JPH11317674A - Error correction decoding device and its method - Google Patents

Abstract

PROBLEM TO BE SOLVED: To decrease the rewriting frequency of coefficients of a divided polynomial and a dividing polynomial and to increase the speed of error correction decoding processing by calculating the coefficient of a quotient polynomial via the arithmetic part of Euclidean algorithm and by means of two coefficients of high orders of both divided and dividing polynomials, when the difference of degrees is equal to 1 between the divided and dividing polynomials. SOLUTION: The arithmetic part of Euclidean algorithm 2000 calculates error correction polynomials, including an error numeric polynomial, an error position polynomial, etc., from a syndrome generated at a syndrome generation part 1000 and by means of the Euclidean algorithm. Then the error numeric and error position polynomials are sent to an error correction part 3000, in which the errors of both polynomials are corrected. When the difference of degrees is equal to 1 between the divided and dividing polynomials, the part 2000 performs a division operation with high orders and by means of two coefficients. Thus, it is possible to decrease the rewriting frequency of coefficients of both the divided and dividing polynomials and to increase the speed of error correction decoding processing.

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to an error correction decoding device and an error correction decoding method for correcting an error using a polynomial for correcting an error numerical polynomial and an error locator polynomial.

[0002]

2. Description of the Related Art FIG. 1 is a block diagram showing an outline of a conventional error correction decoding device. In the figure, reference numeral 1000 denotes a syndrome generation unit that generates a syndrome from a received signal. Reference numeral 2000a denotes a Euclidean algorithm operation unit that calculates an error correction polynomial such as an error position polynomial and an error numerical polynomial from the syndrome generated by the syndrome generation unit 1000 using the Euclidean algorithm. An error correction unit 3000 calculates the root of the error locator polynomial by a chain search operation, calculates the error value using the error locator polynomial and the error value polynomial calculated by the Euclidean algorithm operation unit 2000a, and corrects the error. . As described above, the error correction decoding device mainly includes the syndrome generation unit 1000, the Euclidean algorithm operation unit 2000a, and the error correction unit 3000.

Next, the configuration of the Euclidean algorithm operation unit 2000a in the conventional error correction decoding device will be described.

FIG. 8 is a block diagram showing a conventional Euclidean algorithm operation unit 2000a. In the figure, 30
1 is Euclidean algorithm coefficient storage means,
The coefficients of the divisor polynomial and the polynomial in the Euclidean algorithm are stored in a coefficient storage area corresponding to each of the following. Reference numeral 302 denotes an order calculating unit that calculates the order of a divisor polynomial and a dividend polynomial having coefficients stored in the Euclidean algorithm coefficient storage unit 301. 303
Is an order storage unit, which stores the order of the divisor and the polynomial calculated by the order calculator 302. 3
Reference numeral 04 denotes a comparing unit, which determines whether or not the degree of the divisor polynomial stored in the degree storing unit 303 satisfies the Euclidean algorithm termination condition.

Reference numeral 305 denotes Galois field division means for calculating the highest order coefficient of the quotient polynomial by dividing the highest order coefficient of the dividend polynomial on the Galois field by the highest order coefficient of the divisor polynomial. . Reference numeral 306 denotes a storage unit that stores the coefficient calculated by the Galois field division unit 305. Note that the Galois field division means 305 and the storage means 306 constitute a first calculation means 307.

Reference numeral 308 denotes Galois field arithmetic means, which calculates each coefficient of the remainder polynomial using the coefficients calculated by the Galois field division means 305 and stored in the storage means 306. Reference numeral 309 denotes a storage unit that stores the coefficients of the remainder polynomial calculated by the Galois field arithmetic unit 308.
The Galois field computing means 308 and the storage means 309 constitute a second computing means 310.

Reference numeral 311 denotes a control signal generation means for generating a control signal for controlling the operation of the Euclidean algorithm operation unit 2000a. Each unit operates in accordance with the control signal generated by the control signal generation unit 311. 312 is a data bus,
The signal transmitted from each means flows.

Next, a Euclidean algorithm operation unit 2000a for correcting an error in an RS code having a design distance d
Will be described with reference to the flowchart of FIG.

First, the syndromes S ₀ , S ₁ ,..., S _d-2 generated by the syndrome generation unit 1000 are sent to the Euclidean algorithm operation unit 2000a. This syndrome is stored in the coefficient storage area corresponding to each next as each coefficient of Equation 1 as a divisor polynomial in the Euclidean algorithm coefficient storage unit 301. For example, S _d−2 is stored in the d−2 order coefficient storage area of the divisor polynomial.
At the same time, 1 is stored in the d−1-order coefficient storage area of Equation 2 which is the polynomial to be removed. (Step S30
1).

[0010]

(Equation 1)

[0011]

(Equation 2)

Next, the order calculating means 302 first calculates the degree m of the dividend polynomial U0 (x), and stores it in the storing means 303.
(Step S302), and the divisor polynomial U1 (x)
Is calculated and stored in the storage means 303 (step S303). The degree n of the divisor polynomial U1 (x) calculated in step S303 is sent to the comparing means 304, and the value of the degree n of the divisor polynomial U1 (x) is [(d-1) /
2], that is, whether or not the Euclidean algorithm termination condition is satisfied (step S304).

In step S304, the order n becomes [(d−
1) / 2] or more, the subject polynomial U0 at that time
A _m, a _m-1 leading coefficient, for example, coefficients from higher order coefficients the dividend polynomial U0 (x) in the order of (x), ..., when the a ₀ is the Euclidean algorithm coefficients a _m The data is selected from the storage means 301 and sent to the Galois field division means 305 (step S305), and the highest-order coefficient of the divisor polynomial U1 (x) at that time, for example, the coefficient of the divisor polynomial U1 (x) is calculated in order from the higher-order coefficient to b. _{If n} , b _n−1 ,..., b ₀ ,
b _n is selected from the Euclidean algorithm coefficient storage means 301 and sent to the Galois field division means 305 (step S
306).

In the Galois field division means 305, c = a _m /
b _n is divided to calculate the highest order coefficient c of the quotient polynomial, which is stored in the storage means 306 and sent to the Galois field arithmetic means 308 (step S307). The Galois field arithmetic unit 308 divides the dividend polynomial U0 (x) by the divisor polynomial U1 (x) in accordance with Equation 3 from the coefficients of the dividend polynomial U0 (x) and the divisor polynomial U1 (x) and the coefficient c. The remainder of time, that is, the coefficient of the remainder polynomial is calculated and stored
9 (step S308). Note that in a few 3, e _k represents the coefficient of order k of the remainder polynomial.

[0015]

(Equation 3)

Next, the degree m of the polynomial U0 (x) stored in the degree storage means 303 is subtracted by 1 (step S3).
09), the polynomial U0 (x) from the degree storage means 303.
Is compared with the order m of the divisor polynomial U1 (x).
4 and the magnitudes of the two orders are compared (step S31).
0).

In step S310, the divisor polynomial U1 (x)
Is greater than the order m of the dividend polynomial U0 (x), the Euclidean algorithm storage means 30
1, the coefficients of the divisor polynomial U1 (x) are used as the coefficients of the polynomial U0 (x), and the coefficients of the remainder polynomial stored in the storage unit 309 are used as the coefficients of the divisor polynomial U1 (x). It is stored in the storage means 301 (step S311). This logically corresponds to replacing the divisor polynomial with the polynomial to be removed and the remainder polynomial with the divisor polynomial. Then, the operation after step S302 is performed again.

In step S310, the divisor polynomial U1
If the degree n of (x) is not greater than the degree m of the dividend polynomial U0 (x), the coefficient of the remainder polynomial is calculated as
It is stored in the Euclidean algorithm storage means 301 as a coefficient of 0 (x). This is equivalent to replacing the remainder polynomial with the polynomial to be deleted. Then, the operation after S305 is performed with the remainder polynomial as the polynomial to be removed U0 (x). If the order n is smaller than [(d-1) / 2] in step S304, the Euclidean algorithm operation has been completed, and the remainder polynomial having the coefficient stored in the storage unit 309 is calculated. It is determined as an error numerical polynomial. The error locator polynomial is
It is calculated by performing a product-sum operation using the other two polynomials as initial values. The error position numerical polynomial and the error position polynomial are sent to error correction section 3000, where error correction is performed.

[0019]

At present, gigabit-class mobile communication based on ATM transmission and DVD-ROM for storing a large capacity have been developed. You need to do it fast. However, since the conventional error correction coding apparatus is configured as described above, the number of steps of the Euclidean algorithm required to calculate an error numerical polynomial and an error locator polynomial from a code having a large error correction capability is small. There is a problem that the decoding process cannot be performed at high speed.

A conventional example is disclosed in Japanese Patent Application Laid-Open No. 6-2447.
There is also an error correction circuit using the Euclidean algorithm described in Japanese Patent No. 40. However, in this error correction circuit, when the degree difference between the dividend polynomial and the divisor polynomial is 2 or more, each coefficient of the divisor polynomial is shifted to the higher order side by (degree difference−1) and supplied to the division circuit. Since the division circuit performs processing for each coefficient, the number of steps of the Euclidean algorithm required to calculate an error numerical polynomial and an error position polynomial from a code having a large error correction capability increases. The problem of having been solved has not been solved.

The present invention has been made to solve the above problem, and has as its object to provide an error correction decoding apparatus and method capable of calculating an error numerical value polynomial and an error position polynomial in a small number of steps.

[0022]

In the error correction decoding apparatus according to the present invention, the Euclidean algorithm operation unit determines whether the polynomial of the dividend is polynomial when the degree difference between the degree of the polynomial and the degree of the polynomial is one. Calculate the two coefficients from the higher order of the quotient polynomial using the two coefficients from the higher order of the divisor polynomial. If the order difference is other than 1, calculate the highest order coefficient of each of the subject polynomial and the divisor polynomial. A first calculating means for calculating the highest order coefficient of the quotient polynomial using the first calculating means, and a second calculating means for calculating a coefficient of the remainder polynomial using the coefficient calculated by the first calculating means. It was taken.

The Euclidean algorithm operation unit determines that the degree difference between the degree of the dividend polynomial and the degree of the divisor polynomial is one.
In the above case, the two coefficients from the higher order of the quotient polynomial are calculated using the two higher order coefficients of the dividend polynomial and the divisor polynomial, respectively. First calculating means for calculating the highest order coefficient of the quotient polynomial using the highest order coefficient of each of the divisor polynomials, and calculating the coefficient of the remainder polynomial using the coefficient calculated by the first calculating means And a second calculating means.

Further, the Euclidean algorithm operation unit includes third operation means for calculating coefficients of two polynomials for calculating an error locator polynomial using the coefficients calculated by the first operation means. .

The error correction decoding method according to the present invention further comprises a step of calculating the order of the divisor polynomial and the order of the dividend polynomial, a step of determining the end of the Euclidean algorithm using the order of the divisor polynomial, Determining whether the degree difference between the degree of the polynomial and the degree of the divisor polynomial is 1; and, if the degree difference is 1, using the two coefficients from the higher order of the polynomial and the divisor polynomial to calculate the remainder. Calculating the coefficient of the polynomial; and calculating the coefficient of the remainder polynomial using the highest-order coefficient of each of the dividend polynomial and the divisor polynomial when the degree difference is other than 1, and calculating 1 from the degree of the dividend polynomial. If the result of subtraction is equal to or greater than the degree of the divisor polynomial, a step of repeating after replacing the remainder polynomial with the dividend polynomial, and after one polynomial subtraction operation is completed,
Replacing the divisor polynomial with the polynomial to be removed and replacing the remainder polynomial with the divisor polynomial.

Calculating the degree of the divisor polynomial and the degree of the dividend polynomial; determining the end of the Euclidean algorithm using the degree of the divisor polynomial; and determining the degree of the degree of the dividend polynomial and the degree of the divisor polynomial. Determining whether the difference is equal to or greater than 1; and calculating a coefficient of the remainder polynomial using two coefficients from the higher order of the dividend polynomial and the divisor polynomial when the order difference is equal to or greater than 1. Calculating the coefficient of the remainder polynomial using the highest order coefficient of each of the dividend polynomial and the divisor polynomial when the degree difference is 0; and comparing the degree of the remainder polynomial with the degree of the divisor polynomial; Replacing the remainder polynomial with the dividend polynomial if the degree of the remainder polynomial is greater than or equal to the degree of the divisor polynomial;
When the degree of the remainder polynomial is smaller than the degree of the divisor polynomial, the step of replacing the divisor polynomial with the dividend polynomial and replacing the remainder polynomial with the divisor polynomial is included.

Calculating the degree of the divisor polynomial and the degree of the dividend polynomial; determining the end of the Euclidean algorithm using the degree of the divisor polynomial; and determining the degree of the degree of the dividend polynomial and the degree of the divisor polynomial. Determining whether the difference is 1; and, when the degree difference is 1, using two coefficients from the higher order of the dividend polynomial and the divisor polynomial, respectively, to calculate the coefficient of the remainder polynomial and the error position polynomial. Calculating the coefficients of the two polynomials, and, if the degree difference is other than 1, using the highest order coefficients of the dividend polynomial and the divisor polynomial to calculate the coefficients of the remainder polynomial and the error locator polynomial. Calculating the coefficients of the polynomial and, if the degree obtained by subtracting 1 from the degree of the dividend polynomial is greater than or equal to the degree of the divisor polynomial, repeating the step after replacing the remainder polynomial with the degree of the polynomial; After Xu calculated manipulation of the term formula has been completed,
Replacing the divisor polynomial with the polynomial to be deleted, replacing the remainder polynomial with the divisor polynomial, and replacing the two polynomials for calculating the error locator polynomial with each other.

Calculating the degree of the divisor polynomial and the degree of the dividend polynomial; determining the end of the Euclidean algorithm using the degree of the divisor polynomial; and determining the degree of the degree of the divisor polynomial and the degree of the divisor polynomial. Determining whether the difference is 1 or more, and calculating the coefficient of the remainder polynomial and the error locator polynomial by using two higher-order coefficients of the dividend polynomial and the divisor polynomial if the degree difference is 1 or more Calculating the coefficients of the two polynomials for calculation, and when the degree difference is 0, using the highest order coefficients of the dividend polynomial and the divisor polynomial, respectively, to calculate the coefficients of the remainder polynomial and the error locator polynomial.
Calculating the coefficients of the two polynomials, comparing the degree of the remainder polynomial with the degree of the divisor polynomial, and replacing the remainder polynomial with the subject polynomial if the degree of the remainder polynomial is greater than or equal to the degree of the divisor polynomial. When the degree of the remainder polynomial is smaller than the degree of the divisor polynomial, replacing the divisor polynomial with the dividend polynomial, replacing the remainder polynomial with the divisor polynomial, and replacing the two polynomials for calculating the error position polynomial with each other. Included.

[0029]

DESCRIPTION OF THE PREFERRED EMBODIMENTS Embodiment 1 FIG. 1 is a block diagram showing an outline of an error correction decoding apparatus according to Embodiment 1 of the present invention. In the figure, reference numeral 1000 denotes a syndrome generation unit that generates a syndrome from a received signal. 20
Reference numeral 00 denotes a Euclidean algorithm operation unit that calculates an error correction polynomial such as an error numerical polynomial and an error position polynomial from the syndrome generated by the syndrome generation unit 1000 using the Euclidean algorithm. 3000 calculates the root of the error locator polynomial by a chain search operation, and calculates the Euclidean algorithm operation unit 2
An error correction unit that calculates an error value using the error position polynomial and the error value polynomial calculated at 000, and corrects the error. As described above, the error correction decoding device mainly includes the syndrome generation unit 1000, the Euclidean algorithm operation unit 2000, and the error correction unit 3000.

Next, the configuration of the Euclidean algorithm operation unit 2000 in the error correction decoding device will be described. FIG. 2 is a block diagram of the Euclidean algorithm operation unit 2000 according to the first embodiment. In the figure, reference numeral 1 denotes a Euclidean algorithm coefficient storage unit, which stores coefficients of a divisor polynomial and a polynomial in a Euclidean algorithm in a coefficient storage area corresponding to each of the following. Reference numeral 2 denotes an order calculating means for calculating the order of the divisor polynomial and the dividend polynomial having the coefficients stored in the Euclidean algorithm coefficient storage means 1. Reference numeral 3 denotes an order storage unit which stores the order calculated by the order calculation unit 2. Numeral 4 denotes a comparing means, which determines whether or not the degree of the divisor polynomial stored in the degree storing means 3 satisfies the end condition of the Euclidean algorithm.

Numeral 5 is Galois field division means for calculating the highest order coefficient of the quotient polynomial by dividing the highest order coefficient of the dividend polynomial by the highest order coefficient of the divisor polynomial on the Galois field. . Reference numeral 6 denotes a storage unit that stores the coefficient calculated by the Galois field division unit 5. Reference numeral 7 denotes a first Galois field arithmetic means, which calculates two coefficients from the higher order of the dividend polynomial and two coefficients from the higher order of the divisor polynomial, and calculates two coefficients from the higher order of the quotient polynomial. Is calculated. Reference numeral 8 denotes a storage unit that stores the coefficients calculated by the first Galois field calculation unit 7.
The Galois field division means 5, storage means 6, first Galois field calculation means 7, and storage means 8 form first calculation means 9
Is composed.

10 is a second Galois field arithmetic means,
The coefficients of the remainder polynomial are calculated using the coefficients of the quotient polynomial stored in the storage means 6 and the storage means 8. 11
Is storage means for storing the coefficients of the remainder polynomial calculated by the second Galois field arithmetic means 10. Note that the second Galois field arithmetic unit 10 and the storage unit 11 constitute a second arithmetic unit 12.

Reference numeral 13 denotes a control signal generating means for generating a control signal for controlling the operation of the Euclidean algorithm operation unit 2000. Each unit operates in accordance with the control signal generated by the control signal generation unit 13. 14 is a subtraction means, and the storage means 3
The order difference is calculated by subtracting the order of the divisor polynomial from the order of the polynomial stored in, and it is determined whether or not the order difference is 1. Reference numeral 15 denotes a data bus through which a signal transmitted from each unit flows.

Next, the operation of the Euclidean algorithm operation unit 2000 when correcting the error of the RS code having the design distance d will be described with reference to the flowchart of FIG.

First, the syndromes S ₀ , S ₁ ,..., S _d-2 generated by the syndrome generation unit 1000 are sent to the Euclidean algorithm operation unit 2000. This syndrome is stored in the Euclidean algorithm coefficient storage unit 1 as each coefficient of Equation 4 which is a divisor polynomial U1 (x),
Each coefficient is stored in the corresponding coefficient storage area. For example, S _d−2 is stored in the d−2 order coefficient storage area of the divisor polynomial. At the same time, 1 is stored in the (d−1) -order coefficient storage area of Equation 5, which is the polynomial U0 (x) (step S1).

[0036]

(Equation 4)

[0037]

(Equation 5)

Next, the degree calculating means 2 first calculates the degree m of the dividend polynomial U0 (x) and stores it in the degree storage means 3 (step S2), and the degree n of the divisor polynomial U1 (x). Is calculated and stored in the degree storage means 3 (step S3). The divisor polynomial U1 calculated in step 3
The degree n of (x) is sent to the comparing means 4, and it is determined whether the value of the degree n is smaller than [(d-1) / 2], that is, whether the Euclidean algorithm termination condition is satisfied. (Step S4).

In step S4, the order n is [(d-1) /
2] or more, the subtraction means 14 calculates the polynomial U0
The difference between the degree m of (x) and the degree n of the divisor polynomial U1 (x) is p =
mn is calculated (step S5), and it is determined whether or not the order difference p is 1 (step S6).

[0040] In step S6, when a degree difference p is 1, if a _m, a _m-1 coefficients from the high-order coefficients in the order of the dividend polynomial U0 (x), ..., and a _0, divided Polynomial U1 (x)
B _n, b _n-1 coefficients from the high-order coefficients in the order of, ..., when the b _0, 2 pieces of coefficients a _m of higher order, a _m-1 the selection of the dividend polynomial U0 (x) Then, the coefficients b _n and b _n-1 from the higher order of the divisor polynomial U1 (x) are selected and sent to the first arithmetic means 9 (step S7). Step S8). In the first calculation means 9, the Galois field division means 5, with a leading coefficient b _n of the highest order coefficient a _m a dividend polynomial U1 of the dividend polynomial U0 (x) (x), 6
Is calculated, and the highest order coefficient c of the quotient polynomial is calculated and stored in the storage means 6. The first Galois field calculation means calculates two coefficients a _m , The following equation 7 is calculated from a _m-1 and two coefficients b _m and b _m-1 from the higher order of the divisor polynomial U1 (x) to obtain the second coefficient d from the higher order of the quotient polynomial. (Step S)
9). Next, in step S9, the coefficients c and d of the quotient polynomial stored in the storage unit 6 and the storage unit 8 are:
The second Galois field arithmetic means 10 sends the polynomial U0 (x) to the higher order of the polynomial U1 (x). The remainder when divided by two, that is, the coefficient of the remainder polynomial, is obtained and stored in the storage means 11. Note that Equations 8, 9 and
In a few _{10, e m, e k,} e mn-1 is the order m, k, coefficients in mn-1, respectively remainder polynomial.

[0041]

(Equation 6)

[0042]

(Equation 7)

[0043]

(Equation 8)

[0044]

(Equation 9)

[0045]

(Equation 10)

Thereafter, the coefficients of the divisor polynomial U1 (x) stored in the Euclidean algorithm storage means 1 are used as the coefficients of the polynomial U0 (x), and the coefficients of the remainder polynomial stored in the storage means 11 are used as the divisor polynomial U1 (x). The Euclidean algorithm coefficient storage means 1 stores the coefficient (x) (step S11). Logically, this has replaced the divisor polynomial with the divisor polynomial and the remainder polynomial with the divisor polynomial. Then, the operation after step S2 is performed again.

If the order difference p is not 1 at step S6, the highest order coefficient a _{m of the} polynomial U0 (x) is obtained.
Is selected from the Euclidean algorithm coefficient storage means 1 and sent to the first arithmetic means 9 (step S12), and the highest order coefficient b _n of the divisor polynomial U1 (x) is selected from the Euclidean algorithm coefficient storage means 1 One computing means 9
(Step S13).

In the first arithmetic means 9, the Galois field division means 5 performs a division operation of c = a _m / b _n to calculate the highest order coefficient c of the quotient polynomial, and stores it in the storage means 6. It is sent to the second calculating means 12 (step S14). In the second calculating means 12, the second Galois field calculating means 10 calculates the coefficient of the dividend polynomial U0 (x), the coefficient of the divisor polynomial U1 (x), and the coefficient c in accordance with Equation 11 according to Equation 11. )
Is divided by the highest degree of the divisor polynomial U1 (x), that is, the coefficient of the remainder polynomial is calculated and stored in the storage unit 11
(Step S15). Note that in Equation 11, e _k represents a coefficient at the order k of the remainder polynomial.

[0049]

[Equation 11]

Next, the degree calculation means 2 stores the degree storage means 3
Is subtracted by one from the order m of the dividend polynomial U0 (x) stored in the order storage means 3 (step S16), and the order m of the dividend polynomial U0 (x) and the divisor polynomial U1 are stored in the order storage means 3. The degree n of (x) is sent to the comparing means 4, and the magnitudes of both orders are compared (step S17).

If the order n of the divisor polynomial U1 (x) is greater than the order m of the polynomial U0 (x) in step S17, steps S2 and subsequent steps are executed after executing step S11. If not large, the coefficient of the remainder polynomial stored in the storage unit 11 is replaced by the Euclidean algorithm coefficient storage unit 1 as the coefficient of the polynomial U0 (x) (step S18). This logically corresponds to replacing the remainder polynomial with the dividend polynomial. Thereafter, the coefficients of the residual polynomial are set as the coefficients of the polynomial to be deleted in step S1.
Execute the second and subsequent steps.

In step S4, the order n is [(d
-1) / 2], the Euclidean algorithm operation has been completed, and the storage unit 11
Is determined as an error numerical polynomial. The error locator polynomial is calculated by performing a product-sum operation of the polynomials using another two polynomials as initial values. The error numerical value polynomial and the error position polynomial are sent to error correction section 3000, where error correction is performed.

Steps S2 and S3 are steps for calculating the degree of the divisor polynomial and the degree of the dividend polynomial. Step S4 is a step for determining the end of the Euclidean algorithm using the degree of the divisor polynomial. Steps S5 and S6 are steps for determining the end. Steps S7, S8, S9, and S10 use two coefficients from the higher-order polynomial and the higher-order polynomial in steps S7, S8, S9, and S10, respectively, to determine whether the order difference between the degree of the dividend polynomial and the degree of the divisor polynomial is 1. To calculate the coefficients of the remainder polynomial
2, S13, S14, S15, S16, S17, S18
Calculates the coefficient of the remainder polynomial using the highest order coefficient of the dividend polynomial and the divisor polynomial, and subtracts 1 from the degree of the dividend polynomial if the degree is greater than or equal to the degree of the divisor polynomial. In the step repeated after replacing the polynomial with the polynomial to be deleted, step S11 corresponds to a step of replacing the polynomial with the polynomial and replacing the remainder polynomial with the polynomial.

As described above, in the Euclidean algorithm operation unit 2000, when the degree difference between the dividend polynomial and the divisor polynomial is 1, the division operation is performed by two coefficients from the higher order, so that the dividend polynomial and the divisor polynomial are calculated. The number of times of rewriting the coefficient of is reduced, and the remainder polynomial can be calculated in few steps.
The error correction decoding process can be sped up.

Embodiment 2 FIG. 4 shows a Euclidean algorithm operation unit in the error correction decoding device according to the second embodiment of the present invention. In the Euclidean algorithm operation unit in the first embodiment of FIG. 2, the degree difference between the divisor polynomial and the polynomial to be divided is one. In the above case, two coefficients from the higher order of the polynomial to be removed and the divisor polynomial are selected and calculated.

In the figure, reference numeral 16 denotes an order updating means. 17
Is a subtraction unit, which calculates an order difference by subtracting the order n of the divisor polynomial from the order m of the polynomial stored in the storage unit 3, and determines whether the order difference is 1 or more. .

Next, the operation of the Euclidean algorithm operation unit 2000 for correcting the error of the RS code having the design distance d will be described with reference to the flowchart of FIG.

First, steps S1 to S4 are executed. Next, the subtraction means 17 calculates the polynomial U0
An order difference p = m−n between the order m of (x) and the order n of the divisor polynomial U1 (x) is calculated (step S5), and the order difference p is 1
It is determined whether this is the case (step S101).

If it is determined in step S101 that the degree difference p is 1 or more, steps S7 to S10 are executed, and the coefficients of the remainder polynomial are stored in the storage means 11.

In step S101, the order difference p is 0
If it is determined that step S12
15 is executed, and the coefficients of the remainder polynomial are stored in the storage unit 11.

Next, the degree calculating means 2 calculates the degree k of the remainder polynomial (step S102). The degree k is sent to the comparing means 4 and the divisor polynomial U1 ( The magnitude of x) is compared with the degree n (step S103).

In step S103, the order k of the remainder polynomial
Is greater than or equal to the order n of the divisor polynomial U1 (x), the order updating means 16 determines that the order m of the polynomial U0 (x) is k
And the dividend polynomial U stored in the degree storage means 3
The order of 0 (x) is replaced (step S104).
At the same time, the coefficients of the remainder polynomial stored in the storage means 11 are sent to the Euclidean algorithm coefficient storage means 1,
It is replaced as a coefficient of the dividend polynomial U0 (x) (step S105). This means that the remainder polynomial is logically replaced by the polynomial to be removed. After that, step S5
The following is executed.

If the order k of the remainder polynomial is smaller than the order n of the divisor polynomial U1 (x) in step S103, the order updating means 16 executes step S11, and then the order updating means 16 calculates the order of the polynomial U0 (x). m is updated to the order n of the divisor polynomial U1 (x), the order n of the divisor polynomial U1 (x) is updated to the order k of the remainder polynomial, and stored in the order storage means 3 (step S106). This means that the divisor polynomial is logically replaced by the polynomial to be removed, and the remainder polynomial is replaced by the divisor polynomial. Thereafter, step S4 and subsequent steps are executed again.

If the order difference p is determined to be 0 in step S101, the order k of the remainder polynomial calculated in step S102 is always smaller than the order of the divisor polynomial U1 (x). S11 and subsequent steps will always be performed.

S5 · S101 determines whether the degree difference between the degree of the dividend polynomial and the degree of the divisor polynomial is 1 or more. S7 · S8 · S9 · S10 determines whether the degree of the dividend polynomial and the degree of the divisor polynomial are different. In the step of calculating the coefficients of the remainder polynomial using the two coefficients from the higher order, S12 · S1
3. S14 and S15 calculate the coefficients of the remainder polynomial using the highest order coefficients of the dividend polynomial and the divisor polynomial, and steps S102 and S103 compare the degree of the remainder polynomial with the degree of the divisor polynomial. Steps S104 and S105 correspond to steps of replacing the remainder polynomial with the polynomial to be replaced, and steps S11 and S106 correspond to steps of replacing the divisor polynomial with the polynomial to be replaced and replacing the remainder polynomial with the polynomial.

As described above, when the degree difference between the polynomial U0 (x) and the polynomial U1 (x) is 1 or more, the polynomial U0 (x) can be used without rewriting the coefficients of the polynomial U1 (x).
Since the process can proceed only by converting the coefficient of (x), the remainder polynomial can be calculated in a small number of steps, and the error correction decoding process can be speeded up.

Embodiment 3 FIG. 6 shows a Euclidean algorithm operation unit in the error correction decoding apparatus according to Embodiment 3 of the present invention. In the Euclidean algorithm operation unit in Embodiment 2 in FIG. 4, both the error numerical polynomial and the error position polynomial are set to 1 It is obtained by the number of operations.

In the figure, reference numeral 18 denotes an error locator polynomial calculation coefficient storage means, which is a polynomial for calculating two error locator polynomials:
Each coefficient of M0 (x) and M1 (x) is stored. Reference numeral 19 denotes a third Galois field arithmetic unit which calculates coefficients of two polynomials for calculating an error position polynomial using the coefficients stored in the storage unit 6 and the storage unit 8. Reference numeral 20 denotes a storage unit that stores the respective coefficients calculated by the third Galois field calculation unit 19. The third Galois field arithmetic unit 19 and the storage unit 20 constitute a third arithmetic unit 21. Reference numeral 22 denotes a second data bus through which a signal transmitted from each unit flows.

Next, the operation of the Euclidean algorithm operation unit 2000 for correcting the error of the RS code having the design distance d will be described with reference to the flowchart of FIG. First, in step S1, the divisor polynomial U0 (x)
And the coefficients of the polynomial U1 (x) are stored in the Euclidean algorithm coefficient storage unit 1. Next, two polynomials for calculating the error locator polynomial: M0 (x) and M1
The initial values of (x) are set to M0 (x) = 0 and M1 (x) = 1, and the coefficients are stored in the error locator polynomial calculation coefficient storage unit 18. Thereafter, steps S2 to S5 are executed,
In step S101, it is determined whether the order difference p between the order m of the dividend polynomial U0 (x) and the order n of the divisor polynomial U1 (x) is 1 or more.

In step S101, the order difference p is 1
If it is determined that this is the case, the process proceeds from step S7 to S1.
0 is executed, coefficients c and d of the quotient polynomial and coefficients of the remainder polynomial are calculated, and stored in the storage unit 6, the storage unit 8, and the storage unit 11. After that, the coefficients of the quotient polynomial stored in the storage means 6 and the storage means 8 are sent to the third calculation means. In the third calculation means, in the third Galois field calculation means 19, for example, the polynomial M0 ( x) are calculated in order from the higher-order coefficient as p _u , p _u−1 ,..., p ₀ , polynomial M1
The coefficients of (x) are sequentially calculated from higher-order coefficients as q _{u-m + n} ,
When q _{u−m + n−1} ,..., q ₀ , the operations of Expressions 12, 13, and 14 are performed, and the results are stored in the storage unit 20.
When this calculation is completed, the M
The coefficient of 0 (x) is replaced with the coefficient of M0 (x) stored in the coefficient storage unit 18 for calculating the error locator polynomial (step S202).

[0071]

(Equation 12)

[0072]

(Equation 13)

[0073]

[Equation 14]

In step S101, the order difference p is 0
When it is determined that
Step 15 is executed, and the coefficients of the quotient polynomial are stored in the storage means 6 and the coefficients of the remainder polynomial are stored in the storage means 11. Thereafter, the coefficient stored in the storage means 6 is sent to the third calculation means, and the third Galois field calculation means 19 calculates the equation (15) with the coefficient sent from the error location polynomial calculation coefficient storage means 18. Is executed, and the result is stored in the storage means 20. Thereafter, the contents stored in the storage means 20 are sent to the error locator polynomial calculation coefficient storage means 18 and the polynomial M0
It is replaced by the coefficient of (X) (step S204).

[0075]

(Equation 15)

Next, step S102 is executed. In step S103, the degree k of the remainder polynomial is compared with the degree n of the divisor polynomial. If the degree k of the remainder polynomial is equal to or greater than the degree n of the divisor polynomial U1 (x) in step S103, steps S104 and S105 are executed, and then steps S5 and subsequent steps are executed again. If the degree k of the remainder polynomial is smaller than the degree n of the divisor polynomial U1 (x), after the steps S11 and S106 are executed, the coefficient storage unit 18 for calculating the error position polynomial calculates
The coefficients are mutually replaced between the two polynomials M0 (x) and M1 (x) (step S203). Thereafter, step S4 and subsequent steps are executed again.

In step S4, if the Euclidean algorithm termination condition is satisfied, that is, if n is [(d
-1) / 2], the storage unit 1
The remainder polynomial consisting of the coefficient stored in 1 is determined as the error value polynomial, and the polynomial M0 (x) consisting of the coefficient stored in the error location polynomial calculation storage unit 18 is determined as the error location polynomial, and sent to the error correction unit 3000. Error decoding processing is performed.

Steps S7, S8, S9, S10
In the step of calculating the coefficient of the remainder polynomial and the coefficient of the two polynomials for calculating the error locator polynomial using the two higher-order coefficients of the dividend polynomial and the divisor polynomial, respectively, steps S12 and S13 S14 ・ S15 ・ S20
4 is a coefficient for the remainder polynomial and 2 for calculating the error locator polynomial using the highest order coefficients of the dividend polynomial and the divisor polynomial, respectively.
Calculating the coefficients of the three polynomials includes step S1
Steps S1, S12, and S203 correspond to replacing the divisor polynomial with the polynomial to be deleted, replacing the remainder polynomial with the divisor polynomial, and replacing two polynomials for calculating the error location polynomial with each other.

As described above, both the error value polynomial and the error location polynomial can be obtained by one operation of the Euclidean algorithm, and the error correction decoding processing can be sped up.

In the third embodiment, the error locator polynomial calculation coefficient storage means for calculating the error locator polynomial and the third arithmetic means are provided in the second embodiment. Even if the error storage polynomial calculation coefficient storage means and the third calculation means for calculating
It is possible to form a Euclidean algorithm operation unit that can calculate the error numerical polynomial and the error locator polynomial in one operation.

[0081]

In the error decoding apparatus according to the present invention, the Euclidean algorithm operation unit determines whether the degree of the dividend polynomial and the degree of the divisor polynomial are high when the degree difference between the degree of the dividend polynomial and the degree of the divisor polynomial is one. The two coefficients from the higher order of the quotient polynomial are calculated using the next two coefficients, and the order difference is 1
In other cases, the first calculating means for calculating the highest-order coefficient of the quotient polynomial using the highest-order coefficients of the dividend polynomial and the divisor polynomial, and the coefficient calculated by the first calculating means is used. And a second calculating means for calculating the remainder polynomial.

Thus, when the degree difference between the polynomial to be divided and the polynomial to be divided is 1, the division operation is performed by two coefficients from the higher order, so that the number of times of rewriting the coefficients of the polynomial to be divided and the polynomial to be reduced is reduced. Thus, the remainder polynomial can be calculated in a small number of steps, and the error correction decoding process can be accelerated.

The Euclidean algorithm operation unit determines that the degree difference between the degree of the dividend polynomial and the degree of the divisor polynomial is one.
In the above case, the two coefficients from the higher order of the quotient polynomial are calculated using the two higher order coefficients of the dividend polynomial and the divisor polynomial, respectively. First calculating means for calculating the highest order coefficient of the quotient polynomial using the highest order coefficient of each of the divisor polynomials, and calculating the coefficient of the remainder polynomial using the coefficient calculated by the first calculating means And a second calculating means.

Thus, if the difference between the degree of the polynomial to be divided and the degree of the polynomial is 1 or more, the processing can be performed by simply converting the coefficients of the polynomial to be divided without rewriting the coefficients of the polynomial. The polynomial can be calculated in a small number of steps, and the error correction decoding process can be speeded up.

Further, the Euclidean algorithm operation section includes third operation means for calculating coefficients of two polynomials for calculating an error locator polynomial using the coefficients calculated by the first operation means. .

Thus, both the error numerical polynomial and the error locator polynomial can be obtained by one operation of the Euclidean algorithm, and the error correction decoding processing can be speeded up.

The error correction decoding method according to the present invention further comprises: a step of calculating the order of the divisor polynomial and the order of the dividend polynomial; a step of determining the end of the Euclidean algorithm using the order of the divisor polynomial; Determining whether the degree difference between the degree of the divisor polynomial and the degree of the divisor polynomial is 1; and using the two coefficients from the higher order of the polynomial and the divisor polynomial when the degree difference is one. Calculating the coefficients of the remainder polynomial by using the highest order coefficients of the dividend polynomial and the divisor polynomial if the order difference is other than 1, and calculating the degree of the remainder polynomial If the result of subtracting 1 from の is greater than or equal to the degree of the divisor polynomial, then repeating the step after replacing the remainder polynomial with the divisor polynomial, and removing the divisor polynomial after one polynomial subtraction operation is completed Replacing the section type, and intended to include the step of replacing the remainder polynomial divisor polynomial.

Thus, when the degree difference between the polynomial to be divided and the polynomial is 1, the division operation is performed by two coefficients from the higher order, and the number of times of rewriting the coefficients of the polynomial to be divided and the polynomial is reduced. Thus, the remainder polynomial can be calculated in a small number of steps, and the error correction decoding process can be accelerated.

Further, a step of calculating the degree of the divisor polynomial and the degree of the dividend polynomial, a step of determining the end of the Euclidean algorithm using the degree of the divisor polynomial, and a step of calculating the degree of the divisor polynomial and the degree of the divisor polynomial A step of determining whether the degree difference is 1 or more; and a step of calculating a coefficient of the remainder polynomial using two coefficients from the higher order of the dividend polynomial and the divisor polynomial if the degree difference is 1 or more. And calculating the coefficients of the remainder polynomial using the highest order coefficients of the dividend polynomial and the divisor polynomial when the degree difference is 0, and comparing the degree of the remainder polynomial with the degree of the divisor polynomial. Replacing the remainder polynomial with the dividend polynomial if the degree of the remainder polynomial is greater than or equal to the degree of the divisor polynomial; and applying the divisor polynomial if the degree of the remainder polynomial is smaller than the degree of the divisor polynomial. Replaced by polynomials, and shall include the step of replacing the remainder polynomial divisor polynomial.

Thus, when the degree difference between the polynomial to be divided and the polynomial to be divided is 1 or more, the processing can be carried out only by converting the coefficients of the polynomial to be divided without rewriting the coefficients of the polynomial. The polynomial can be calculated in a small number of steps, and the error correction decoding process can be speeded up.

Calculating the degree of the divisor polynomial and the degree of the dividend polynomial; determining the end of the Euclidean algorithm using the degree of the divisor polynomial; and determining the degree of the degree of the dividend polynomial and the degree of the divisor polynomial. Determining whether the difference is 1; and, when the degree difference is 1, using two coefficients from the higher order of the dividend polynomial and the divisor polynomial, respectively, to calculate the coefficient of the remainder polynomial and the error position polynomial. Calculating the coefficients of the two polynomials, and, if the degree difference is other than 1, using the highest order coefficients of the dividend polynomial and the divisor polynomial to calculate the coefficients of the remainder polynomial and the error locator polynomial. Calculating the coefficients of the polynomial and, if the degree obtained by subtracting 1 from the degree of the dividend polynomial is greater than or equal to the degree of the divisor polynomial, repeating the step after replacing the remainder polynomial with the degree of the polynomial; After Xu calculated manipulation of the term formula has been completed,
Replacing the divisor polynomial with the polynomial to be deleted, replacing the remainder polynomial with the divisor polynomial, and replacing the two polynomials for calculating the error locator polynomial with each other.

Calculating the degree of the divisor polynomial and the degree of the dividend polynomial; determining the end of the Euclidean algorithm using the degree of the divisor polynomial; and determining the degree of the degree of the dividend polynomial and the degree of the divisor polynomial. Determining whether the difference is 1 or more, and calculating the coefficient of the remainder polynomial and the error locator polynomial by using two higher-order coefficients of the dividend polynomial and the divisor polynomial if the degree difference is 1 or more Calculating the coefficients of the two polynomials for calculation, and when the degree difference is 0, using the highest-order coefficients of the dividend polynomial and the divisor polynomial to calculate the coefficients of the remainder polynomial and the error locator polynomial.
Calculating the coefficients of the two polynomials, comparing the degree of the remainder polynomial with the degree of the divisor polynomial, and replacing the remainder polynomial with the subject polynomial if the degree of the remainder polynomial is greater than or equal to the degree of the divisor polynomial. When the degree of the remainder polynomial is smaller than the degree of the divisor polynomial, replacing the divisor polynomial with the dividend polynomial, replacing the remainder polynomial with the divisor polynomial, and replacing the two polynomials for calculating the error position polynomial with each other. Included.

As a result, both the error numerical polynomial and the error locator polynomial can be obtained by one operation of the Euclidean algorithm, and the error correction decoding process can be sped up.

[Brief description of the drawings]

FIG. 1 is a configuration diagram of an error decoding device according to Embodiment 1 of the present invention.

FIG. 2 is a configuration diagram of a Euclidean algorithm operation unit according to the first embodiment of the present invention.

FIG. 3 is an operation flowchart of a Euclidean algorithm operation unit according to the first embodiment of the present invention.

FIG. 4 is a configuration diagram of a Euclidean algorithm operation unit according to Embodiment 2 of the present invention.

FIG. 5 is an operation flowchart of a Euclidean algorithm operation unit according to the second embodiment of the present invention.

FIG. 6 is a configuration diagram of a Euclidean algorithm operation unit according to Embodiment 3 of the present invention.

FIG. 7 is an operation flowchart of a Euclidean algorithm operation unit according to Embodiment 3 of the present invention.

FIG. 8 is a configuration diagram of a Euclidean algorithm operation unit in a conventional example.

FIG. 9 is an operation flowchart of a Euclidean algorithm operation unit in a conventional example.

[Explanation of symbols]

 Reference Signs List 4 comparison means, 9 first calculation means, 12 second calculation means, 14 subtraction means, 21 third calculation means, 1000 syndrome generation section, 2000 Euclidean algorithm calculation section, 3000 error correction section

Claims (7)

[Claims] An Euclidean algorithm operation unit that calculates an error correction polynomial from the syndrome generated by the syndrome generation unit, and an error correction polynomial calculated by the Euclidean algorithm operation unit. An error correction decoding device having an error correction unit for correcting an error by using the Euclidean algorithm operation unit, wherein when the degree difference between the degree of the dividend polynomial and the degree of the divisor polynomial is 1, the dividend polynomial and the divisor polynomial Calculate the two coefficients from the higher order of the quotient polynomial using the two coefficients from the higher order, and if the order difference is other than 1, calculate the highest order coefficient of each of the subject polynomial and the divisor polynomial. First calculating means for calculating the highest order coefficient of the quotient polynomial using the coefficient, and calculating the coefficient of the remainder polynomial using the coefficient calculated by the first calculating means An error correction decoding device, comprising: 2. A method comprising: using a syndrome generation unit, a Euclidean algorithm operation unit for calculating a polynomial for error correction from the syndrome generated by the syndrome generation unit, and an error correction polynomial calculated from the Euclidean algorithm operation unit. An error correction decoding device having an error correction unit that corrects an error by using the Euclidean algorithm operation unit, when the degree difference between the degree of the dividend polynomial and the degree of the divisor polynomial is 1 or more, the dividend polynomial and the divisor polynomial Calculate the two coefficients from the higher order of the quotient polynomial using the two coefficients from the higher order, and use the highest order coefficients of the subject polynomial and the divisor polynomial when the order difference is 0. First calculating means for calculating the highest order coefficient of the quotient polynomial,
An error correction decoding device comprising: a second calculating means for calculating a coefficient of a remainder polynomial using the coefficient calculated by the first calculating means. 3. The method according to claim 1, wherein the Euclidean algorithm operation unit includes third operation means for calculating coefficients of two polynomials for calculating an error locator polynomial using the coefficients calculated by the first operation means. The error correction coding device according to claim 1 or 2, wherein 4. An error correction decoding method for correcting an error using a polynomial for error correction, comprising: calculating a degree of a divisor polynomial and a degree of a polynomial to be divided; and a Euclidean algorithm using the degree of the divisor polynomial. And determining whether the degree difference between the degree of the dividend polynomial and the degree of the divisor polynomial is 1. If the degree difference is 1, the degree of the divisor polynomial and the degree of the divisor polynomial are determined. Calculating the coefficients of the remainder polynomial using the two coefficients from the higher order, and using the highest order coefficients of the subject polynomial and the divisor polynomial when the order difference is other than 1. Calculating the coefficient of the remainder polynomial and, if the degree obtained by subtracting 1 from the degree of the dividend polynomial is greater than or equal to the degree of the divisor polynomial, repeating the step after replacing the remainder polynomial with the dividend polynomial; , After one polynomial subtraction operation is completed, replacing the divisor polynomial with the divisor polynomial and replacing the remainder polynomial with the divisor polynomial. 5. An error correction decoding method for correcting an error using a polynomial for error correction, the step of calculating the degree of a divisor polynomial and the degree of a polynomial to be deleted, and a Euclidean algorithm using the degree of the divisor polynomial. And determining whether the degree difference between the degree of the dividend polynomial and the degree of the divisor polynomial is 1 or more,
Calculating the coefficient of the remainder polynomial using two coefficients from the higher order of the dividend polynomial and the divisor polynomial when the degree difference is 1 or more, and when the degree difference is 0, Calculating the coefficients of the remainder polynomial using the highest order coefficients of the dividend polynomial and the divisor polynomial, and comparing the degree of the remainder polynomial with the degree of the divisor polynomial, and the degree of the remainder polynomial is Replacing the remainder polynomial with the dividend polynomial if the degree is greater than or equal to the degree of the divisor polynomial; and replacing the remainder polynomial with the dividend polynomial if the degree of the remainder polynomial is less than the degree of the divisor polynomial, Replacing a polynomial with the divisor polynomial. 6. An error correction decoding method for correcting an error using a polynomial for error correction, wherein a step of calculating a degree of a divisor polynomial and a degree of a polynomial to be deleted, and a Euclidean algorithm using the degree of the divisor polynomial Determining whether or not the degree difference between the degree of the dividend polynomial and the degree of the divisor polynomial is 1; and Calculating a coefficient of a residual polynomial and a coefficient of two polynomials for calculating an error locator polynomial by using two coefficients from each higher order of the polynomial; Using the highest order coefficients of the polynomial and the divisor polynomial to calculate the coefficients of the remainder polynomial and the two polynomials for calculating the error locator polynomial, subtract 1 from the degree of the polynomial to be deleted. If the result is equal to or greater than the degree of the divisor polynomial, the step is repeated after replacing the remainder polynomial with the divisor polynomial. Replacing the remainder polynomial with the divisor polynomial, and replacing the two polynomials for calculating the error locator polynomial with each other. 7. An error correction decoding method for performing error correction using a polynomial for error correction, a step of calculating an order of a divisor polynomial and an order of a dividend polynomial, and a Euclidean algorithm using the order of the divisor polynomial. And determining whether the degree difference between the degree of the dividend polynomial and the degree of the divisor polynomial is 1 or more,
When the degree difference is 1 or more, the coefficient of the remainder polynomial and the coefficient of two polynomials for calculating the error locator polynomial are calculated using two coefficients from the higher order of the dividend polynomial and the divisor polynomial, respectively. Calculating the coefficient of the remainder polynomial and the coefficient of the two polynomials for calculating the error locator polynomial by using the highest order coefficients of the dividend polynomial and the divisor polynomial when the degree difference is 0; Comparing the degree of the remainder polynomial and the degree of the divisor polynomial, and replacing the remainder polynomial with the dividend polynomial if the degree of the remainder polynomial is greater than or equal to the degree of the divisor polynomial,
If the degree of the remainder polynomial is smaller than the degree of the divisor polynomial, replace the divisor polynomial with the dividend polynomial,
While replacing the remainder polynomial with the divisor polynomial,
Replacing the two polynomials for calculating the error locator polynomial with each other.