1To the constant ｛1,
0｝ to the register m_wTo the constant 1 and the register dB to the constant
(0 <v <i; 0 ≦ w <j; v and w are integers),
If the monitoring signal is 0, register until the monitoring signal becomes 1.
Ta_k-1~ A₀, B_k-1~ B₀The data to be stored
The subscript is shifted to the larger one, and the
Increments or decrements the value stored in the register dB.
Euclid mutual exchange device
The coefficient of the syndrome equation S (z)
It is possible to execute Euclidean mutual
Reduces the number of Galois field operations required to perform
Furthermore, since part of the first Galois field operation can be omitted,
It has the effect that it can respond to an increase in the processing speed.

According to an eighth aspect of the present invention, in the sixth aspect,
The polynomial storage device A includes registers a _{k to} a ₀ , the polynomial storage device B includes registers b _{k−1 to} b ₀ , and the polynomial storage device L includes registers l _{i−1 to} l ₀ (i >0; i is an integer), the polynomial storage device M has registers m _{j−1 to} m ₀ (j>0; j is an integer), monitors the coefficients of the syndrome equation S (z), and stores 0 or 1 A syndrome monitoring device which outputs a monitoring signal and sets the monitoring signal to 0 if at least the coefficient S _{k-1 of} the syndrome equation S (z) is 0 is provided. At initial setting, the syndrome equations are stored in registers b _{k-1 to} b _0. The coefficients {S _k−1 , S _k−2 ,..., S ₀ } of S (z) are
A constant 1 is input to the register m _w (0 ≦ w <j; w is an integer). If the monitoring signal is 0, constants {1,..., 0, 0} are stored in the registers a _{k to} a ₀ and a register l _v (0 ≦ v <i; v is an integer), and if the monitoring signal is 1, the coefficients of the syndrome equation S (z) and the constant ｛S _k− are stored in the registers a _{p to} a _{p-k + 1. 2, S k-3, ...} , S 0, 0} a (p = k or k-1), the constants {1,0} to register _{l q ~l q-1 (0} <q <i; q is In addition, the polynomial storage device A is provided with a register dA, and the syndrome monitoring device has at least one of the coefficients S _{k−1 to} S _{k / 2} of the syndrome equation S (z). If 0, the monitoring signal is set to 0; otherwise, 1 is set.
Then, input a constant e (e is an integer) to the register dA,
If the monitor signal is 1, a constant f (f ≠ e;
f is an integer), and a syndrome equation S (z)
Euclidean algorithm can be executed regardless of the coefficient, and when at least one of the coefficients S _{k−1 to} S _{k / 2} of the syndrome equation S (z) is 0, the Galois field operation required for executing the Euclidean algorithm is performed. Since the number of times is reduced and a part of the first Galois field operation can be omitted, an effect that the processing speed can be increased can be achieved.

Hereinafter, embodiments of the present invention will be described with reference to the drawings. It should be noted that the Euclidean mutual division method and apparatus of the present invention are not limited to the operation after the initial setting as shown in FIG.
The general Euclidean mutual exchange method after the initial setting shown in (1) can be applied. The feature of the Euclidean mutual exchange method and apparatus of the present invention resides in the initial setting method. Therefore, the initial setting method will be described in detail.
This is easily performed using the general Euclidean mutual exchange method after the initial setting shown in FIG.

(Embodiment 1) FIG. 1 is a flowchart showing an initial setting method of the Euclidean mutual exclusion method according to Embodiment 1 of the present invention.

In the Euclidean mutual division method according to the present embodiment, a syndrome equation S based on a Reed-Solomon encoded signal is set according to the initialization method shown in FIG.
(Z) = S ₁₅ z ¹⁵ + S ₁₄ z ^K14 +... + S ₀ , (S _{15 to} S ₀
Is an element on the Galois field GF (2 ⁸ )) from the polynomial A (z),
Initialization of B (z), L (z), and M (z) is performed, Galois field operation is performed according to a general Euclidean mutual division method after the initialization shown in FIG.
Find (z). In Galois field arithmetic, the polynomials A (z),
A process for reducing the order of B (z) is performed. Polynomial A
If the order of any of (z) and B (z) becomes equal to or lower than the seventh order, the process ends.

An example of the operation of the Euclidean mutual division method according to the present embodiment shown in FIGS. 1 and 16 will be described below.

(Equation 4) shows a first calculation example according to the present embodiment. This operation example uses the same syndrome equation as the first operation example of the method of the conventional example shown in (Equation 1).
That is, coefficients S _{15 to} S _{8 of} the syndrome equation S (z)
This is the case of 0.

[0037]

(Equation 4)

The polynomial A (z),
B (z), L (z) and M (z) are the first in the conventional method.
Polynomial A (z), after the first Galois field operation in the operation example of
B (z), L (z), and M (z). As a result, the number of Galois field operations required to obtain the error locator polynomial σ (z) is five, which is one less than the first operation example of the conventional example.

(Equation 5) shows a second operation example of the Euclidean mutual division method according to the present embodiment. This calculation example is given by (Equation 2)
The same syndrome equation as in the second operation example of the conventional example shown in FIG. That is, this is a case where the coefficient S ₁₅ ≠ 0 of the syndrome equation S (z) and at least one of S _{14 to} S ₈ is 0.

[0040]

(Equation 5)

The polynomials A (z),
B (z), L (z), and M (z) are polynomials A (z), B (z), L () after the first Galois field operation in the second operation example of the conventional Euclidean algorithm. z) and M (z). As a result, the number of Galois field operations required until the error locator polynomial σ (z) is obtained is one more than the second operation example of the conventional example
3 times less.

As described above, the Euclidean mutual division method of the present embodiment uses the coefficient S ₁₅ ≠ of the syndrome equation S (z).
Under the condition of 0, the Euclidean algorithm can be executed, and the number of Galois field operations required for executing the Euclidean algorithm is reduced. Under other conditions, execution of Euclidean mutual division is impossible, but an error exists in the received signal, that is, syndrome equation S (z) ≠ 0, and coefficient S ₁₅ = 0 of syndrome equation S (z). It is extremely rare that this condition is established, so there is no practical problem.

As described above, the Euclidean mutual division method of the present embodiment can execute Euclidean mutual division by the coefficient of the syndrome equation S (z), and reduces the number of Galois field operations required for performing Euclidean mutual division. Therefore, the processing speed can be increased.

Note that the Euclidean mutual division method of the present embodiment
The method uses the syndrome equation S (z) = S_k-1z^k-1+ S
_k-2z^k-2+ ... + S₀Coefficient S_k-1When ≠ 0, polynomial A
(Z) = S _k-2z^k-1+ S_k-3z^k-2+ ... + S₀z, L
Initialization of the polynomials A (z) and L (z) such that (z) = z
By doing so, the coefficient S of the syndrome equation S (z)
_k-1Execution of Euclidean algorithm under condition of ≠ 0
And reduce the number of Galois field operations required at that time.
But it is possible to use the syndrome equation S (z)
The condition of the coefficient need not be the above condition. For example,
Polynomial A regardless of the coefficients of the syndrome equation S (z)
(Z) = S_k-2z^k-1+ S_k-3z^k-2+ ... + S₀z, L
Initialization of the polynomials A (z) and L (z) such that (z) = z
Even if it does, the coefficient S of the syndrome equation S (z)_k-1
Euclidean algorithm can be executed under the condition of $ 0
And reduce the number of Galois field operations required at that time
It becomes possible.

The Euclidean mutual division method of this embodiment is as follows.
Syndrome equations _{S (z) = S k- 1} z k-1 + S k-2 z k-2
+... + S ₀ from the polynomials A (z), B (z), L (z),
In the Euclidean algorithm for initializing M (z) and performing a Galois field operation to obtain an error locator polynomial, the initial setting method is a polynomial B (z) = S _k−1 z ^k
−1 + S _k−2 z ^k−2 +... + S ₀ , M (z) = 1, and the polynomial A (z) = S by the coefficient of the syndrome equation S (z)
_By using the Euclidean mutual division method, which is a method of setting _k−2 z ^k−1 + S _k−3 z ^k−2 +... + S ₀ z and L (z) = z, by the coefficient of the syndrome equation S (z), The present invention enables the execution of Euclidean algorithm, reduces the number of Galois field operations required for the execution of Euclidean algorithm, and responds to an increase in processing speed.

(Embodiment 2) FIG. 2 is a flowchart showing the initial setting method of the Euclidean mutual exclusion method according to Embodiment 2 of the present invention.

In the Euclidean mutual division method according to the present embodiment, the syndrome equation S based on the Reed-Solomon encoded signal is set according to the initialization method shown in FIG.
(Z) = S ₁₅ z ¹⁵ + S ₁₄ z ^K14 +... + S ₀ , (S _{15 to} S ₀
Is an element on the Galois field GF (2 ⁸ )) from the polynomial A (z),
Initialization of B (z), L (z), and M (z) is performed, Galois field operation is performed according to a general Euclidean mutual division method after the initialization shown in FIG.
Find (z). In Galois field arithmetic, the polynomials A (z),
A process for reducing the order of B (z) is performed. Polynomial A
If the order of any of (z) and B (z) becomes equal to or lower than the seventh order, the process ends.

An example of the operation of the Euclidean mutual division method according to the present embodiment shown in FIGS. 2 and 16 will be described below.

(Equation 4) shown above is also a first operation example of the Euclidean mutual division method of the present embodiment. This calculation example uses the same syndrome equation as the first calculation example of the conventional example shown in (Equation 1). That is, the syndrome equation S
Is the case of the coefficient S ₁₅ ~S ₈ ≠ 0 in (z).

The polynomials A (z),
B (z), L (z), and M (z) are polynomials A (z), B after the first Galois field operation in the first operation example of the conventional example.
(Z), L (z), and M (z). as a result,
The number of Galois field operations required to obtain the error locator polynomial σ (z) is five, which is one less than the first operation example of the conventional example.

(Equation 5) shown above is a unit of this embodiment.
This is also the second operation example of the method for mutual algorithm. This calculation example
Is the same as the second operation example of the conventional example shown in (Equation 2).
The drome equation was used. That is, the syndrome equation S
Coefficient S of (z)_Fifteen$ 0 and S ₁₄~ S₈At least one of
One is 0.

The polynomial A (z),
B (z), L (z), and M (z) are polynomials A (z), B after the first Galois field operation in the second operation example of the conventional example.
(Z), L (z), and M (z). as a result,
The number of Galois field operations required to obtain the error locator polynomial σ (z) is three, one less than the second operation example of the conventional example.

(Equation 6) shows a third operation example of the Euclidean mutual division method according to the present embodiment. This calculation example is given by (Equation 3)
The same syndrome equation as in the third operation example of the conventional example shown in FIG. That is, this is the case where the coefficients S _{15 to} S _n = 0 and S _n-1 ≠ 0 of the syndrome equation S (z) (n ≦ 15; n is an integer).

[0054]

(Equation 6)

The polynomials A (z), after the initial setting in this operation example,
B (z), L (z), and M (z) are polynomials A (z), B after the first Galois field operation in the third operation example of the related art.
(Z), L (z), and M (z). as a result,
The number of Galois field computations until the error locator polynomial σ (z) is obtained is three, one less than the third computation example of the conventional example.

As described above, the Euclidean mutual division method of the present embodiment can execute Euclidean mutual division irrespective of the coefficient of the syndrome equation S (z), and performs the number of Galois field operations required for performing Euclidean mutual division. Therefore, the processing speed can be increased.

The Euclidean mutual division method of this embodiment is as follows.
Syndrome equation S (z) = S_{k- 1}z^k-1+ S_k-2z^k-2
+ ... + S₀From the polynomials A (z), B (z), L (z),
Initialize M (z) and perform Galois field arithmetic
The Euclidean algorithm for finding the error locator polynomial
And the initial setting method is a polynomial B (z) = S_k-1z^k
-1+ S_k-2z^k-2+ ... + S₀, M (z) = 1 and S_Fifteen~
S_n= 0 and S_n-1When ≠ 0 (n ≦ 15; n is an integer),
Term A (z) = S_n-2z^k-1+ S_n-3z^k-2+ ... + S ₀z
^{k-n + 1}, L (z) = z^{k-n + 1}, Otherwise, the polynomial A
(Z) = S_k-2z^k-1+ S_k-3z^k-2+ ... + S₀z, L
(Z) = z
By doing so, regardless of the coefficient of the syndrome equation S (z),
Enables the execution of Euclidean mutual
Reduces the number of Galois field operations required to perform
This corresponds to a higher speed.

(Embodiment 3) FIG. 3 is a flowchart showing an initial setting method of the Euclidean mutual exclusion method according to Embodiment 3 of the present invention.

In the Euclidean mutual division method according to the present embodiment, the syndrome equation S based on the Reed-Solomon encoded signal is set in accordance with the initialization method shown in FIG.
(Z) = S ₁₅ z ¹⁵ + S ₁₄ z ^K14 +... + S ₀ , (S _{15 to} S ₀
Is an element on the Galois field GF (2 ⁸ )) from the polynomial A (z),
Initialization of B (z), L (z), and M (z) is performed, Galois field operation is performed according to a general Euclidean mutual division method after the initialization shown in FIG.
Find (z). In Galois field arithmetic, the polynomials A (z),
A process for reducing the order of B (z) is performed. Polynomial A
If the order of any of (z) and B (z) becomes equal to or lower than the seventh order, the process ends.

An example of the operation of the Euclidean mutual division method according to the present embodiment shown in FIGS. 3 and 16 will be described below.

(Equation 4) shown above is also a first operation example of the Euclidean mutual division method of the present embodiment. This calculation example uses the same syndrome equation as the first calculation example of the conventional example shown in (Equation 1). That is, the syndrome equation S
Is the case of the coefficient S ₁₅ ~S ₈ ≠ 0 in (z).

The polynomials A (z),
B (z), L (z), and M (z) are polynomials A (z), B after the first Galois field operation in the first operation example of the conventional example.
(Z), L (z), and M (z). as a result,
The number of Galois field operations required to obtain the error locator polynomial σ (z) is five, which is one less than the first operation example of the conventional example.

(Equation 5) shown above is the unit of the present embodiment.
This is also the second operation example of the method for mutual algorithm. This calculation example
Is the same as the second operation example of the conventional example shown in (Equation 2).
The drome equation was used. That is, the syndrome equation S
Coefficient S of (z)_Fifteen$ 0 and S ₁₄~ S₈At least one of
One is 0.

The polynomials A (z),
B (z), L (z), and M (z) are polynomials A (z), B after the first Galois field operation in the second operation example of the conventional example.
(Z), L (z), and M (z). as a result,
The number of Galois field operations required to obtain the error locator polynomial σ (z) is three, one less than the second operation example of the conventional example.

Next, as (Equation 3) shown above, a third example of the Euclidean mutual division method of this embodiment will be described.
This calculation example uses the same syndrome equation as the third calculation example of the conventional example shown in (Equation 3). That is, this is the case where the coefficients S _{15 to} S _n = 0 and S _n-1 ≠ 0 of the syndrome equation S (z) (n ≦ 15; n is an integer). This calculation example is exactly the same as the third calculation example of the conventional example. As a result, the number of Galois field operations until the error locator polynomial σ (z) is obtained is exactly the same as in the third operation example of the conventional example.

As described above, in the Euclidean mutual division method according to the present embodiment, the number of Galois field operations may be smaller than that in the conventional example depending on the form of the syndrome.

[0067] However, because same as the number of conventional example of Galois field operation, the third coefficient S ₁₅ to S _n = 0 and S _n-1 ≠ syndrome equations S as in operation example (z)
0 (n ≦ 15; n is an integer) only, and in other cases, ie, S ₁₅ ≠ 0, Galois as shown in the first and second operation examples. The number of field operations is reduced.

As described above, the Euclidean mutual division method of the present embodiment can execute the Euclidean mutual division regardless of the coefficient of the syndrome equation S (z), and can perform the Euclidean mutual division by the coefficient of the syndrome equation S (z). Since the number of Galois field operations required for execution is reduced, the processing speed can be increased.

The Euclidean mutual division method of the present embodiment
The method uses the syndrome equation S (z) = S_k-1z^k-1+ S
_k-2z^k-2+ ... + S₀Coefficient S_k-1= 0, polynomial A
(Z) = z ^k, L (z) = 1, otherwise, the polynomial A
(Z) = S_k-2z^k-1+ S_k-3z^k-2+ ... + S₀z, L
Initialization of the polynomials A (z) and L (z) such that (z) = z
By doing so, the coefficient S of the syndrome equation S (z)
_k-1Execution of Euclidean algorithm under condition of ≠ 0
Reduced the number of Galois field operations required for
However, the condition of the coefficient of the syndrome equation S (z) is
The condition does not have to be satisfied. For example, the syndrome equation S
Coefficient S of (z)_k-1~ S_{k / 2}When at least one of is 0,
Polynomial A (z) = z^k, L (z) = 1, otherwise,
Polynomial, A (z) = S_{k -2}z^k-1+ S_k-3z^k-2+ ... + S₀
z, L (z) = Initial polynomials A (z), L (z) such that z
After setting, the coefficient S of the syndrome equation S (z)
_k-1~ S_{k / 2}Euclidean exchange under the condition of ≠ 0
Can reduce the number of Galois field operations required to execute
Becomes

The Euclidean mutual division method of the present embodiment is as follows.
Syndrome equations _{S (z) = S k- 1} z k-1 + S k-2 z k-2
+... + S ₀ from the polynomials A (z), B (z), L (z),
In the Euclidean algorithm for initializing M (z) and performing a Galois field operation to obtain an error locator polynomial, the initial setting method is a polynomial B (z) = S _k−1 z ^k
−1 + S _k−2 z ^k−2 +... + S ₀ , M (z) = 1, and the polynomial A (z) = S by the coefficient of the syndrome equation S (z)
_k−2 z ^k−1 + S _k−3 z ^k−2 +... + S ₀ z, which is a Euclidean mutual division method in which L (z) = z, and the initial setting method is at least the syndrome equation S (z when the coefficient S _k-1 = 0) of the polynomial ^{a (z) = z k,} L (z) = 1,
The Euclidean mutual exchange method is characterized in that the Euclidean mutual exchange method can be executed irrespective of the coefficient of the syndrome equation S (z), and the Euclidean mutual exchange method can be performed by the coefficient of the syndrome equation S (z). The number of Galois field operations required for execution is reduced, and the processing speed is increased.

(Embodiment 4) FIG. 4 is a block diagram showing a Euclidean mutual exchange apparatus according to Embodiment 4 of the present invention.

In FIG. 4, 0 to 15 indicate syndromes.
Equation S (z) = S_Fifteenz^Fifteen+ S₁₄z ^K14+ ... + S₀, (S
_Fifteen~ S₀Is the Galois field GF (2⁸) The coefficient S of the element above₀~ S
_FifteenIt is a syndrome showing. 17 is a monitoring signal
You. 50 inputs the syndrome 15, and the syndrome
If the value 15 is "0", the monitoring signal 17 is set to 0;
And a syndrome monitoring device that outputs a monitoring signal 17
is there. Numeral 60 performs Galois field arithmetic after initialization is completed.
Galois field arithmetic unit.

Reference numeral 100 denotes registers 101 to 116. When the monitoring signal 17 is 1 at the time of initialization, a value "0" is input to the register 101 and syndromes 0 to 14 are input to the registers 102 to 116, respectively. After setting,
This is a polynomial storage device that inputs and outputs data to and from the Galois field arithmetic unit 60.

Reference numeral 120 denotes registers 121 to 136. At the time of initialization, syndromes 0 to 15 are input to the registers 121 to 136, respectively.
This is a polynomial storage device that inputs and outputs data to and from the Galois field arithmetic unit 60.

Reference numeral 140 denotes registers 141 to 149. If the monitoring signal 17 is 1 at the time of initial setting, the values 141 and 142 are respectively stored in the registers 141, 142 and 143 to 149.
This is a polynomial storage device that inputs 0 ”,“ 1 ”, and“ 0 ”, and inputs and outputs data to and from the Galois field arithmetic unit 60 after initialization is completed.

Reference numeral 160 denotes a register 161 to 169. At the time of initial setting, the registers 160, 162 to 169
These are polynomial storage devices for inputting values "1" and "0", respectively, and inputting / outputting data to / from the Galois field arithmetic unit 60 after completion of initialization.

The operation of the thus configured Euclidean mutual exclusion apparatus of this embodiment will be described.

The Euclidean mutual exchange apparatus according to the present embodiment
Syndrome equations _{S (z) = S 15 z} 15 + S 14 z K14 +
... + the S ₀ and input. At initial setting, polynomial storage device 1
20 and 160, respectively, the polynomial B (z) = S ₁₅ z ¹⁵
+ S ₁₄ z ^K14 +... + S ₀ , and M (z) = 1 are stored. If the coefficient S ₁₅ ≠ 0 of the syndrome equation S (z), the polynomial storage devices 100 and 140 store the polynomial A (z) =
S ₁₄ z ¹⁵ + S ₁₃ z ¹⁴ +... + S ₀ z and L (z) = z are stored.

The polynomial storage devices 100, 120, 140,
160 stores the coefficients of the polynomial,
The polynomials A (z), B (z), L (z), and M (z) are stored. Registers 101, 121, 141, 1 respectively
61 is a polynomial A (z), B (z), L (z), M (z)
Is the position of the zero-order term of

After the initialization, the polynomial storage device 100,
Data is input and output between the Galois field arithmetic unit 120 and the Galois field arithmetic unit 60.
Performs Galois field arithmetic multiple times.

As a result, the polynomial storage device 140 or 1
60 stores the error locator polynomial σ (z).

The Euclidean mutual exchange device of the present embodiment
Since the initial setting method has a feature, an operation at the time of the initial setting will be described in detail below with reference to a calculation example.

A first operation example of the Euclidean algorithm according to the present embodiment will be described. This operation example uses the same syndrome equation as the first operation example of the conventional Euclidean mutual division method shown in (Equation 1). That is, this is the case where the coefficients S _{15 to} S ₈ ≠ 0 of the syndrome equation S (z).

Since the syndrome 15 has the value “85”, the syndrome monitoring device 50 outputs 1 as the monitoring signal 17. The polynomial storage device 120 stores the register 12
Syndromes 0 to 15 are input to 1 to 136, respectively, and the polynomial storage device 160 stores the registers 161, 162
To 169, values "1" and "0" are input, respectively.
Since the monitoring signal 17 is 1, the polynomial storage device 100
Are stored in the registers 101, 102 to 116, respectively.
The value “0” and the syndromes 0 to 14 are input, and the polynomial storage device 140 stores the registers 141, 142, 143 to 14.
9, values "0", "1", and "0" are input, respectively. At this time, the polynomial storage devices 100, 120, 140,
The state at 160 is shown in FIG. This completes the initial setting.

The polynomial storage device 1 after the initial setting of this operation example
Polynomial A stored in 00, 120, 140, 160
(Z), B (z), L (z), and M (z) are polynomials A after the first Galois field operation in the first operation example of the conventional method.
(Z), B (z), L (z), M (z).
As a result, the number of Galois field operations required to obtain the error locator polynomial σ (z) is five, which is one less than the first operation example of the conventional example.

A second operation example of the Euclidean algorithm device of the present embodiment will be described. In this calculation example, the same syndrome equation as that of the second calculation example of the conventional Euclidean mutual division method shown in (Equation 2) is used. That is, this is a case where the coefficient S ₁₅ ≠ 0 of the syndrome equation S (z) and at least one of S _{14 to} S ₈ is 0.

Since the value of the syndrome 15 is “9F”, the syndrome monitoring device 50 outputs 1 as the monitoring signal 17. The polynomial storage device 120 stores the register 12
Syndromes 0 to 15 are input to 1 to 136, respectively, and the polynomial storage device 160 stores the registers 161, 162
To 169, values "1" and "0" are input, respectively.
Since the monitoring signal 17 is 1, the polynomial storage device 100
Are stored in the registers 101, 102 to 116, respectively.
Input value “0” and syndromes 0 to 14
41, 142, and 143 to 149, respectively.
0 "," 1 ", and" 0 "are input, and the states of the polynomial storage devices 100, 120, 140, and 160 at this time are shown in Fig. 6. The initialization is completed.

The polynomial storage device 1 after the initial setting of this operation example
Polynomial A stored in 00, 120, 140, 160
(Z), B (z), L (z), M (z) are polynomials A (z), B (z) after the first Galois field operation in the second operation example of the conventional Euclidean algorithm. ), L (z), M
(Z). As a result, the error locator polynomial σ
The number of Galois field operations until (z) is obtained is three, one less than the second operation example of the conventional example.

As described above, the Euclidean mutual division apparatus according to the present embodiment uses the coefficient S ₁₅ ≠ of the syndrome equation S (z).
Under the condition of 0, the Euclidean algorithm can be executed, and the number of Galois field operations required for executing the Euclidean algorithm is reduced. Under other conditions, execution of Euclidean mutual division is impossible, but an error exists in the received signal, that is, syndrome equation S (z) ≠ 0, and coefficient S ₁₅ = 0 of syndrome equation S (z). It is extremely rare that this condition is established, so there is no practical problem.

As described above, the Euclidean algorithm according to the present embodiment can execute the Euclidean algorithm by the coefficient of the syndrome equation S (z), and the number of Galois field operations required to execute the Euclidean algorithm is reduced. Because it decreases
It can respond to high processing speed.

The Euclidean algorithm according to the present embodiment uses the syndrome equation S (z) = S _k−1 z ^k−1 + S
_When the coefficient S _k−1 ≠ 0 of _k−2 z ^k−2 +... + S ₀ , the polynomial storage device A stores the polynomial A (z) = S _k−2 z ^k−1 + S _k−3 z ^k−2 + ...
+ S ₀ z, the polynomial storage device L stores the polynomial L (z) = z,
, The Euclidean algorithm can be executed under the condition that the coefficient S _k-1の 0 of the syndrome equation S (z), and the number of Galois field operations required at that time can be reduced. But the syndrome equation S (z)
The condition of the coefficient may not be the above condition. For example,
Regardless of the coefficients of the syndrome equation S (z), the polynomial storage device A stores the polynomial A (z) = S _k−2 z ^{k −1} + S _k−3 z
^k−2 +... + S ₀ z, the polynomial L (z) is stored in the polynomial storage device L.
= Z, the coefficient S of the syndrome equation S (z) can be obtained even when the polynomial storage devices A and L are initialized.
The Euclidean algorithm can be executed under the condition of _k-1 ≠ 0, and the number of Galois field operations required at that time can be reduced.

The Euclidean mutual exchange apparatus of the present embodiment
Syndrome equations _{S (z) = S k- 1} z k-1 + S k-2 z k-2
+... + S ₀ as inputs, and polynomial storage devices A, B, L, M
And a Galois field arithmetic unit, and initializes the polynomial storage devices A, B, L, and M from the syndrome equations,
In a Euclidean mutual elimination device that performs Galois field arithmetic using the polynomial storage devices A, B, L, and M and a Galois field arithmetic device to obtain an error locator polynomial, the polynomial expression B (z) is stored in the polynomial storage device B during initialization. = S _k-1 z ^k-1 + S _k-2 z
^k−2 +... + S ₀ , the polynomial storage device M stores the polynomial M (z) =
1 is stored in the polynomial storage device A according to the coefficients of the syndrome equation S (z), and the polynomial A (z) = S _k−2 z ^k−1
+ S _k−3 z ^k−2 +... + S ₀ z, a polynomial storage device L stores a polynomial L (z) = z, and the syndrome equation S (z)
The execution of the Euclidean algorithm can be performed by the coefficient of, the number of Galois field operations required for the execution of the Euclidean algorithm can be reduced, and the processing speed can be increased.

(Embodiment 5) FIG. 7 is a block diagram showing a Euclidean mutual exchange apparatus according to Embodiment 5 of the present invention.

The Euclidean mutual exchange device according to the fifth embodiment includes:
The syndromes 0 to 15, the monitoring signal 17, and the Galois field arithmetic unit 60 have exactly the same configuration as that of the Euclidean mutual exclusion device of the fourth embodiment shown in FIG.

In FIG. 7, reference numeral 18 denotes a B (z) order. 19 is the B (z) highest order coefficient. 51 is B
(Z) This is a syndrome monitoring device that inputs the highest-order coefficient 19, sets the monitor signal 17 to 0 if the B (z) highest-order coefficient 19 is a value “0”, and sets the monitor signal 17 to 1 otherwise, and outputs the monitor signal 17.

Reference numeral 200 designates registers 201 to 206. At the time of initial setting, values "0" and syndromes 0 to 14 are inputted to the registers 201 to 216, respectively. The data stored in the registers 201 to 216 is shifted to the right (in the direction of larger numbers) until the value becomes 1, and after the initialization is completed, a polynomial storage device that inputs and outputs data to and from the Galois field arithmetic unit 60 is there.

Reference numeral 220 is provided with registers 221 to 236, a register 239, and an inverting device 238.
Is output to the syndrome monitoring device 51 as the B (z) highest order coefficient 19, and the data stored in the register 239 is inverted by the inverting device 238 to obtain the B (z).
Output as order 18 and register 221 at the time of initial setting.
~ 236,239, respectively, syndrome 0 ~ 1
5, if the value "0" is input and the monitoring signal 17 is 0, the data stored in the registers 201 to 216 is shifted rightward (in the direction of larger numbers) until the monitoring signal 17 becomes 1;
The value stored in the register 219 is incremented by the number of shifts, and after the initialization is completed, the Galois field arithmetic unit 60
And a polynomial storage device for inputting and outputting data to and from the storage device.

Reference numeral 240 designates registers 241 to 249, and the registers 241, 242, 243
To 249, the values "0", "1", and "0" are input. If the monitoring signal 17 is 0, the data stored in the registers 241 to 249 is shifted to the right (until the monitoring signal 17 becomes 1). To the larger number), and after the initial setting,
This is a polynomial storage device that inputs and outputs data to and from the Galois field arithmetic unit 60.

Reference numeral 260 designates registers 261 to 269, and the registers 261 and 262 to 269
, The values “1” and “0” are input to the
If 7 is 0, register 2 is used until monitor signal 17 becomes 1.
This is a polynomial storage device that shifts the data stored in 61 to 269 to the right (in the direction of larger numbers), and inputs and outputs data to and from the Galois field arithmetic unit 60 after the initialization is completed.

The operation of the thus configured Euclidean mutual exclusion apparatus of the present embodiment will be described.

The Euclidean mutual exchange apparatus according to the present embodiment
Syndrome equations _{S (z) = S 15 z} 15 + S 14 z K14 +
.. + S ₀ , (S _{15 to} S ₀ are elements on Galois field GF (2 ⁸ ))
Is input. At the time of initialization, the polynomial storage devices 220 and 2
60, the polynomial B (z) = S ₁₅ z ¹⁵ + S ₁₄ z
^K14 +... + S ₀ and M (z) = 1 are stored. Coefficient of the syndrome equations _{S (z) S 15 ~S n} = 0 and S _n-1 ≠ 0 _(n
≤15; n is an integer), the polynomial storage devices 200, 24
0, respectively, polynomial A (z) = S _n−2 z ¹⁵ + S _n−3 z
^{_{14 + ... + S 0 z 17}} -n, L (z) = z 17-n, if otherwise, the polynomial _{A (z) = S 14 z} 15 + S 13 z 14 + ... + S
₀ z, L (z) = z are stored.

The polynomial storage devices 200 and 240 store the coefficients of the polynomial, so that the polynomial A (z),
L (z) is stored. The registers 201,
Reference numeral 241 denotes the position of the zero-order term of the polynomials A (z) and L (z).

In the polynomial storage device 220, the internal registers 221 to 236 store the coefficients of the polynomial B (z), and the register 239 stores the position of the zero-order term of the polynomial B (z). (Z) is stored. Register 239
Are "0" to "15 (octal)", the registers 221 to 236 are the positions of the zero-order terms of the polynomial B (z).

In polynomial storage device 260, internal registers 261 to 269 store the coefficients of polynomial M (z), and register 239 in polynomial storage device 220 stores polynomial M (z).
By storing the position of the zero-order term of (z), the polynomial M
(Z) is stored. The value stored in the register 239 is "
In the case of 0 ”to“ 8 (octal) ”, each of the registers 261
269 is the position of the zero-order term of the polynomial B (z).

After the initialization is completed, the polynomial storage device 200,
Data input / output is performed between 220, 240, 260 and Galois field arithmetic unit 60, and the Galois field arithmetic unit performs Galois field arithmetic a plurality of times. As a result, the error locator polynomial σ (z) is stored in the polynomial storage device 240 or 260.

The Euclidean mutual exchange apparatus according to the present embodiment
Since the initial setting method has a feature, an operation at the time of the initial setting will be described in detail below with reference to a calculation example.

A first calculation example of the Euclidean mutual elimination apparatus of the present embodiment will be described. This calculation example uses the same syndrome equation as the first calculation example of the conventional example shown in (Equation 1). That is, this is the case where the coefficients S _{15 to} S ₈ ≠ 0 of the syndrome equation S (z).

First, the polynomial storage device 200 inputs the value “0” and the syndromes 0 to 14 to the registers 201, 202 to 216, respectively.
The syndromes 0 to 15 and the value “0” are input to the registers 221 to 236 and 239, respectively.
40 is stored in registers 241, 242, 243-249,
The values “0”, “1”, and “0” are input, respectively, and the polynomial storage device 260 stores the registers 261, 262 to 269,
279, the values "1", "0", and "0" are input, respectively. The B (z) highest order coefficient 19 has a value “85”.

Since the B (z) highest order coefficient 19 has the value “85”, the syndrome monitoring device 51
Is output as 1. Since the monitor signal 17 is 1, the shift and increment operations are not performed.

At this time, the polynomial storage devices 200, 220,
FIG. 8 shows the states of 240 and 260. This completes the initial setting.

The polynomial storage device 2 after the initialization in this operation example
Polynomial A stored in 00, 220, 240, 260
(Z), B (z), L (z), and M (z) are polynomials A after the first Galois field operation in the first operation example of the conventional method.
(Z), B (z), L (z), M (z).
As a result, the number of Galois field operations required to obtain the error locator polynomial σ (z) is five, which is one less than the first operation example of the conventional example.

The B (z) highest order coefficient 19 has a value “85” which is the coefficient of the highest order term of the polynomial B (z). Further, the B (z) degree 18 is represented by a polynomial B (z)
Is a value “15 (octal)” which is the order of These B (z) highest order coefficient 19 and B (z) order 18 are
As shown in the flowchart of the general Euclidean mutual division method after the initial setting in FIG. 16, since it can be used as it is in the first Galois field calculation, the amount of calculation in the first Galois field calculation is reduced.

A second operation example of the Euclidean algorithm according to the present embodiment will be described. In this calculation example, the same syndrome equation as that of the second calculation example of the conventional Euclidean mutual division method shown in (Equation 2) is used. That is, this is a case where the coefficient S ₁₅ ≠ 0 of the syndrome equation S (z) and at least one of S _{14 to} S ₈ is 0.

First, the polynomial storage device 200 inputs the value “0” and the syndromes 0 to 14 to the registers 201 and 202 to 216, respectively.
The syndromes 0 to 15 and the value “0” are input to the registers 221 to 236 and 239, respectively.
40 is stored in registers 241, 242, 243-249,
The values “0”, “1”, and “0” are input, respectively, and the polynomial storage device 260 stores the registers 261, 262 to 269
, The values “1” and “0” are input, respectively. B (z)
The highest order coefficient 19 has a value “9F”.

Since the B (z) highest order coefficient 19 has the value “9F”, the syndrome monitoring device 51
Is output as 1. Since the monitor signal 17 is 1, the shift and increment operations are not performed.

At this time, the polynomial storage devices 200, 220,
The state of 240 and 260 is shown in FIG. This completes the initial setting.

The polynomial storage device 2 after the initialization in this operation example
Polynomial A stored in 00, 220, 240, 260
(Z), B (z), L (z), M (z) are polynomials A (z), B (z) after the first Galois field operation in the second operation example of the conventional Euclidean algorithm. ), L (z), M
(Z). As a result, the error locator polynomial σ
The number of Galois field operations until (z) is obtained is three, one less than the second operation example of the conventional Euclidean algorithm.

The B (z) highest order coefficient 19 has a value “9F” which is the coefficient of the highest order term of the polynomial B (z). Further, the B (z) degree 18 is represented by a polynomial B (z)
Is a value “15 (octal)” which is the order of These B (z) highest order coefficient 19 and B (z) order 18 are
As shown in the flowchart of the general Euclidean mutual division method after the initial setting in FIG. 16, since it can be used as it is in the first Galois field calculation, the amount of calculation in the first Galois field calculation is reduced.

A third calculation example of the Euclidean mutual elimination apparatus of the present embodiment will be described. In this calculation example, the same syndrome equation as that of the third calculation example of the conventional Euclidean mutual division method shown in (Equation 3) is used. That is, this is the case where the coefficients S _{15 to} S _n = 0 and S _n-1 ≠ 0 of the syndrome equation S (z) (n ≦ 15; n is an integer).

First, the polynomial storage device 200 inputs the value “0” and the syndromes 0 to 14 to the registers 201, 202 to 216, respectively.
The syndromes 0 to 15 and the value “0” are input to the registers 221 to 236 and 239, respectively.
40 is stored in registers 241, 242, 243-249,
The values “0”, “1”, and “0” are input, respectively, and the polynomial storage device 260 stores the registers 261, 262 to 269
, The values “1”, “0”, and “0” are input, respectively.
The B (z) highest order coefficient 19 has a value “0”. FIG. 10A shows the states of the polynomial storage devices 200, 220, 240, and 260 at this time.

Since the B (z) highest order coefficient 19 has the value “0”, the syndrome monitoring device 51 outputs “0” as the monitoring signal 17. Since the monitoring signal 17 is 0, the polynomial storage devices 200, 220, 240, and 260 store the registers 201 to 21 until the monitoring signal 17 becomes 1, respectively.
6,221 to 236,241 to 249,261 to 269
Is shifted rightward (in the direction of larger numbers). When the value “FE” is stored in the register 221, the B (z) highest order coefficient 19 becomes the value “FE”, and the syndrome monitoring device 51 outputs 1 as the monitoring signal 17. The polynomial storage devices 200, 220, 24 at this time
The state of 0,260 is shown in FIG. This completes the initial setting.

The polynomial storage device 2 after the initialization in this operation example
Polynomial A stored in 00, 220, 240, 260
(Z), B (z), L (z), M (z) are polynomials A (z), B (z) after the first Galois field operation in the third operation example of the conventional Euclidean mutual division method. ), L (z), M
(Z). As a result, the error locator polynomial σ
The number of Galois field operations required to obtain (z) is three, which is one less than the third operation example of the conventional Euclidean algorithm.

The B (z) highest order coefficient 19 has a value "FE" which is the coefficient of the highest order term of the polynomial B (z). Further, the B (z) degree 18 is represented by a polynomial B (z)
Is "13", which is the order of.

These B (z) highest order coefficients 19 and B
(Z) The degree 18 is 1 as shown in the flowchart of the general Euclidean mutual division method after the initial setting in FIG.
Since it can be used as it is in the first Galois field calculation, the amount of calculation in the first Galois field calculation is reduced.

As described above, the Euclidean algorithm according to the present embodiment can execute Euclidean algorithm irrespective of the coefficient of the syndrome equation S (z), and the number of Galois field operations required for executing Euclidean algorithm is performed. And the amount of calculation in the first Galois field calculation is reduced, so that the processing speed can be increased.

In the Euclidean mutual division apparatus of the present embodiment, the register 239 stores the polynomials B (z) and M (z)
Although the position of the zero-order term is stored, the position of another order term may be stored. Further, the order of the coefficient stored in a certain register may be stored.

In the polynomial storage device 240, the coefficient of the zero-order term of the polynomial L (z) is stored in the register 241; however, another register may store it.

In the polynomial storage device 260, the position of the zeroth-order term of the polynomial M (z) is stored in the register 239 inside the polynomial storage device 220, but the position of the zeroth-order item may be fixed.

The Euclidean mutual exchange apparatus according to the present embodiment
Syndrome process S (z) = S_k-1z^k-1+ S_k-2z^k-2+
… + S₀, And the polynomial storage devices A, B, L, M
And a Galois field arithmetic unit.
Initialize the polynomial storage devices A, B, L, and M,
Polynomial storage devices A, B, L, M and Galois field arithmetic unit
Performs Galois field operation to find error locator polynomial
In the Euclidean algorithm, the polynomial
In the storage device B, a polynomial B (z) = S_k-1z^k-1+ S _k-2z
^k-2+ ... + S₀, The polynomial storage device M stores the polynomial M (z) =
1 and the coefficient S of the syndrome equation S (z)_k-1
~ S_n= 0 and S_n-1When ≠ 0 (n ≦ k−1; k is an integer
Number), the polynomial storage device A stores the polynomial A (z) = S_n-2z
^k-1+ S_n-3z^k-2+ ... + S₀z^{k-n + 1}, Polynomial storage device L
Where the polynomial L (z) = z^{k-n + 1}And store the other
At time, the polynomial storage device A stores the polynomial A (z) = S_k-2z^k-1
+ S_k-3z^k-2+ ... + S₀z, a polynomial in the polynomial storage device L
The equation L (z) = z is stored.
By using a decimation unit, the syndrome equation S (z)
Enables the execution of Euclidean algorithm regardless of the coefficient of
The number of Galois field operations required to perform Euclidean mutual
This corresponds to reduction of the processing speed.

Further, the polynomial storage device A includes a register a
_{k−1 to} a ₀ , and the polynomial storage device B stores the register b _k−1
~b comprising a ₀ and register dB, the polynomial storage device L is provided with a register _{l i-1 ~l 0 (i} >0; i is an integer), the polynomial storage device M, the register m _j-1 ~m ₀ Provision (j>0; j
Is an integer), to monitor the register b _k-1, 1 if other than the register b if _k-1 data stored in the 0 0,0 comprises a syndrome monitoring device for output as a monitor signal, during initialization, register The syndrome equation S is given by a _{k-1 to} a ₀
Factor (z) and a constant _{{S k-2, S k} -3, ..., S 0, 0}
Is stored in the registers b _{k−1 to} b ₀ as a syndrome equation S (z).
{S _k−1 , S _k−2 ,..., S ₀ } in the registers l _{v to} l
Input a constant {1, 0} to _v-1 , a constant 1 to the register _mw, and a constant to the register dB (0 <v <i; 0 ≦ w <j;
v and w are integers). If the monitoring signal is ₀ , the data stored in the registers a _{k-1 to} a ₀ and b _{k-1 to} b ₀ are stored in the larger subscript until the monitoring signal becomes 1. And the value stored in the register dB is incremented or decremented by the number of shifts, thereby reducing the amount of operation in the first Galois field operation and increasing the processing speed It corresponds to.

(Embodiment 6) FIG. 11 is a block diagram showing a Euclidean mutual exchange apparatus according to Embodiment 6 of the present invention.

The Euclidean mutual exchange device of the sixth embodiment is
The syndromes 0 to 15, the monitoring signal 17, and the Galois field arithmetic unit 60 have exactly the same configuration as that of the Euclidean mutual exchange apparatus of the fourth embodiment shown in FIG.

In FIG. 11, reference numeral 20 denotes the A (z) order. 21 is the A (z) highest order coefficient. 52 is
Enter syndromes 8-15, and enter syndromes 8-15
Is a syndrome monitoring device that outputs the monitoring signal 17 as 0 if at least one of the values is “0”, and 1 otherwise.

Reference numeral 300 denotes a register 300 composed of registers 301 to 317 and a register 319. The data stored in the register 317 is output as the A (z) highest-order coefficient 21. The data stored in the register 319 is converted to the A (z) order 20. When the monitoring signal 17 is 0 at the time of the initial setting, the values "" are respectively stored in the registers 301 to 316, 317 and 319.
0 ”,“ 1 ”,“ 16 (octal) ”, and the monitoring signal 17 is 1
Then, the registers 301, 302, 303 to 317, 3
19, the values “0”, “0”, and syndrome 0, respectively.
This is a polynomial storage device which inputs .about.14, value "15 (octal)", and inputs and outputs data to and from the Galois field arithmetic unit 60 after the initialization is completed.

Reference numeral 320 designates registers 321 to 336. At the time of initial setting, the syndromes 0 to 15 are input to the registers 321 to 336, respectively, and after completion of the initial setting, data is exchanged with the Galois field arithmetic unit 60. It is a polynomial storage device that performs input and output.

340 is composed of registers 341 to 349. At the time of initial setting, if the monitor signal 17 is 0, a value "0" is inputted to the registers 341 to 349. If the monitor signal 17 is 1, the register 341 and 341 are inputted. 342, 343-349
Is a polynomial storage device that inputs and outputs values "0", "1", and "0", respectively, and inputs and outputs data to and from the Galois field arithmetic unit 60 after completion of initialization.

Reference numeral 360 denotes registers 361 to 369, which are initially set to registers 361, 362 to 369.
These are polynomial storage devices for inputting values "1" and "0", respectively, and inputting / outputting data to / from the Galois field arithmetic unit 60 after completion of initialization.

The operation of the thus configured Euclidean mutual exclusion apparatus of the present embodiment will be described.

The Euclidean mutual exchange device of the present embodiment
Syndrome equations _{S (z) = S 15 z} 15 + S 14 z K14 +
.. + S ₀ , (S _{15 to} S ₀ are elements on Galois field GF (2 ⁸ ))
Is input. At the time of initialization, the polynomial storage devices 320 and 3
60, the polynomial B (z) = S ₁₅ z ¹⁵ + S ₁₄ z
^K14 +... + S ₀ and M (z) = 1 are stored. If at least one of the coefficients S _{15 to} S ₈ of the syndrome equation S (z) is 0, the polynomial storage devices 300 and 340 respectively store
The polynomial ^{A (z) = z 16,} L (z) = 0, if otherwise, the polynomial _{A (z) = S 14 z} 15 + S 13 z 14 + ... + S
₀ z, L (z) = z are stored.

The polynomial storage devices 320, 340, 360
Stores the coefficients of the polynomial, thereby storing the polynomials B (z), L (z), and M (z), respectively. Respectively,
Registers 321, 341 and 361 are polynomials B (z) and L
(Z), the position of the zero-order term of M (z). In the polynomial storage device 300, the registers 301 to 317 internally store the coefficients of the polynomial A (z), and the register 319 stores the order of the coefficients stored in the register 317, thereby storing the polynomial A (z). . The value stored in the register 319 is "
In the case of "15 (octal)" and "16 (octal)", the register 317
Are 15th order and 16th order, respectively. After the initialization, the polynomial storage devices 300 and 32
Data is input / output between 0, 340, 360 and the Galois field arithmetic unit 60, and the Galois field arithmetic unit performs Galois field arithmetic a plurality of times. As a result, the polynomial storage device 3
Error location polynomial σ (z) is stored in 40 or 360.

The Euclidean mutual exchange apparatus of the present embodiment
Since the initial setting method has a feature, an operation at the time of the initial setting will be described in detail below with reference to a calculation example.

A first calculation example of the Euclidean mutual elimination apparatus of the present embodiment will be described. This operation example uses the same syndrome equation as the first operation example of the conventional Euclidean mutual division method shown in (Equation 1). That is, this is the case where the coefficients S _{15 to} S ₈ ≠ 0 of the syndrome equation S (z).

Since all of the syndromes 8 to 15 have values other than “0”, the syndrome monitoring device 52 outputs the monitoring signal 1
1 is output as 7. The polynomial storage device 320 inputs syndromes 0 to 15 to the registers 321 to 336, and the polynomial storage device 360 stores the registers 361 and 362
To 369, the values "1" and "0" are input, respectively.
Since the monitoring signal 17 is 1, the polynomial storage device 300
Are registers 301, 302, 303 to 317, 319
, The values “0”, “0”, and the syndromes S0 to S0, respectively.
S14, The value “15 (octal)” is input, and the storage device 340 is input.
Inputs the values "0", "1", and "0" to the registers 341, 342, and 343 to 349, respectively. The state of the polynomial storage devices 300, 320, 340, 360 at this time is shown in FIG. This completes the initial setting.

The polynomial storage device 3 after the initialization in this operation example
Polynomial A stored in 00, 320, 340, 360
(Z), B (z), L (z), M (z) are polynomials A (z), B (z) after the first Galois field operation in the first operation example of the conventional Euclidean algorithm. ), L (z), M
(Z). As a result, the error locator polynomial σ
The number of Galois field operations until (z) is obtained is five, one less than the first operation example of the conventional Euclidean algorithm.

The A (z) highest order coefficient 20 is a value “EB” which is the coefficient of the highest order term of the polynomial A (z). Further, the B (z) degree 18 is represented by a polynomial B (z)
Is a value “15 (octal)” which is the order of These B (z) highest order coefficient 19 and B (z) order 18 are
As shown in the flowchart of the general Euclidean mutual division method after the initial setting in FIG. 16, since it can be used as it is in the first Galois field calculation, the amount of calculation in the first Galois field calculation is reduced.

A description will be given of a second operation example of the Euclidean algorithm device according to the present embodiment. In this calculation example, the same syndrome equation as that of the second calculation example of the conventional Euclidean mutual division method shown in (Equation 2) is used. That is, this is a case where the coefficient S ₁₅ ≠ 0 of the syndrome equation S (z) and at least one of S _{14 to} S ₈ is 0.

Since the syndromes 13 and 14 have the value “0”, the syndrome monitoring device 52
Is output as 0. The polynomial storage device 320 inputs the syndromes 0 to 15 to the registers 321 to 336,
The polynomial storage device 360 includes registers 361, 362-3
69, the values “1” and “0” are input, respectively.

Since the monitoring signal 17 is 0, the polynomial storage device 300 stores the registers 301 to 316, 317, 31
9, values "0", "1", "16 (octal)"
And the storage device 340 stores the registers 341 to 349
Is input the value "0". The polynomial storage device 30 at this time
The states of 0, 320, 340, 360 are shown in FIG. This completes the initial setting.

The polynomial storage device 3 after the initial setting of this operation example
Polynomial A stored in 00, 320, 340, 360
(Z), B (z), L (z), M (z) are polynomials A (z), B (z), L () after the initial setting of the second operation example of the conventional Euclidean mutual division method. z) and M (z). As a result, the number of Galois field operations until the error locator polynomial σ (z) is obtained is four, which is the same as in the second operation example of the conventional method.

The A (z) highest-order coefficient 20 has a value “1” which is the coefficient of the highest-order term of the polynomial A (z). Further, the B (z) order 18 is a value “16 (octal)” which is the order of the polynomial B (z). These B
(Z) The highest order coefficient 19 and the B (z) order 18 can be used as they are in the first Galois field operation as shown in the flowchart of the general Euclidean mutual division method after the initial setting in FIG. (1) The amount of calculation in the first Galois field calculation is reduced.

A third operation example of the Euclidean mutual elimination apparatus according to the present embodiment will be described. In this calculation example, the same syndrome equation as that of the third calculation example of the conventional Euclidean mutual division method shown in (Equation 3) is used. That is, this is the case where the coefficients S _{15 to} S _n = 0 and S _n-1 ≠ 0 of the syndrome equation S (z) (n ≦ 15; n is an integer).

Since the syndromes 14 and 15 have the value “0”, the syndrome monitoring device 52
Is output as 0. The polynomial storage device 320 inputs the syndromes 0 to 15 to the registers 321 to 336,
The polynomial storage device 360 includes registers 361, 362-3
69, the values “1” and “0” are input, respectively. Since the monitoring signal 17 is 0, the polynomial storage device 300 stores the value "" in the registers 301 to 316, 317, and 319.
0 ”,“ 1 ”, and“ 16 (octal) ”are input to the storage device 3
40 inputs the value “0” to the registers 341 to 349. At this time, the polynomial storage devices 300, 320, 340,
The state of 360 is shown in FIG. This completes the initial setting.

The polynomial storage device 3 after the initialization in this operation example
Polynomial A stored in 00, 320, 340, 360
(Z), B (z), L (z), M (z) are polynomials A (z), B (z), L () after the initial setting of the third operation example of the conventional Euclidean algorithm. z) and M (z). As a result, the number of Galois field operations until the error locator polynomial σ (z) is obtained is the same four times as in the third operation example of the method of the conventional example.

The A (z) highest order coefficient 20 has a value “1” which is the coefficient of the highest order term of the polynomial A (z). Further, the B (z) order 18 is a value “16 (octal)” which is the order of the polynomial B (z). These B
(Z) The highest order coefficient 19 and the B (z) order 18 can be used as they are in the first Galois field operation as shown in the flowchart of the general Euclidean mutual division method after the initial setting in FIG. (1) The amount of calculation in the first Galois field calculation is reduced.

As described above, in the Euclidean mutual division method according to the sixth embodiment of the present invention, the number of Galois field operations may be the same as in the conventional example or reduced depending on the form of the syndrome.

However, the case where the number of Galois field operations is the same as that of the conventional example is that the coefficients S ₁₅ to S ₁₅ of the syndrome equation S (z) are different from those of the second and third operation examples.
Only in the special case where at least one of S ₈ is 0, and in other cases, that is, when S _{15 to} S ₈ ≠ 0, the first
The number of Galois field operations is reduced as shown in the example of the operation.

As described above, the Euclidean algorithm of the present embodiment can execute the Euclidean algorithm regardless of the coefficient of the syndrome equation S (z). , The number of Galois field operations required for the execution is reduced, and the amount of calculation in the first Galois field operation is reduced irrespective of the coefficient of the syndrome equation S (z), so that the processing speed can be increased.

Although the register 319 stores the order of the coefficient stored in the register 317 in the Euclidean mutual exchange apparatus of the present embodiment, the register 319 may store the order of the data stored in another register. Further, the position of a term of a certain degree in the polynomial may be stored.

In the polynomial storage devices 340 and 341, the coefficient of the zero-order term of the polynomial is stored in the register 3
01 and 341 are stored, but another register may store them.

In the polynomial storage device 300, the register 301 or 302 stores the coefficient of the zero-order term of the polynomial A (z), so that the data stored in the register 317 is stored in the A (z) highest-order coefficient 21. However, the polynomial A (z)
Register 301 for storing the coefficient of the zero-order term of
And the data stored in the register 317 or 316 may be the A (z) highest order coefficient 21.

The Euclidean mutual eliminator of the present embodiment sets the polynomials A and L as initial settings when the coefficients S _{k−1 to} S _{k / 2} = 0 of the syndrome equation S (z). (Z) = z ^k , L (z) = 1, otherwise, the polynomial A (z) = S _k−2 z ^k−1 + S _k−3 z ^k−2 +... + S ₀ z,
By storing L (z) = z, the syndrome equation S
Euclidean mutual execution can be performed regardless of the coefficient of (z), and the coefficients S _{k−1 to} S _{k / 2 of the} syndrome equation S (z)
It is possible to reduce the number of Galois field operations required to execute Euclidean mutual division under the condition of ≠ 0, and to reduce the amount of operation in the first Galois field operation regardless of the coefficient of the syndrome equation S (z). However, the condition of the coefficient of the syndrome equation S (z) does not have to be the above condition. For example, the coefficient S _{k-1 of} the syndrome equation S (z)
= 0, polynomial A (z) = z ^k , L (z) = 1, otherwise, polynomial A (z) = S _k−2 z ^k−1 + S _k−3 z ^k−2 +
.. + S ₀ z, L (z) = z, the Euclidean algorithm can be executed regardless of the coefficient of the syndrome equation S (z), and the coefficient S of the syndrome equation S (z) can be executed.
It is possible to reduce the number of Galois field operations required for performing Euclidean mutual exchange under the condition that _k-1 ≠ 0.

When at least one of the coefficients S _{k−1 to} S ₀ of the syndrome equation S (z) is 0, the polynomial A
(Z) = z ^k , L (z) = 1, otherwise, polynomial A
(Z) = S _k−2 z ^k−1 + S _k−3 z ^k−2 +... + S ₀ z, L
If (z) = z is stored, the syndrome equation S (z)
Euclidean mutual exclusion can be performed regardless of the coefficient of the syndromes, and the coefficients S _{k−1 to} S ₀ ≠ 0 of the syndrome equation S (z)
The number of Galois field operations required to perform Euclidean mutual exchange under the condition
Regardless of the coefficient of (z), the amount of calculation in the first Galois field calculation can be reduced.

The Euclidean mutual exchange device of the present embodiment
Syndrome equations _{S (z) = S k- 1} z k-1 + S k-2 z k-2
+... + S ₀ as inputs, and polynomial storage devices A, B, L, M
And a Galois field arithmetic unit, and initializes the polynomial storage devices A, B, L, and M from the syndrome equations,
In a Euclidean mutual elimination device that performs Galois field arithmetic using the polynomial storage devices A, B, L, and M and a Galois field arithmetic device to obtain an error locator polynomial, the polynomial expression B (z) is stored in the polynomial storage device B during initialization. = S _k-1 z ^k-1 + S _k-2 z
^k−2 +... + S ₀ , the polynomial storage device M stores the polynomial M (z) =
1 is stored in the polynomial storage device A according to the coefficients of the syndrome equation S (z), and the polynomial A (z) = S _k−2 z ^k−1
+ S _k−3 z ^k−2 +... + S ₀ z, a polynomial storage device L storing a polynomial L (z) = z, and a coefficient S of a syndrome equation S (z). _{When K-1} = 0, the polynomial A (z) is stored in the polynomial storage device A.
= Z ^k , the polynomial storage device L stores the polynomial L (z) = 1, so that the Euclidean algorithm can be executed regardless of the coefficient of the syndrome equation S (z). Thus, the number of Galois field operations required for executing Euclidean mutual division is reduced by the coefficient of the syndrome equation S (z), and the processing speed is increased.

Further, the polynomial storage device A includes a register a
_k~ A₀And the polynomial storage device B includes a register b_k-1~
b₀And the polynomial storage device L has a register l_i-1~ L₀
(I> 0; i is an integer), and the polynomial storage device M
Jista m_j-1~ M₀(J> 0; j is an integer), and
Monitor the coefficient of the ROHM equation S (z) and use the syndrome method
According to the coefficient of the equation S (z), 0 or 1 is used as a monitoring signal.
Equipped with a syndrome monitoring device that outputs
And register b_k-1~ B₀The syndrome equation S (z)
Coefficient ｛S_k-1, S_k-2, ..., S₀｝ To register m_wFixed
Enter Equation 1 (0 ≦ w <j; w is an integer) and set the monitoring signal to 0
Then register a_k~ A₀To the constant {1, ..., 0,0}
To register l_vAnd enter a constant 0 (0 ≦ v <i; v is
Integer), if the monitoring signal is 1, register a_p~ A_{p-k + 1}To
Coefficient and constant of syndrome equation S (z) ｛S_k-2, S
_k-3, ..., S₀, 0} (p = k or k-1),
Ta_q~ L _q-1With the constant {1,0} (0 <q <i; q is an integer
Number) with the Euclidean mutual exchange device characterized by inputting
The polynomial storage device A has a register dA,
The drome monitoring device is used to calculate the syndrome equation S (z).
Number S_k-1~ S_{k / 2}If at least one of them is 0
0, otherwise, 1
Then, input a constant e (e is an integer) to the register dA,
If the monitor signal is 1, a constant f (f ≠ e;
f is an integer).
In the first Galois field operation,
It is designed to reduce the amount of computation and increase the processing speed.
You.

In the embodiment of the present invention, the description has been given of the Reed-Solomon error correction system based on the report of the Digital Broadcasting System Committee of the Telecommunications Technology Council. However, the present invention does not apply to BCH
The present invention relates to a Euclidean algorithm and an Euclidean algorithm used in an error correction method such as an error correction method and a Reed-Solomon error correction method, wherein a syndrome equation S (z) = S
_k−1 z ^k−1 + S _k−2 z ^k−2 +... + S ₀ from the polynomial A (z),
Initialization of B (z), L (z), and M (z) is performed, and Galois field arithmetic is performed to obtain an error locator polynomial.
_{(Z) = S k-1} z k-1 + S k-2 z k-2 + ... + S 0, M (z)
= 1, the coefficient of the syndrome equation S (z) gives
(Z) = S _k−2 z ^k−1 + S _k−3 z ^k−2 +... + S ₀ z, L
The Euclidean mutual division method in which (z) = z or the syndrome equation S (z) = S _k−1 z ^k−1 + S
_k−2 z ^k−2 +... + S ₀ are input, and the polynomial storage devices A,
B, L, M, and a Galois field arithmetic unit, and initializes the polynomial storage devices A, B, L, M from the syndrome equations, and stores the polynomial storage devices A, B, L, M, the Galois field arithmetic device, In the Euclidean mutual elimination apparatus which performs a Galois field operation using and calculates an error locator polynomial, the polynomial B (z) = S _k−1 z ^k−1 in the polynomial storage B at the time of initialization.
+ S _k−2 z ^k−2 +... + S ₀ , the polynomial M (z) = 1 is stored in the polynomial storage M, and the polynomial A (z) is stored in the polynomial storage A by the coefficient of the syndrome equation S (z). ) = S
_k−2 z ^k−1 + S _k−3 z ^{k− 2} +... + S ₀ z, polynomial storage device L
By storing the polynomial L (z) = z in the Euclidean mutual elimination apparatus, the same effect as in the present embodiment can be obtained.

[0166]

As described above, according to the present invention, the operation amount of Galois field arithmetic is reduced, so that a Euclidean mutual exclusion method and apparatus which can cope with an increase in processing speed can be realized.

[Brief description of the drawings]

FIG. 1 is a flowchart showing an initial setting method of a Euclidean mutual exclusion method according to a first embodiment of the present invention.

FIG. 2 is a flowchart illustrating an initial setting method of a Euclidean mutual division method according to the second embodiment;

FIG. 3 is a flowchart showing an initial setting method of a Euclidean mutual exclusion method according to the third embodiment;

FIG. 4 is a block diagram showing a configuration of a Euclidean mutual exchange apparatus according to the fourth embodiment;

FIG. 5 is a state diagram of a polynomial storage device in a first operation example of the Euclidean algorithm.

FIG. 6 is a state diagram of a polynomial storage device in a second operation example of the Euclidean algorithm unit;

FIG. 7 is a block diagram showing a configuration of a Euclidean mutual exchange apparatus according to a fifth embodiment of the present invention.

FIG. 8 is a state diagram of a polynomial storage device in a first operation example of the Euclidean algorithm unit;

FIG. 9 is a state diagram of a polynomial storage device in a second operation example of the Euclidean algorithm unit;

FIG. 10 is a state diagram of a polynomial storage device in a third operation example of the Euclidean algorithm unit;

FIG. 11 is a block diagram showing a configuration of an Euclidean mutual exchange device according to a sixth embodiment of the present invention.

FIG. 12 is a state diagram of a polynomial storage device in a first operation example of the Euclidean algorithm unit;

FIG. 13 is a state diagram of a polynomial storage device in a second operation example of the Euclidean algorithm unit;

FIG. 14 is a state diagram of a polynomial storage device in a third operation example of the Euclidean algorithm unit;

FIG. 15 is a flowchart showing an initial setting method of a conventional Euclidean mutual division method.

FIG. 16 is a flowchart showing a general Euclidean mutual exchange method after initialization.

[Explanation of symbols]

 0-15 Syndrome 17 Monitoring signal 50 Syndrome monitoring device 60 Galois field arithmetic device 100, 120, 140, 160 Polynomial storage device

Claims (12)

[Claims] 1. The syndrome equation S (z) = S _k-1 z
_{^{k-1 + S k-2}} z k-2 + ... + S 0, (k is k> 0 of the integer, S
_k-1 to S ₀ polynomial A (z) from the original) in a Galois field, B
(Z), L (z), and M (z) are initialized, and a Galois field operation is performed to obtain an error locator polynomial. In the Euclidean mutual division method, the initial setting method is the polynomial B (z), M (Z)
B (z) = S _k−1 z ^{k− 1} + S _k−2 z ^k−2 +... + S ₀ , M
(Z) = 1, and the polynomials A (z) and L (z) are converted into A (z) = S _k−2 z ^k−1 + S by the coefficient of the syndrome equation S (z).
_k-3 z ^k-2 +... + S ₀ z, L (z) = z, a Euclidean mutual division method. 2. An initialization method according to claim 1, wherein the syndrome equation S
When the coefficients of _{(z) S k-1 ~S} n = 0 and S _n-1 ≠ 0 _(n is n ≦ k-1 integer) polynomial A (z), L a (z), A
_{(Z) = S n-2} z k-1 + S n-3 z k-2 + ... + S 0 z k-n + 1, L
2. The method according to claim 1, wherein (z) = z ^{k−n + 1} . 3. When the initial setting method is at least when the coefficient S _k-1 = 0 of the syndrome equation S (z), the polynomial A
2. The Euclidean mutual division method according to claim 1, wherein (z) and L (z) are set as A (z) = z ^k and L (z) = 1. 4. An initialization method according to claim 1, wherein the syndrome equation S
When at least one of the coefficients S _{k−1 to} S _{k / 2} of (z) is 0, the polynomials A (z) and L (z) are expressed as A (z) = z ^k , L
4. The method according to claim 3, wherein (z) = 1. 5. The syndrome equation S (z) = S _k−1 z
_{^{k-1 + S k-2}} z k-2 + ... + S 0, (k is k> 0 of the integer, S
_k-1 to S ₀ as an input the original) in a Galois field, the polynomial storage device A, B, L, M and, a Galois field arithmetic unit, wherein from the syndrome equations polynomial storage device A, B,
L and M are initialized, and the polynomial storage devices A and
A Euclidean algorithm for performing a Galois field operation using B, L, and M and the Galois field arithmetic unit to obtain an error locator polynomial. The polynomial B is stored in the polynomial storage device B at the time of initialization.
(Z) = S _k−1 z ^k−1 + S _{k− 2} z ^k−2 +... + S ₀ and the polynomial M (z) = 1 are stored in the polynomial storage device M, and the syndrome equation S (z ), The polynomial storage device A stores the polynomial A (z) = S _k−2 z ^k−1 + S
The ^{_{k-3 z k-2 +}} ... + S 0 z, the polynomial storage device L, the Euclidean mutual division apparatus characterized by storing the polynomial L (z) = z. 6. Initialization, when coefficients S _{k-1 to} S _n = 0 and S _n-1 ≠ 0 of the syndrome equation S (z) are satisfied (n
Is an integer of n ≦ k−1), and the polynomial storage device A stores the polynomial A
The _{(z) = S n-2} z k-1 + S n-3 z k-2 + ... + S 0 z k-n + 1,
6. The Euclidean algorithm according to claim 5, wherein a polynomial L (z) = zk ^{-n + 1} is stored in the polynomial storage device L. 7. At the time of initialization, at least when the coefficient S _K-1 = 0 of the syndrome equation S (z), the polynomial A (z) = z ^k is stored in the polynomial storage A, and the polynomial storage L
The Euclidean mutual division apparatus according to claim 5, wherein a polynomial L (z) = 1 is stored in the Eq. 8. At the time of initialization, the syndrome equation S
When at least one of the coefficients S _{k−1 to} S _{k / 2} of (z) is 0, the polynomial A (z) = z ^k is stored in the polynomial storage device A, and the polynomial L (z) is stored in the polynomial storage device L. 8. The Euclidean mutual exchange apparatus according to claim 7, wherein = 1 is stored. 9. The polynomial storage device A includes a register a_k-1~
a₀And the polynomial storage device B includes a register b_k-1~ B₀
And the polynomial storage device L has a register l_i-1~ L₀(I
Is an integer of i> 0), and the polynomial storage device M
M_j-1~ M₀(J is an integer of j> 0), and the coefficient of the syndrome equation S (z) is monitored.
0 or 1 is monitored by the coefficient of the Drome equation S (z).
A syndrome monitoring device that outputs a visual signal;_k-1~ B₀The Syndrome
｛S of the equation of equation S (z)_k-1, S_k-2, ..., S₀｝
With the register m_w(W is an integer of 0 ≦ w <j)
If the monitor signal is 1, the register a_k-1~ A₀Before
Coefficient and constant ｛S of the syndrome equation S (z)_k-2,
S_k-3, ..., S₀, 0} in the register l_v~ L _v-1(V
Is an integer of 0 <v <i) and input the constant {1,0}
The Euclidean mutual exchange device according to claim 5, characterized in that: 10. The polynomial storage device A includes a register a _k-1
Ａa ₀ , and the polynomial storage device B has registers b _k−1 ｂb
₀ and a register dB, the polynomial storage device L includes registers l _{i-1 to} l ₀ (i is an integer of i> 0), and the polynomial storage device M includes registers m _{j-1 to} m ₀ (j comprising a j> 0 integer), monitoring the register b _k-1, a syndrome monitoring device for outputting 1 if other than the register b if _k-1 data stored in the 0 0,0 as the monitoring signal comprising, at initialization, the register a _k-1 ~a ₀ to the coefficients and constants of the syndrome equations _{S (z) {S k-} 2, S k-3, ...,
S ₀ , 0} are stored in the registers b _{k−1 to} b ₀ as coefficients {S _k−1 , S _k−2 ,..., S ₀ } of the syndrome equation S (z).
In the registers l _{v to} l _{v -1} (v is an integer of 0 <v <i)
To the register m _w (w is 0 ≦ w <
(integer of j) and a constant to the register dB. If the monitoring signal is 0, the registers a _{k-1 to} a ₀ and b _k-1 to b ₀ until the monitoring signal becomes ₁ . the data stored in b _0, is shifted towards larger subscript each letter, it shifted number of times, the Euclidean mutual division apparatus according to claim 6, wherein the increment or decrement the value to be stored in the register dB. 11. The polynomial storage device A includes registers a _k to
a ₀ , and the polynomial storage device B includes registers b _{k−1 to} b ₀
And the polynomial storage device L includes registers l _{i-1 to} l ₀ (i
Is an integer of i> 0), the polynomial storage device M is provided with registers m _{j−1 to} m ₀ (j is an integer of j> 0), and monitors the coefficients of the syndrome equation S (z). 1 outputs as a monitor signal, at least, the coefficient S _k-1 of the syndrome equations S (z) comprises a syndrome monitoring device to 0 the monitoring signal if 0, at initialization, the register b _k-1 ~ In b ₀ , coefficients {S _k−1 , S _k−2 ,..., S ₀ } of the syndrome equation S (z)
Is input to the register m _w (w is an integer of 0 ≦ w <j). If the monitoring signal is 0, the constants {1,..., 0, 0} are stored in the registers a _{k to} a ₀ . With the register l _v (v is 0 ≦ v
<Integer of i>, a constant 0 is input, and if the monitoring signal is 1, the registers a _{p to} a
_p-k + 1 coefficients (p = k or k-1) to the syndrome equations S (z) and a constant _{{S k-2, S k} -3, ..., S 0,
0}, the register l _q ~l _{q-1 (q} is 0 <q <i integer) Euclid apparatus according to claim 7, wherein the inputting the constant {1,0} to. 12. The polynomial storage device A has a register dA, and the syndrome monitoring device has a syndrome equation S
If at least one of the coefficients S _{k−1 to} S _{k / 2} of (z) is 0, the monitoring signal is set to 0, otherwise, 1 is set. If the monitoring signal is 0 at the time of initial setting, a constant is set in the register dA. 12. The Euclidean mutual exchange apparatus according to claim 11, wherein e (e is an integer) is input, and if the monitor signal is 1, a constant f (f is an integer of f ≠ e) is input to the register dA.