JP3255130B2 - Data inspection method and apparatus, and recording medium - Google Patents

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a data inspection method and apparatus for inspecting the presence or absence of data errors based on a CRC and a recording medium on which a program for executing the inspection method is recorded.

[0002]

2. Description of the Related Art As a method for checking whether there is an error in data recorded on a recording medium and data transmitted through a transmission line, a parity check (to match an odd number or an even number in a byte unit) is performed. A method of adding 1-bit parity to each byte) and a sum check (a method of adding 2 bytes which are the addition result of each byte over the entire medium) are used. These methods are simple error checking methods that require less computational load and test storage capacity. However, these methods do not have high inspection accuracy and often fail to perform accurate error inspection.

As an error checking method having a higher checking accuracy than such checking methods, a CRC (Cyclic Redundancy Ch.
eck: cyclic redundancy check) is known. The CRC is often used for inspection when data reliability is insufficient, and is mainly used for applications such as serial communication and access to a hard disk.

Hereinafter, the concept of the CRC will be briefly described. CRC uses a cyclic code (a code in which a vector obtained by cyclically shifting an arbitrary code word of a certain code by an arbitrary bit is also a code word) that is a code effective for error checking, and uses a predetermined code as a code. Divide by the number and use the remainder for inspection. This cyclic code data block is composed of k information bits and (nk) check bits.

[0005] Then, consider the data as a polynomial of a variable x,
Treat mathematically. For example, for data "101011",
1 of leftmost x ^5, 1 second from the left end x ^3, likewise the third 1 x ^1, when one of the right-most were considered constant term, expressed the data polynomial x ⁵ + x ³ + x + 1.

For such a polynomial expression, the following modulo 2 addition of a polynomial is defined and an operation based on this is performed. In general, mod N addition indicates addition within a range of a number N, and portions exceeding N are discarded. Therefore, in mod 2 addition, 0 + 1 = 1, 1 + 1 = 0, which means “binary addition without carry”, which is an exclusive OR operation of both bits in addition of binary values. (EX-O
R). Specifically, it is as follows. 1x ⁿ + a ^{1x n = 0x n 1x n +} 0x n = 0x n + 1x n = 1x n 0x n + 0x n = 0x n -1x n = 1x n above, in the mod 2 adder, associativity, distributivity, exchange It can be seen that the rule holds. Further, the mod 2 adder, because it is -1x ⁿ = 1x ^n, subtraction is the same as additive.

A cyclic code can be uniquely defined by a (n−k) -th order residue generating polynomial G (x) that determines a check bit of data. This residue generating polynomial G
Generation of a cyclic code by (x) is performed as follows.

Message polynomial M indicating information bits
In order to encode (x), x ( ^nk ) is multiplied by M (x) to obtain x ( ^nk ) M (x), and the multiplication formula is divided by the remainder generator polynomial G (x). The quotient and remainder of this division are Q
Assuming that (x) and R (x), the following equation (1) holds. x ^nk · M (x) = Q (x) · G (x) + R (x) (1)

For example, transmission data U (x) in communication
Is generated by dividing the remainder R (x) by x ^nk・ Addition to M (x)
Calculate. Addition and subtraction are the same in mod 2 addition
Then, U (x) is expressed by the following equation (2). U (x) = x^nkM (x) + R (x) = Q (x) G (x) (2) Therefore, in the transmission data, the information bits of the upper k bits are
x^nk-Inspection of lower (nk) bits, representing M (x)
The bits represent R (x). From the above equation (2),
Expression (3) is derived. U (x) ÷ G (x) = (x^nkM (x) + R (x)) ÷ G (x) = Q (x) (3) As can be seen from equation (3), the data including the check bits
Dividing the entire data U (x) by the remainder generator polynomial G (x)
The remainder is 0. Therefore, the remainder of this division is 0 on the receiving side.
Whether the transmission data is correct or not.
I can get out. Here, the division is mod 2 addition, that is, 2
EX so that carry and borrow do not occur.
-OR. Therefore, in this case, the remainder is always
One bit less than the divisor, so that the remainder is
And the divisor is a remainder generator polynomial.

Next, such a specific example will be described. For example,
Residue generating polynomial G (x) = x^Five+ X ^Four+ X^TwoUsing +1
Consider a cyclic code where n = 15, k = 10, and nk = 5. Me
Message polynomial M (x) = x⁹+ X^Five+ X^TwoCorresponds to +1
To encode the message “1000100101”
x^Five-Divide M (x) by G (x) to get the remainder R (x)
Ask like.

[0011]

(Equation 1)

Therefore, x ⁵ · M (x) is expressed by the following equation (4), and transmission data U (x) is expressed by x ⁵ · M (x)
And the remainder R (x) = x + 1, so that the following equation (5) is obtained. ^{x 5 · M (x) =} x 14 + x 10 + x 7 + x 5 = (x 5 + x 4 + x 2 +1) × (x 9 + x 8 + x 7 + x 3 + x 2 + x + 1) + (x + 1) ... (4) U (X) = (x ¹⁴ + x ¹⁰ + x ⁷ + x ⁵ ) + (x + 1) (5)

The transmission data U (x) generated by the (nk) -order remainder generation polynomial G (x) in this way can detect any burst error of length (nk) or less. Proven.

[0014]

As a general method for obtaining a remainder in CRC, the following two methods have conventionally been used. In the first conventional method, division is performed sequentially from the upper digit while shifting by one bit.
In the first conventional method, the calculation is simple, but there is a problem that many loops are required and the execution speed is slow.
On the other hand, the second conventional method is a method of increasing the execution speed by using a remainder table, in which the remainder in all kinds of dividends (2 ^k ) of k bits is stored in advance as a table, and division is performed. In this case, the necessary remainder is obtained by referring to the table. Although the second conventional method has a high execution speed, it has a problem that a memory for storing a table having a huge data amount is required.

[0015] The present invention has been made in view of such circumstances, and can provide a faster execution speed than the first conventional method without providing a table having a huge amount of data unlike the second conventional method. An object of the present invention is to provide a data inspection method and apparatus based on CRC, which can shorten the calculation time, and a recording medium on which a program for executing the inspection method is recorded.

[0016]

According to a first aspect of the present invention, there is provided a data inspection method comprising: multiplying a polynomial of x representing k-bit data by x ^nk in a predetermined (n−k) -th remainder generation polynomial of x; In a data inspection method based on CRC for inspecting whether there is an error in the data according to the remainder when the obtained polynomial is divided, each polynomial of x indicating each of k kinds of data is multiplied by x ^nk The k remainders obtained by dividing the polynomial by the remainder generation polynomial are stored, and the k remainders in the k remainders are stored .
An exclusive OR operation is performed on a plurality of remainders, and a remainder obtained by dividing a polynomial obtained by multiplying x ^nk by a polynomial of x indicating any of the data by the remainder generation polynomial is obtained.

According to a second aspect of the present invention, in the data inspection method according to the first aspect, the k kinds of data are stored in a j-th digit (j
= 1, 2, ..., k) is 1, and all other digits are
It is characterized in that it is k kinds of data, where

The data checking method according to claim 3, claim
In 2, k = 8, and the eight types of data are:
“10000000”, “01000000”, “00100000”, “000100
00 "," 00001000 "," 00000100 "," 00000010 ",
It is characterized by being "00000001" .

[0019]

According to a fourth aspect of the present invention, there is provided a data inspection method, wherein a (n−k) / th remainder generation polynomial of x is given by (n−k) /
Sequentially obtains a 2-bit unit of data a plurality continuously such the x of a portion of Lud over data polynomial when divided by a polynomial obtained by multiplying the x ^nk (nk) bits remainder, calculated remainder a data inspection method which, based on the CRC to check whether there is an error in the data formed by the succession depending on the communication
Continued to become the data in (n-k) / 2 bits of data and the said in continuous comprising data (n-k) / preceding adjacent to 2-bit data (n-k) / 2 (N−k) bits of upper (nk) /
A first step of obtaining an exclusive OR with two bits, and a second step of obtaining a remainder when a polynomial obtained by multiplying a polynomial of x indicating the exclusive OR result by ^xnk is divided by the remainder generating polynomial. X ^{(nk) / 2 in} a polynomial in x indicating the lower ^{(nk) / 2} bits of the remainder of the ^(nk) bits for the preceding adjacent (nk) / 2 bits of data
And a third step of obtaining an exclusive OR of a polynomial multiplied by x and a polynomial of x indicating the remainder obtained in the second step, wherein the first, second, and third steps are repeated. I do.

According to a fifth aspect of the present invention, there is provided a data inspection method comprising:
In 4 , when obtaining the remainder in the second step,
A method for determining a remainder according to any one of claims 1 to 3 is applied.

According to a sixth aspect of the present invention, in the data inspection apparatus, when a polynomial in which a polynomial of x indicating k-bit data is multiplied by x ^nk is divided by a predetermined (nk) -order remainder generation polynomial of x. In a data inspection apparatus based on CRC for inspecting whether or not there is an error in the data according to the remainder, each polynomial obtained by multiplying each polynomial of x indicating each of the k kinds of data by x ^nk is represented by the remainder generation polynomial. Storage means for storing k remainders obtained by dividing by k, and performing an exclusive OR operation on a plurality of remainders among the k remainders to obtain x ^nk in a polynomial of x indicating any of the data. Means for calculating a remainder when the multiplied polynomial is divided by the remainder generating polynomial .

According to a seventh aspect of the present invention, there is provided a data inspection apparatus, wherein a predetermined (n−k) -th order remainder generation polynomial of x is (nk) /
Sequentially obtains a 2-bit unit of data a plurality continuously such the x of a portion of Lud over data polynomial when divided by a polynomial obtained by multiplying the x ^nk (nk) bits remainder, calculated remainder a data inspection apparatus according to the CRC to check whether there is an error, the data formed by the succession depending on the communication
Continued to become the data in (n-k) / 2 bits of data and the said in continuous comprising data (n-k) / preceding adjacent to 2-bit data (n-k) / 2 (N−k) bits of upper (nk) /
First operation means for obtaining an exclusive OR with two bits, and second operation for obtaining a remainder when a polynomial obtained by multiplying a polynomial of x indicating the exclusive OR result by ^xnk is divided by the remainder generation polynomial Means and x ^{(nk) / 2 in} a polynomial of x indicating the lower ^{(nk) / 2} bits of the remainder of the ^(nk) bits with respect to the preceding adjacent (nk) / 2 bits of data.
And a third operation means for obtaining an exclusive-OR of a polynomial multiplied by x and a polynomial of x indicating the remainder obtained by the second operation means , wherein the first, second and third operation means Is repeated.

[0024] The data inspection apparatus according to claim 8 can be configured as follows.
In 7 , the second arithmetic means calculates the remainder,
The method for determining a remainder according to any one of claims 1 to 3 is applied.

According to a ninth aspect of the present invention , there is provided a recording medium having a predetermined (n-
k) In the next remainder generation polynomial of x, according to a remainder obtained by dividing a polynomial obtained by multiplying x ^nk by a polynomial of x indicating k-bit data, a CRC is used to determine whether or not the data has an error.
In a computer-readable recording medium on which a program for testing based on is recorded, a polynomial obtained by multiplying each polynomial of x indicating k kinds of data by x ^nk is divided by the remainder generating polynomial. A program code means for causing the computer to store k remainders at the time of execution, and performing an exclusive OR operation on a plurality of remainders in the k remainders to indicate any of the data. x
And a program code means for causing the computer to determine a remainder when a polynomial obtained by multiplying the polynomial by ^xnk with the remainder generation polynomial is obtained .

According to a tenth aspect of the present invention, there is provided a recording medium having a predetermined (n-
At remainder generator polynomial k) the next x, divided by the polynomial obtained by multiplying the x ^nk to polynomial in x of a portion of the (nk) / 2 bits Lud over data, such a plurality consecutive data units (N
−k) The remainder of bits is sequentially obtained, and according to the obtained remainder,
In-readable recording medium in are recorded computer programs for inspection to the basis whether the there is an error in continuously formed by data in CRC, the communication
Continued to become the data in (n-k) / 2 bits of data and the said in continuous comprising data (n-k) / preceding adjacent to 2-bit data (n-k) / 2 (N−k) bits of upper (nk) /
A first program code means for causing the computer to calculate an exclusive OR with two bits, and a polynomial obtained by multiplying a polynomial of x indicating the exclusive OR result by ^xnk by the remainder generating polynomial. A second program code means for causing the computer to determine the remainder of (k), and the lower (nk) / (k) of the remainder of the (nk) bits with respect to the preceding adjacent (nk) / 2 bits of data.
The computer obtains an exclusive OR of a polynomial obtained by multiplying a polynomial of x representing 2 bits by x ^{(nk) / 2} and a polynomial of x representing the remainder obtained by the processing by the second program code means. A third program code means for causing the computer to repeat the processing by the first, second, and third program code means.
Program code means.

The recording medium according to claim 11 is the recording medium according to claim 10 , wherein the method according to any one of claims 1 to 3 is applied when the remainder is determined by the processing by the second program code means. The program further comprises program code means for causing the computer to perform the operation.

[0028] In the first invention according to claim 1 3,5,6,8,9 and 11, when one unit of data is constant k bits, 2 ^k kinds k types among all data of the data K is obtained by dividing the polynomial corresponding to by the remainder generation polynomial, and a plurality of residues are selected from the k residues according to arbitrary k-bit data to be inspected,
The remainder when the polynomial corresponding to each k-bit data is divided by the remainder generating polynomial is obtained by an exclusive OR operation of the selected plurality of remainders. Therefore, only by preparing a table having a data amount much smaller than that of the second conventional method, the calculation load is extremely small and the execution speed is faster than that of the first conventional method.

In the second invention according to claims 4, 7 and 10 ,
In this way, a new remainder can be obtained, and the calculation load is extremely small and the execution speed is increased as compared with the conventional case.

[0030]

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS The present invention will be specifically described below with reference to the drawings showing the embodiments. As a typical CRC, a 16-bit CRC with nk = 16 is often used. The remainder generation polynomial in this 16-bit CRC is G (x) = x ¹⁶ + x ¹⁵ + x ² +1, and burst error detection can be performed up to a maximum length of 16 bits. It has also been proven that if the burst of errors is larger than 16 bits, the error can be detected with a 99% probability. Below, this
Using a 16-bit CRC, one unit of data is 8 bits (k
= 8), the present invention will be specifically described by taking the case where it is constant as an example.

In the case of a 16-bit CRC, the remainder generator polynomial G
(X) = x ¹⁶ + x ¹⁵ + x ² +1 and the coefficient x ^nk is n
Because it is -k = 16 becomes x ^16.

Data string M in arbitrary 8-bit data units
(X) is generally represented by the following equation (6). _{M (x) = k 7 ·} x 7 + k 6 · x 6 + k 5 · x 5 + k 4 · x 4 + k 3 · x 3 + k 2 · x 2 + k 1 · x 1 + k 0 · x 0 ... (6) ( However, k _i = 0 or 1)

Therefore, the polynomial which is the dividend corresponding to this data string is as shown in the following equation (7). ^{x 16 · M (x) =} x 16 · (k 7 · x 7 + k 6 · x 6 + k 5 · x 5 + k 4 · x 4 + k 3 · x 3 + k 2 · x 2 + k 1 · x 1 + k 0 · _{^{x 0) = k 7 · x}} 16 · x 7 + k 6 · x 16 · x 6 + k 5 · x 16 · x 5 + k 4 · x 16 · x 4 + k 3 · x 16 · x 3 + k 2 · x 16 · x ² + k ₁ · x ¹⁶ · x ¹ + k ₀ · x ¹⁶ · x ⁰ (7)

Here, x ¹⁶ · x ⁷ = Q ₇ (x) · G
(X) + R ₇ (x), x ¹⁶ · x ⁶ = Q ₆ (x) · G
(X) + R ₆ (x),..., X ¹⁶ × x ⁰ = Q ₀ (x)
When G (x) + R ₀ (x) is set, the above equation (7) can be transformed into the following equation (8). ^{x 16 · M (x) =} k 7 · {Q 7 (x) · G (x) + R 7 (x)} + k 6 · {Q 6 (x) · G (x) + R 6 (x)} + · _{·· + k 0 · {Q 0} (x) · G (x) + R 0 (x)} = {k 7 · Q 7 (x) + k 6 · Q 6 (x) + ··· + k 0 · Q 0 ( x)｝ · G (x) + {k ₇ · R ₇ (x) + k ₆ · R ₆ (x) +... + k ₀ · R ₀ (x)} (8)

Therefore, the arbitrary 8 shown in the above formula (6)
The remainder when the polynomial corresponding to the data sequence M (x) in bit data units is divided by the remainder generating polynomial G (x) is expressed by the following equation (9). k ₇ · R ₇ (x) + k ₆ · R ₆ (x) + k ₅ · R ₅ (x) + k ₄ · R ₄ (x) + k ₃ · R ₃ (x) + k ₂ · R ₂ (x) + k _{1 · R 1 (x) + k} 0 · R 0 (x) ... (9)

In the equation (9), R₇(X), R
₆(X), R_Five(X), R_Four(X), R _Three(X), R_Two
(X), R₁(X), R₀(X) is x⁷,
x⁶, X ^Five, X^Four, X^Three, X^Two, X¹, X⁰Corresponding to
This is the remainder obtained by dividing the polynomial by the remainder generating polynomial G (x).
Therefore, one unit of data is composed of a constant 8 bits.
Data, “10000000”, “01000000”, “0010
0000 "," 00010000 "," 00001000 "," 00000100 ",
Polynomials corresponding to “00000010” and “00000001” are surplus
Divide by the polynomial G (x) and calculate the remainder by R₇
(X), R₆(X), R_Five(X), R_Four(X), R
_Three(X), R_Two(X), R₁(X), R₀(X)
In some cases, the combination of these eight types of remainders
The remainder (check) in any unit of 8-bit data
Bit).

An 8-bit code, and the remainder generator polynomial G
Table 1 below shows specific values of R _i (x) (i = 7,..., 0) when (x) is a 16-bit CRC in which x ¹⁶ + x ¹⁵ + x ² +1.

[0038]

[Table 1]

For example, R_Five(X) is "00100000", that is, x
^FiveRepresents the remainder of (x¹⁶・ X ^Five) ÷ (x¹⁶+ X^Fifteen
+ X^Two+1) is calculated as follows to obtain R
_Five(X) = x^Fifteen+ X⁷+ X⁶+ X + 1. Therefore,
In Table 1, R_FiveX in the column of (x)^Fifteen, X⁷, X⁶, X¹,
Each x of 1^j"1" is described at the position of.

[0040]

(Equation 2)

Using these eight types of remainders, an arbitrary 1
Polynomials corresponding to 8-bit data are generated as remainder generation polynomials
An example will be described in which the remainder when dividing by an expression is obtained.
If any 8-bit data is set to “01010001”, for example,
The corresponding polynomial x ¹⁶・ (X⁶+ X^Four+1)
x¹⁶+ X^Fifteen+ X^TwoThe remainder when actually dividing by +1 is
It becomes “1000000111100101” as follows.

[0042]

(Equation 3)

The 8-bit data "010100"
01 "are x ⁶ , x ⁴ , and x ⁰ , and the corresponding bits are the remainders R ₆ (x), R ₆ shown in Table 1 above.
_The same remainder result “1000000111100101” can be obtained by adding mod 2 to ₄ (x) and R ₀ (x) as follows.

[0044]

(Equation 4)

Therefore, the mod of a plurality of R _i (x) corresponding to the position of “1” in each unit of arbitrary 8-bit data
By 2 addition, a remainder can be obtained when the polynomial corresponding to the 8-bit data is divided by the remainder generating polynomial.

The lower part of Table 1 shows a polynomial expression of the remainder of a 16-bit CRC for 8-bit data. When the above-mentioned 8-bit data “01010001” is applied to the more generalized notation, k ₇ = 0 and k ₆ =
1, k ₅ = 0, k ₄ = 1, k ₃ = 0, k ₂ = 0, k ₁ =
Since 0 and k ₀ = 1, the same remainder result “1000000111100101” can be obtained by substituting these “0” and “1” values and adding mod 2 as follows.

[0047]

(Equation 5)

Deriving this remainder polynomial from 8-bit data in this manner is referred to as "combination division" in the following description.

As described above, 8 bits of 8-bit data
Type data “10000000”, “01000000”, “0010000”
0 "," 00010000 "," 00001000 "," 00000100 "," 0
0000010 "," only and stored in the memory to eight remainder as a table in 00000001 ", by referring to the table value, it is possible to easily obtain the remainder of the 8-bit 2 all ^eight data.

Next, using such combination division,
An example of performing a remainder operation on two consecutive data units will be described.

FIG. 1 is a functional block diagram of an inspection apparatus 10 for inspecting a data error by CRC. The inspection device 10
A reading unit 11 for reading recorded data from the memory card 1 to be inspected, a writing unit 12 for writing an inspection result to the memory card 1 by CRC, a ROM 13 for storing a CRC inspection program, and various calculations for CRC inspection. Calculation unit 14 for performing calculation and an RA for storing an intermediate value calculated at the time of the CRC check.
M15 and a CPU 16 for controlling these components.
The RAM 15 stores a remainder table 15a calculated in advance and representing the eight types of remainders as described above.

Considering a certain 8-bit data,
The remainder (ie, 16
The data to be inspected is formed by adding the check bits of the bits, and the data including the remainder must be divided as the dividend.

Assuming that the preceding data string, quotient, and remainder are M '(x), Q' (x), and R '(x), the following equation (10) holds. x ¹⁶ · M ′ (x) = Q ′ (x) · G (x) + R ′ (x) (10)

Therefore, the following equation (11) holds for a data string M (x) obtained by adding new data D (x) to the data string M (x). ^{x 16 · M (x) =} x 16 · {x 8 · M '(x) + D (x)} = x 8 · x 16 · M' (x) + x 16 · D (x) = x 8 · Q ' (X) · G (x) + x ⁸ · R ′ (x) + x ¹⁶ · D (x) (11)

Here, R '(x) is replaced with R' of the upper 8 bits.
_Up (x) and lower 8 bits R ' _lo (x)
R ′ (x) is represented by the following equation (12), and using this to rewrite equation (11) gives the following equation (13). ^{R '(x) = x 8} · R' up (x) + R 'lo (x) ... (12) x 16 · M (x) = x 8 · Q' (x) · G (x) + x 16 · R ^{_{'up (x) + x 8}} · R' lo (x) + x 16 · D (x) = x 8 · Q '(x) · G (x) + x 16 · {R' up (x) + D (x)} + X ⁸ · R ' _lo (x) ... (13)

In the equation (13), x ¹⁶ · ｛R ' _up (x)
Since + term D (x)} is greater than x ¹⁶ degree can be divided by the remainder generator polynomial G (x). Assuming that the quotient and the remainder at this time are Q ″ (x) and R ″ (x), the following equation (14) holds. x ¹⁶ · {R ′ _up (x) + D (x)} = Q ″ (x) · G (x) + R ″ (x) (14)

By rewriting equation (13) using the relation of equation (14), the following equation (15) is obtained. ^{x 16 · M (x) =} x 8 · Q '(x) · G (x) + Q "(x) · G (x) + R" (x) + x 8 · R' lo (x) = {x 8 · Q ′ (x) + Q ″ (x)｝ · G (x) + R ″ (x) + x ⁸ · R ′ _lo (x) (15) The first term {x ⁸ · Q ′ (x) in equation (15) ) + Q ″
Since (x)｝ · G (x) is divisible by G (x), x ¹⁶
The remainder when M (x) is divided by G (x) is R ″ (x)
+ X ⁸ · R ' _lo (x).

Therefore, to summarize the above, by performing the following steps, new data D (x)
To obtain a new remainder. (Step 1): mod 2 is added to the new data D (x) and the upper 8 bits R ′ _up (x) of the previous residue. (Step 2): A residue R ″ (x) in a 16-bit CRC using the addition result as a dividend is calculated. (Step 3): The calculated R ″ (x) and the lower 8 bits R of the immediately preceding residue. ' _Lo (x) by x ⁸ and mod 2 addition, and the addition result (R ″ (x) + x ⁸ · R ′ _lo (x))
Is the new remainder.

If the above-described combination division is used in step 2, the remainder R ″ (x) can be obtained in a short time. FIG. FIG.

Next, the remainder in two consecutive units of data
A specific example of the remainder operation will be described. Two consecutive days
Polynomial (x) corresponding to the data “01010001” and “10010001”¹⁶
・ (X¹⁴+ X¹²+ X⁸+ X⁷+ X^Four+1)) is 16 bits
CRC (G (x) = x¹⁶+ X ^Fifteen+ X^Two+1)
The remainder in the case is calculated as “011001
0101100011 ".

[0061]

(Equation 6)

When this calculation process is viewed before and after the broken line, 1
The previous residue (corresponding to R ′ (x)) is “100001110010
1 "and the new data (corresponding to D (x)) is" 0000
Therefore, the degree is adjusted, and the remainder is represented by the upper 8 bits (corresponding to R ' _up (x)) of "00010000" and the lower 8 bits (corresponding to R' _lo (x)) of "11100101". And modulo 2 of the upper eight bits “00010000” and the new data “00000000”. The remainder (R ″ (x) is obtained by dividing “00010000” by the remainder generating polynomial G (x) as a dividend. Equivalent) "1000000001100011" is calculated. Then, mod 2 is added to the remainder “1000000001100011” with the order of the lower 8 bits “11100101” of the previous residue set to mod 1, and the final remainder “0110010101100011” is added.
Get. Such a calculation process will be described below.

[0063]

(Equation 7)

FIG. 3 is a block diagram showing the configuration of an embodiment of the recording medium of the present invention. The program exemplified here includes a step of inputting new data D (x), a step of mod 2 adding the new data D (x) and the upper 8 bits R ′ _up (x) of the previous residue. , The remainder R ″ (x) in a 16-bit CRC using the result of addition as a dividend
And a value obtained by modulating the obtained R ″ (x) and the value obtained by x ⁸ of the lower 8 bits R ′ _lo (x) of the previous remainder is mod 2
Step of addition and the result of addition (R ″ (x) + x ⁸
And outputting R ′ _lo (x)) as a new remainder, which is recorded on a recording medium described below.

In FIG. 3, a recording medium 21 that is connected online to the computer 20 is, for example, a WWW (World Wide Web) server computer that is installed separately from a place where the computer 20 is installed. The program 21a is recorded as follows. The program 20a read from the recording medium 21 controls the computer 20 so that the computer 20 calculates the remainder in the CRC.

The recording medium 22 provided inside the computer 20 uses, for example, a hard disk drive or a ROM installed therein. The recording medium 22 stores the program 22a as described above. When the program 22a read from the recording medium 22 controls the computer 20, the computer 20 calculates the remainder in the CRC.

The recording medium 23 loaded and used in the disk drive 20a provided in the computer 20 is a transportable medium such as a magneto-optical disk, a CD-ROM or a flexible disk. The program 23a is recorded as follows. By controlling the computer 20 by the program 23a read from the recording medium 23, the computer 20 calculates the remainder in the CRC.

In the above example, one unit is 8 bits and the remainder is 16 bits. However, the present invention is not limited to this.
Of course, if it is twice the unit, the same can be done.

Although the description has been given of the case where the data error in the memory card is checked, it goes without saying that the present invention can be applied to the data error check of another recording medium such as a flash memory and the data error check in serial communication. .

[0070]

As described above, according to the present invention, if a table representing the remainder for k kinds of data is prepared, 2
^The remainder for all the ^k types of data can be easily obtained, and the remainder can be easily obtained only by using a table with a small amount of data, which can contribute to a reduction in calculation load in CRC.

Further, the remainder for two consecutive data units can be obtained very easily, the calculation load on the CRC is extremely small, and the execution speed of the data inspection based on the CRC can be increased.

As described above, according to the present invention, the calculation load on the CRC can be reduced. Therefore, the application of the CRC to a recording medium, such as a memory card or a flash memory, to which the CRC has not been applied due to a large calculation load, is promoted. It is possible to do.

[Brief description of the drawings]

FIG. 1 is a functional block diagram of an inspection device that inspects a data error by a CRC.

FIG. 2 is an explanatory diagram showing a process of obtaining a new remainder for two consecutive units of data.

FIG. 3 is a block diagram illustrating a configuration of an embodiment of a recording medium.

[Explanation of symbols]

 10 Inspection device 14 Calculator 15a Remainder table 16 CPU 20 Computer 21, 22, 23 Recording medium

Claims (11)

(57) [Claims] In a predetermined (n−k) -th order remainder generation polynomial of x, a polynomial obtained by multiplying a polynomial obtained by multiplying a polynomial of x representing k-bit data by x ^nk is divided into the data according to the remainder. In a data checking method based on CRC for checking whether or not there is an error, k polynomials obtained by multiplying each polynomial of x indicating each of k kinds of data by x ^nk by the remainder generation polynomial are k number of times. The remainder is stored, a plurality of remainders among the k remainders are subjected to an exclusive OR operation, and a polynomial obtained by multiplying a polynomial of x indicating any data by x ^nk is represented by the remainder generation polynomial. A data inspection method characterized by obtaining a remainder when divided. 2. The k kinds of data are k kinds of data in which the number of the j-th digit (j = 1, 2,..., K) is 1 and the numbers of other digits are all 0. The data inspection method according to claim 1. 3. k = 8, and the eight kinds of data are:
“10000000”, “01000000”, “00100000”, “000100
00 "," 00001000 "," 00000100 "," 00000010 ",
3. The data inspection method according to claim 2, wherein the value is "00000001". At 4. The predetermined (n-k) modulo the generator polynomial for the next x, of x of a portion of the (n-k) / 2 bits Lud over data, such a plurality consecutive data units A residue of (n−k) bits when a polynomial multiplied by x ^nk is divided is sequentially calculated, and according to the determined remainder, a CRC for checking whether or not the continuous data has an error is determined. a data inspection methods based, in the data formed by the succession (n-
(k) / 2-bit data and (n−k) / 2-bit data preceding and preceding (n−k) / 2-bit data in the continuous data.
-K) A first step of calculating an exclusive OR with the upper (n−k) / 2 bits of the remainder of the (n−k) bits of the data of 2 bits, and x of x indicating the exclusive OR result thereof A second step of obtaining a remainder when a polynomial obtained by multiplying the polynomial by ^xnk is divided by the remainder generating polynomial; and (n) regarding the preceding adjacent (nk) / 2-bit data.
-K) Exclusive use of a polynomial in which a polynomial in x representing the lower ( ^{nk) / 2} bits of the remainder of bits is multiplied by x ^{(nk) / 2} and a polynomial in x representing the remainder obtained in the second step A third step of obtaining a logical sum, and repeating the first, second, and third steps. 5. A method for determining a remainder in the second step.
A method for determining a remainder according to any one of claims 1 to 3
The data inspection method according to claim 4, which is applied . 6. A remainder generating polynomial of a predetermined (nk) degree x
In the formula, x ^nk is ^added to a polynomial of x indicating k-bit data.
The data is multiplied according to the remainder when the polynomial is divided.
CRC based data inspection to check for errors
In the apparatus, each polynomial of x indicating k kinds of the respective data
Each polynomial obtained by multiplying the expression by x ^nk is represented by the remainder generator polynomial.
Storage means for storing k remainders when divided,
Performs exclusive OR operation on multiple remainders in the remainder, and
Multiplied by x ^nk to a polynomial in x indicating the desired data
A method for calculating the remainder when the term is divided by the remainder generator polynomial
A data inspection device comprising: a step ; At 7. predetermined (n-k) modulo the generator polynomial for the next x, of x of a portion of the (n-k) / 2 bits Lud over data, such a plurality consecutive data units A residue of (n−k) bits when a polynomial multiplied by x ^nk is divided is sequentially calculated, and according to the determined remainder, a CRC for checking whether or not the continuous data has an error is determined. a data inspection apparatus according, in the data formed by the succession (n-
(k) / 2-bit data and (n−k) / 2-bit data preceding and preceding (n−k) / 2-bit data in the continuous data.
First arithmetic means for calculating the exclusive OR of the (k) / 2 bits of data with the higher (nk) / 2 bits of the remainder of the (nk) bits, and x indicating the exclusive OR result thereof Second arithmetic means for obtaining a remainder when a polynomial obtained by multiplying the polynomial of x by x ^nk is divided by the remainder generation polynomial, and the (n-k) / 2-bit data related to the preceding adjacent (n−k) / 2 bits
-K) a polynomial obtained by multiplying x ^{(nk) / 2} by a polynomial in x indicating the lower ( ^{nk) / 2} bits of the remainder of the bit, and the second function
Characterized in that a third arithmetic means for obtaining the exclusive OR of the polynomial of x indicating a remainder obtained by calculation means, and repeats the processing in the first, second and third arithmetic means Data inspection device. 8. The method according to claim 1, wherein the second computing means calculates a remainder.
A method for determining a remainder according to any one of claims 1 to 3
The data inspection device according to claim 7, wherein the data inspection device is applied. 9. In a predetermined (n−k) -th order remainder generation polynomial of x, x ^nk is ^added to a polynomial of x representing k-bit data.
According to the remainder when dividing the multiplied polynomial, the data
To check if there is an error on the basis of the CRC
Readable on the computer where the program is recorded
X indicating each of the k types of data on a capable recording medium
Generating each polynomial obtained by multiplying each polynomial of x by x ^nk
Before storing k remainders when dividing by polynomial
Program code means for causing the computer;
Performs exclusive OR operation on multiple remainders among the remainders
Multiply x ^nk by any polynomial in x indicating the data
Is obtained by dividing the obtained polynomial by the remainder generating polynomial.
Program code for causing the computer to
Recording medium characterized by having a means. At 10. predetermined (n-k) modulo the generator polynomial for the next x, of x of a portion of the (n-k) / 2 bits Lud over data, such a plurality consecutive data units A (n−k) -bit remainder obtained by dividing the polynomial by multiplying x ^nk by the polynomial is sequentially obtained, and according to the obtained remainder, whether or not there is an error in the continuous data is determined based on the CRC. in-readable recording medium on a computer that is recorded a program for inspecting, (n-k) in the data formed by the continuous / 2-bit data formed by said successive data <br/> And (n−k) / 2 bits of the remainder of the (nk) bits related to (n−k) / 2 bits that precede the (nk) / 2 bits in the data. First program code means for causing the computer to determine an exclusive OR; A second program code means for the determination of the remainder when divided by a polynomial obtained by multiplying the x ^nk polynomial of x indicating the result of exclusive OR operation with the remainder generating polynomial to said computer, said previous adjacent (n
-K) / 2 multiplied by x ^{(nk) / 2} to a polynomial of x indicating the lower ^{(nk) / 2} bits of the remainder of ^(nk) bits for the 2-bit data, and the second program code
Third program code means for causing the computer to calculate an exclusive OR with a polynomial of x indicating the remainder obtained by the processing by the processing means, and processing by the first, second and third program code means And a fourth program code means for causing the computer to repeat the above. 11. The apparatus according to claim 2, wherein
When asking you to remainder in the process, the serial to claim 1
Applying the method of determining the remainder of the
2. The method according to claim 1, further comprising:
0 recording medium.