JPS60114037A - Error correcting device - Google Patents

Abstract

PURPOSE:To attain detection and correction of an error arisen without being detected and corrected at the 1st decoder by means of the 2nd decoder by constituting the titled circuit with a coder generating the 1st code and the 2nd code on a matrix while being subject to orthogonal opertion and a decoder detecting and correcting the error in the order of the 1st code and the 2nd code. CONSTITUTION:In an error correcting device using a coder 10, the 2nd coder 11, the 1st coder 12, a transmission or recording medium 20, a decoder 30, the 1st decoder 31, and the 2nd decoder 32, the 2nd coder generates the 2nd check code Q1(i=1, 2,...7) satisfying Equation I the same as the 1st coder. The 2nd decoder attains correction as expressed in Equation II depending on the number P of pointers. Thus, the error overlooking is suppressed lower by giving an error detecting capability to the 2nd decoder in this way, and the error correcting capability is the product of the both by giving a single error correcting capability to the 1st code and a 7-fold error correcting capability to the 2nd code so as to realize a very high correcting capability and also to decrease remarkably the number of times of arithmetic for error detection and correction.

Description

DETAILED DESCRIPTION OF THE INVENTION Field of Industrial Application The present invention relates to an error correction device that can be used for transmitting, recording and reproducing digital data.

Conventional configuration and its problems In recent years, P
GM recorders have been developed, but defects and scratches on the recording medium,
Error correction codes are used to correct code errors caused by dust or the like.

A conventional error correction device will be described below with reference to the drawings. FIG. 1 is a configuration diagram of an error correction code used in a conventional error correction device, where 1 indicates audio data such as a signal w, 21d a first check code P, and 3 a second check code t21'. The first code C1 is composed of eight pieces of data W or second check code Q and one first check code P in the vertical direction of the figure, and is referred to as one block.

The second code C2 is composed of six pieces of data W and two pieces of second check code Q at every interleaving distance D' (=16 blocks) in the diagonally lower right direction in the figure. First code C
1 is a cyclic redundancy check code (O
(abbreviated as RCG), which only detects errors. The second code C is a 2-digit adjacent code, and the decoding information of the first code (
In other words, error correction is performed based on information on whether or not an error has been detected.

FIG. 2 is a block diagram of a conventional error correction device.
0 is an encoder, 11 is a second encoder, %12 is a first encoder, 20 is a transmission/mechanism recording medium, 3o is a decoder%3
1 is a first decoder, 32 is a second decoder 7...h).

The operation of the error correction device configured as described above will be explained below.

A data string such as a digitized audio signal is inputted from the input terminal of the encoder 1o, and first, along with the second check code Q generated by the second encoder 11, it is directed to D in the 02 direction in FIG. ’ Arranged every other block. When 6 data and 2 second check codes are placed in the C2 direction, the next set of 6 data and 2 check codes is placed in the 402 direction from a position shifted one block to the right. . They are arranged in the following order. Next, the first encoder 11 takes out the data arranged above and the second check code eight by one in the 01 direction of FIG. 1, adds the first check code p2, and transmits or sends out the recording medium 20vC . When the first column is sent out, the second and third columns are sent out in order, and this data and check code string form an error correction code in which 246 blocks are called one segment unit.

The data transmitted or received or reproduced from the recording medium 2o and the check code string are input to the decoder 3°, and first, the first decoder 31 detects the presence or absence of errors.

This decoding information is sent to the second decoder 32 together with the data W and the second check code Q as a 1-bit pointer for every 11 columns in the 01 direction of FIG. The second decoder 32 is
Check the number of pointers to which each data W in the C2 direction and the second check code Q belong, and if it is 0, there is no error, if it is 1 or 2, error correction is performed, and if it is 3 or more, correction is not possible. The data W is read out in the C2 direction while adding a flag indicated to each data W, and outputted through the output terminal of the decoder 3o. The output data is again converted into analog data and returned to the original audio signal.

However, the above configuration has a serious problem in that if the number of errors in the %C2 direction exceeds 3, the errors cannot be corrected. Furthermore, if an error is overlooked by the first decoder, there is a serious problem in that the error is not corrected by the second decoder and is passed through.

OBJECTS OF THE INVENTION An object of the present invention is to provide an error correction device that can correct more than three errors and also detect and correct errors missed by the first decoder.

Structure of the Invention The error correction device of the present invention is configured to handle arbitrary positive integers m and h (m>h
) and m b pit data towns (
]=1+2t...h) and (m-h) b-bit check codes Qj(j-1, 2,...m-h)
a second encoder that generates a second code by arranging them in a second array state, and b bits specified by arbitrary positive integers n and k(n)k) and the positive integer Data Wi (i=1.2....k) and (n-k)
b-bit check codes Pi(i-1, 2,...
n-k) ((a first encoder that generates a first code by placing it in a first array state orthogonal to the second array state; an encoder that generates an error correction code by the encoder; A first decoder transmits or records the error correction code outputted by the encoder, receives or reproduces it, first detects and corrects errors using the first code, and then detects and corrects errors using the second code. A decoder consisting of a second decoder E, and this makes it possible to
The code is a (32°25) Reed-Solomon code on Galois field GF(28), and the first code is also on Galois field GF(28).
2) By using the above (32, 29) Reed-Solomon code and further using the second code total interleave distance 1) = data for every 4 blocks or the second check code, error detection ability and correction ability can be improved. Both have dramatically improved.

DESCRIPTION OF EMBODIMENTS An embodiment of the present invention will be described below with reference to the drawings.

FIG. 3 shows a configuration diagram of an error correction code used in an error correction device in an embodiment of the present invention.

In FIG. 3, 1 is data W, 2 is first check code P,
It is a 3-digit second check code Q, and a (n, k) Reed-Solomon code (in the case of this embodiment, n=32.-29) is constructed in the vertical direction of the first code C11d, and the second code C2 is an array that is orthogonal to the first code C1 in the horizontal direction of the figure, and m pieces of data W are arranged for every interleave distance D (D=4 in this example).
Or from the second check code Q (mth) Reed-Solomon code (in this example, l11=321 h”26)
It constitutes.

FIG. 4 is a block diagram of an error correction device according to the present invention,
1o is an encoder, 11 is a second encoder, 12 is a first encoder, 20 is a transmission or recording medium, 30 is a decoder,
Reference numeral 31 denotes a first decoder, and 32 denotes a second decoder Z-'.The operation of the error correction apparatus of this embodiment constructed as described above will be described below. Since the signal flow is the same as in the conventional example, the differences from the conventional example will be explained here.

In the case of this example, the first code is (32,2 on GF(2)
9) It is a Reed-Solomon code, and its generator polynomial is given by the following equation.

G, (X) = (X-1) (X-a) (1-(1
2) GF (28) (1) ic iron a Id-GF (
28) is the root of the modulus polynomial g(X) on GF(28). For example, the following equation is used as the modulus polynomial g.

g(X)=X8+X'+X'+X2+I GF(2)
(2) 29 data W11W2...W29
Assuming that there are %3 first check codes 'Fr Pl, P2+PM, the check determinant to be satisfied by the first code is given by the following equation.

Then, equation (3) can be expressed as follows. From this, it can be expressed as . The first encoder encodes 29 data Wi(
i=IF 2.・・・-・29) 'i rA, B
, C and find Pi (i=1+21 a). The first encoder that performs this calculation can be realized as a software using a computer program.

Further, those skilled in the art know that it can also be implemented as hardware for a logic circuit, and a detailed explanation will be omitted.

The first code has 3 check codes, so the inter-code distance is 4.
Therefore, single error detection and correction and double or more error detection are possible. Generally, the intersymbol distance is d.

If the number of correctable errors is 'It, then 2t+1≦d holds true.

The first decoder therefore performs single error correction.

If double or more errors are detected, a pointer is set.

This error detection/correction process is as follows.

The received or reproduced first code is wi(i-1, 2°...
...32) Express ze. For convenience, no distinction is made between data and check codes.

First, syndrome 5i (1=Or 1 + 2)
I can claim it.

Assuming that an error has occurred on the first word Wi, the received word R4 is expressed by the following equation if the error button 't ``x s location is expressed by α''ThX1.

R1=wi+yl@ Also, the value of the syndrome satisfies equation (3).

It is expressed as Therefore, the first decoder sOI s,
+822 is calculated, each value is not 0, l: detects the occurrence of an error, and S, /S ro =S2/S, =: is 1 (1<:1(a2
) (s) and check whether it is a single error or not.
1l + set. (8) If there is an i that satisfies the formula, % 1M
It is determined that it is an error, and the error pattern obtained by the first equation is
The error correction is completed by adding the received word)=R4 of the number]].

W4=R1+71 (9) If there is no i that satisfies equation (8), it is determined that there is an error of %2 or more, a pointer is generated, and the pointer is sent to the memory in the second decoder.

The configuration of the first decoder that implements the above error detection/correction process is well known to those skilled in the art, as is the case with the first encoder, and detailed description thereof will be omitted. Further, details are described in, for example, "Coding Theory" by Imai et al., Shokodo, 1976.

In this example, the second code is (32
, 25) is a Reed-Solomon code, and its inter-code distance is 8, so if it is used alone, it can detect and correct triple errors, and if the position of the error is known by a pointer or the like.

Sevenfold correction is possible. In general, error correction when the location is known is called erasure correction, and the intersymbol distance f
d, and the number of erasure correctable errors is f6, then e
+1≦d holds true.

It is also possible to combine erasure correction with individual error detection and correction (abbreviated as error correction), in which case Fi.

2t+15+1(d holds true.

The second encoder is a second encoder that satisfies the following equation like the first encoder.
A check code Qi (i""1+21...7) is generated.

In this embodiment, the second decoder performs all of the following corrections depending on the number of pointers P.

(1) When P=o or ≧8 2. Correct the error.

(2) When 1≦P≦6 Performs 5 erasure + 1 error correction.

(a) When P=7 Perform fillage correction.

The temporary correction process for each error will be explained below. First.

The number of pointers is checked and one of s (1) + (2) + (3) is corrected. There is one pointer in each column in FIG. 3, and from the point of view of the second code orthogonal to the first code, this pointer is common to the second code in each row, so
If calculations related to pointers and locations are calculated once, they can be used commonly for each row, and the number of calculations can be reduced.

(1) 2 error correction Syndrome 5j (j=0. Ru.

Two error slams? Y+lY2% location x
If l and xJ, then the syndrome is.

A location polynomial with locations as roots.

σ(Z)selfπ(1+xiz)=1+σ1z+σ2z2(
13)-1, then the coefficient σ1. Since the following relationship holds between σ2 and syndrome Sj, the value of m in equation (14); O
Otherwise, σ1. σ2 is round. If it is 0, it is determined that there are three or more errors, a flag is set, and the correction operation ends. σ1. σ
If 2 is counted, then to find the location, (13)
Find the root of the formula = 0.

2-σ, Mu (16) And then.

Person 2 + Person = a2/σ1' (16) Since the person who satisfies equation (16) is uniquely determined, σ2/σ1
By pre-preparing the value e6 of m according to the value of 2 and having this as a root table, it is possible to find the root using equation (16) with someone else's help.

If the location is correct, the correction will be made.

(2) 5 erasures + 1 error correction destination, eraser location polynomial A' (5) Find the error position.The location of the error can be determined by the number of words where the pointer is placed.For example, if the pointer is placed on the word number, then Its location is obtained as X = a. Now, assuming that there are 6 pointers, 6 locations error slam f
Yi (1-1+2+...5).

(18) Since it is a 6th order equation of formula Z, it is expanded as follows and each coefficient Di (i -0,1,...6)
I put it on.

Then, equation (18) is.

It is expressed as next, Then, equation (18) is.

becomes. Similarly, And then.

Then, Then, A can be calculated.

Next, if we set the location of the error to be detected and corrected as 'e ''b s pattern Y6, the syndrome S
j (j ” Or 1...6) is, so by removing this, the location stops. When the denominator of equation (24) is -0, % From equation (23), X6=Y6 =
o, and it is determined to be a quintuple error.

When the denominator≠0, if X6=n' (0≦≦31) that satisfies the formula (24) exists, it is the sixth location to be found, and if it does not exist, it is determined that it cannot be corrected, flag.

If the number of pointers is 6, the value obtained by formula (24) is
By checking whether or not the location matches the location set by the sixth pointer, it is possible to determine whether or not correction is possible. If it doesn't match.

It cannot be corrected.

If the number of pointers is 4 or less, the XiO value exceeding the number of pointers in equation (18) and later may be set to 0.

Once the location is determined, the value of the error pattern is determined by solving equation (23). Y6 is full.

S4+Y5X5 (i=o, 1=-=4) If (26) is newly set as Si, Y5 becomes.

Similarly, S4+Y5X5 (i==o, 1・=・−3) (27
) is newly set as Si.

Next, 81+ Y4X4 (i = Or 1 + 2) (
29) is newly set as Si.Furthermore, when (31) is newly set as Si, Y2'='(81+X+So)/(X+ 1X
2) (32)Y1=So+Y2(33) It freezes. If the number of pointers is 4 or less, the YiO value that is greater than or equal to the number of pointers can be set to 0.0 From above, if the error pattern is correct, correction is Wi = R1
+ Yl (i = 1, 2...6) (3
4).

(3) Fillage correction In the same way as above, we first solve for the Loqueyon polynomial.

(36) Expand 8 and find each coefficient Ei in the same way as above.

Therefore, by subtracting the error button Y7, the following equation is obtained.

When Yl is full, as above, 8j+Y7X7 (j = o, 1-,..., ts)
If (4o) is set as a new town, Y6 is calculated from equation (26).

Similarly, Yl (i=5.4...1) is formed.

Corrections will be made.

The second decoder has the same configuration as the first decoder and executes the above operations to detect and correct errors.

As described above, according to this embodiment, by providing the second decoder with error construction capability, the possibility of overlooking errors is kept low, and by providing the first code with single error correction capability, the second decoder is provided with error construction capability. By providing 7-fold error correction capability to the two codes, the error correction capability is the product of both, and a very high correction capability is achieved. Furthermore, the number of calculations required for error detection and correction is extremely small as described above.

In the above embodiment, if the bill value is calculated in advance when checking the pointer, it can be used commonly for each row in FIG. 3, so that the total number of calculations can be further reduced.

Effects of the Invention As is clear from the above description, the present invention provides an encoder that generates a first code and a second code by orthogonally arranged them in order to detect and correct errors, and a first code.

Since it is configured with a decoder that detects and corrects errors in the order of the second code, errors that are not detected or corrected in the first decoder are also detected and corrected in the second decoder. This excellent effect can be obtained. As a result, when this error correction device is used in a PGM recorder, an excellent effect can be obtained in that the corrected signal will not deteriorate semi-permanently under normal usage conditions.

Furthermore, by configuring the second decoder to perform error detection and correction using the decoding information of the first decoder,
The effect is that the error detection/correction ability can be much higher than that of the second code alone.

Furthermore, by interleaving the second code, it is possible to completely correct even very long burst errors.

Further, the first code is a (32,29) Reed-Nromon code on GF(2), the second code is a (32,25) Reed-Nromon code on i7GF(2), and the first decoder performs single error correction and performs double or more error detection to generate pointers, and the second decoder depends on the number of pointers.

(1) When the number of pointers - 0 or ≧8, 2 error correction.

(2) When 1≦number of pointers≦6, 6 erasure + 1
Error correction.

(3) When the number of pointers is minus 7, by using a configuration that performs filler correction, even in the worst case (error rate per word is 163) when using a normal recording medium, the probability of uncorrectability becomes 1 million years. At a rate of once.

An excellent effect can be obtained in that the probability of non-detection is once in a trillion years.

[Brief Description of the Drawings] Fig. 1 is a block diagram of a correction code used in a conventional error correction device, Fig. 2 is a block diagram of the same conventional error correction device, and Fig. 3 is a block diagram of a conventional error correction device. FIG. 4 is a block diagram of an error correction device according to an embodiment of the present invention. 1... Data W, 2... First check code P, 3... Second check code Q, 10...
・Encoder, 11...Second encoder, 12...
...First encoder, 30...Decoder, 3
1...First decoder, 32... Second decoder. ′

Claims (1)

[Claims] (1) h b-bit data Wj (j = 1. 2, . . . h) specified by arbitrary positive integers m and h (m) h) and b; a second encoder that generates a second code by arranging (m-h) b-bit check codes Qj (j = 1 + 2+ . . . 1-h) in a second array state; , arbitrary positive integers n and k(n)k) and b pit data Wi(i-1, 2,...k) and (n-k) specified by the above positive integer b-bit check codes Pi, (1-1+2+...
. . n-k)i a first encoder that generates a first code by being arranged in a first array state orthogonal to the second array state, and an encoder that generates an error correction code by the first encoder; After transmitting or recording the error correction code output by the encoder, the first decoder first detects and corrects errors using the first code, and then the second code detects and corrects errors. An error correction device comprising: a second decoder that detects and corrects ll; (2) The second encoder is defined by a positive integer GF(2b) above (m, h )') −)”−
The first encoder is an encoder for a Romanromon code. ( on the Galois field GF(2) defined by positive integers
The first decoder is a decoder for the above (nyk) J-de Nromont code, and the second decoder is an encoder for the above (m, h) The error correction device according to claim 1, which is a decoder of a Reed-Nromon code. (3) The error correction device according to claim 2, wherein the second decoder detects and corrects errors using decoding information from the first decoder. (4) The second encoder arranges m pieces of data or check codes constituting the second code for each interleaving distance specified by an arbitrary positive integer, and the second decoder 1-
4. The error correction apparatus according to claim 3, wherein error detection and correction is performed using m pieces of data or check codes arranged for each interleaving distance D. (@ Encoder and decoder are b=8. m=32Th
=25. n=32. ni=29. 5. The error correction device according to claim 4, wherein n=4. (6) The first decoder performs single error correction and detects double or more errors to generate a pointer, and the second decoder generates a pointer that is decoded information of the first decoder. 7. The error correction device according to claim 6, wherein the error correction device performs the following correction 17j using the following. (1) When the number of pointers - 0 or ≧8, 2 error correction. (1) When 1≦number of pointers≦6, 6 erasure +
1 error corrected. Ge1) When the number of pointers = 7, γ erasure correction.