JPH02260823A - Decoding system for error correction code - Google Patents

Abstract

PURPOSE:To use the correction capability of a code in each axis direction at the maximum, to suppress the occurrence of mis-correction lower and to attain high correction capability as a whole by taking a code constituting to be a 3-dimensional rectangular prism as an object and discriminating generally the 3 ways of decoding results of each direction. CONSTITUTION:A single code in directions of axes X, Y, Z forming the 3-dimensional code of a rectangular prism is corrected and when an error which can not be corrected remains, some points (CP) where 3 codes whose error is detected intersect with each other exist. Then error is corrected to each CP and when the code is decided correct by a prescribed criterion, the error in the position of the CP is corrected. Then the CP is deleted (it is not regarded as the CP in the succeeding processing) and the other CPs in existence on the code are deleted, as well. That is, the error is being corrected one after another by repeating the correction and deleting over the entire rectangular prism for many number of times. Thus, while using the correction capability of the code in each axial direction up to the maximum and preventing the occurrence of mis-correction, high correction capability is realized.

Description

DETAILED DESCRIPTION OF THE INVENTION [Industrial Application Field 1] The present invention relates to a method for configuring error correction codes that are essential for large-capacity magnetic recording devices such as digital VTRs and digital communications, as well as a decoding method and a decoding device. It's about configuration.

[Summary of the Invention] The error correction code decoding method according to the present invention targets a Reed-5olomon code configured in the shape of a three-dimensional rectangular parallelepiped, and comprehensively judges three decoding results in each axis direction. This is a decoding method that uses the correction ability of the code in each axis direction to the maximum, suppresses the occurrence of erroneous corrections to a significantly low level, and achieves high correction ability as a whole. Therefore, even if the code has a low ability with a small number of parities in each axis direction, the overall correction ability is a two-dimensional product with an equal coding rate and more parities in each axis direction. Higher correction ability can be achieved than with codes.

[Prior art 1] Conventionally, as this type of error correction code, Ileed-5o
Log+on codes are often used. In particular, in the field of image recording such as digital VTR, the need-5ol
It is used in the form of a two-dimensional product code of the omon code.

An outline of the construction principle and decoding method of Reed-Solomon codes will be explained.

Let GF (2D) be a finite field with order 2°, and GF
Consider a polynomial ring of indefinite light X whose coefficients are elements of (2').

Let the arbitrary elements of GF (2°) be ao+...*aK-1, and let these be the information to be transmitted. Here, I (X)-ao"atX"・=◆a(-1X"1. Let α be the primitive light of GF (2D), polynomial
) is called the "code generating polynomial", and T(X)=I(X)・X2t+I(X) mod G(
X), information aO2””* r Reed- of aK-1
5olomon code.

Q(X) (or I(X) mad G(X)) (7
) The coefficients from the 0th order to the (2t-1)th order are expressed as information ao
+ ”・−aK−1 is called “parity”. Obviously T
The coefficients from the second to the (k-11th) of (X) are a
. ,..., becomes aK-1.

The Reed-5 olomon code created in this way is written as RS (k◆2t, 2t+1). It has the ability to correct up to a maximum of symbol errors that are summed.

If a polynomial in which an error is added to T(X) is written as Y(X), then the operation of restoring the original T(X) from y(x) is called "error correction." Error correction is performed using an element of GF (2°) called "syndrome" defined below.

Sl-Y(α') (where i-0,..., 2t-1
) Details are omitted, but if all SllJ<GF(2D) is equal to the zero element O, it is assumed that there is no error in Y(X), and in other cases, the position and value of the error up to can be calculated from the syndrome. In practice, the number of errors may be greater than t, and in this case, either the position and value of some error can be determined, or the position and value of the error cannot be calculated. In the former case, the determined error position and value do not match the true error position and value, and this is called "erroneous correction." In the latter case, although the position and value of the error in y(x) are not known, it is said that ``error detection'' has been achieved in the sense that it has been determined that Y(x) contains an error. In reality, when using the code R5 (k+2t, 2t+1), error correction is not performed up to the maximum capacity t, but a certain appropriate natural number n is set, and up to (t-n) errors are corrected. When the position and value are determined, the result is generally accepted as correct, and in other cases, it is assumed that an error has been detected. In other words, the correction ability is n
In other words, the amount is reduced and the amount is allocated to the detection ability.

In addition, along with the received code y (x), r Y (X
) may be incorrect. ” (this is called “disappearance”) is given. At this time, when all true errors are included in these erasures, all errors can be corrected if (number of erasures)≦2t.

This correction is called "erasure correction."

In the decoding of the two-dimensional product code mentioned above, the first step is to perform "error correction" in one direction, and codes that cannot be corrected are treated as erasures and passed on to the next stage.In the second step, error correction is performed in one direction. It is common to perform "erasure correction" in the direction. When viewed from the axis of the direction of the first stage, the disappearance is one 1
Although it is the entire dimensional code, when viewed from the axis of the second stage, it is only a few points in one one-dimensional code, and that is why erasure correction works effectively.

[Problem to be solved by the invention] Conventionally, in the field of digital video and audio recording, Reed
-5oloa+on code is used in the form of a product code configured in two dimensions, but with the demand for higher recording density, correction with higher correction ability can be put to practical use even in areas where the probability of error occurrence is higher. A sign is required. Generally speaking, in order to increase the correction ability of a code, it is sufficient to increase the number of parities added (2t), but this not only increases the proportion of parity in the entire code (coding rate), but also increases the number of parities added (2t). If , the procedure for calculating the location and value of an error from the syndrome becomes exponentially more complex, making it extremely difficult to implement hardware that can operate in real time at high data rates, such as in image recording.

An object of the present invention is to provide an error correction code decoding system that solves the above-mentioned problems.

0! Means for Solving the Problems] In order to solve the above problems, the present invention has a rectangular parallelepiped shape with side lengths L, M, and H, respectively, and M×N parallelepipeds to the length sides. , L×N individual symbols parallel to a side of length M, and L×M individual symbols parallel to a side of length N, forming a three-dimensional shape as a whole. The present invention is characterized by detecting a point CP at which three individual codes, each of which has an error, intersect in decoding the code.

[Function] According to the present invention, the three-dimensionally configured l1eed-5ol
The main target is ornon codes, and by comprehensively judging the two decoding results in each axis direction, we can significantly reduce the occurrence of erroneous corrections while maximizing the correction ability of the code in each axis direction. Achieves high correction ability while maintaining low pressure.

Therefore, even if the code has a low ability with a small number of parities in each axis direction, the overall correction ability is significantly lower than the code with a significantly higher coding rate.
It is possible to achieve higher correction ability than the dimensional product code.

In this way, the code of each axis that makes up the three dimensions is different from the conventional two-dimensional code.
Since it is possible to use a simple code with less parity than the codes on each axis of the dimensional product code, with a combination of simple decoders,
A decoding device with high correction ability that operates in real time at high data rates such as image recording can be constructed.

Example C] The principle of decoding a three-dimensionally configured rectangular parallelepiped code using a tree method will be briefly described.

In the first stage, most of the correction ability of each code is used for error detection for individual codes in the direction of each axis that make up the rectangular parallelepiped-shaped three-dimensional code, and error correction is performed with error detection as the main purpose. (As will be explained later, for codes with two parities on each axis, only detection is performed.) If all the individual codes in the rectangular parallelepiped are corrected, and there are still errors that cannot be corrected, the error will be detected in the trunk. There are several points at which the detected codes of the three trees intersect (these are called CPs). If error detection is performed correctly in each individual code, all remaining errors will be contained in these CPs.

In the second stage, remaining errors are corrected with a higher ability than in the first stage, but this increases the risk of erroneous correction. In this three-dimensional code, there are three independent codes that intersect in three directions for each arbitrary point of the rectangular parallelepiped, so three decoding results can be obtained for each point of the rectangular parallelepiped. Therefore, (1) among the three decoding results at a certain point, the one that is determined to be correct by majority vote is adopted (in other words, if at least two decoding results match, it is considered correct), thereby eliminating error correction. You can reduce the risk. (This criterion (1) can also be used in the first stage.) Furthermore, using the cp described above, (2) all error positions in the decoding result of a single code are C
If only the code result that is P is subject to the majority decision in (1), then
The risk of incorrect correction can be further reduced.

By the way, the majority decision method (1) also has drawbacks.

In other words, if there is only one correct result among the decoding results of three codes that intersect at a certain point, and the other two cannot be corrected or are incorrectly corrected, this correct result should be adopted. I can't.

In such a case, the decoding result of a single code is (2
), and (3) if the number of CPs existing on the code is less than or equal to the number of correctable errors, this decoding result is adopted (irrespective of majority decision). (The validity of this criterion (3) will be discussed later.) In this way, we decided to adopt not only decoding results that satisfy (2) and (1), but also decoding results that satisfy (2) and (3). If so, more errors can be corrected.

By the way, as mentioned above, "all remaining errors are included in CP," so in the second stage, it is not necessary to perform such corrections on all points of the rectangular parallelepiped, but only on CP. , just make the correction.

In this way, if correction is performed for each CP, when the decoding result of a code that intersects a certain CP is determined to be correct according to the criteria described above, it is not only necessary to correct the error in the position of that CP; If all the determined decoding results are used, more errors can be corrected per second.

At this time, this CP is deleted (it will not be considered as a CP in subsequent processing), and other CPs existing on these codes are also deleted.

In the third stage, errors that could not be corrected in the second stage are corrected using erasure correction with cp as the erasure position. As in the second stage, CPs existing on codes that have been successfully corrected are erased.

By repeating erasure correction over the entire rectangular parallelepiped as many times as necessary, it is possible to correct errors one after another. This repetition effect is one of the features of three-dimensional codes that is not found in codes with two-dimensional or less structures.

Details of these steps are described below.

FIG. 1 is a configuration diagram of a code having a three-dimensional rectangular parallelepiped shape.

First, let G F (2') be a finite field whose order is 2° (the primitive light of G F (2D) is written as α, and the zero element is written as O).

Consider a set V consisting of L×M elements of G F (2°). The elemental metal bodies of V are arranged in a rectangular parallelepiped shape with each side having lengths M and H, and any element v(k, i.

j) (where k = O,..., L-1, i=o,
... M-1, j=o, ..., N-1).

It is assumed that the rectangular parallelepiped V consists of two regions.

U unit r2tL≦k<L and 2t, ≦i<M and 2
Coordinates where tN≦j<NJ (k.

i, j), here v (k.

i, j) values are arbitrary.

Region 2: “0≦k<2t, or 0≦iku2
tM or coordinates (k,
i, j), here the value of v (k, i, j) is Oo.Area 1 is an area where information to be transmitted is stored, and area 2 is an area where parity is stored.

Now, (α'I'sQ, ・+, 2Lt-11 is the root of 2t
GL(X) is an L-order polynomial, 2t has a root of (a '1rsO,..., 2tM-1), and G is a 4th-order polynomial. (X), (a'1r-0,--,2tN-1) 2t whose root is the following polynomial is GN(x).

Now, the encoding procedure E2, EY described below.

According to E, parity is set in area 2 to construct a code.

Encoding procedure E2 (L-2
tL) elements v(2tL, i, j), v(2tL+1.i, j),
・-, polynomial % expression %) with coefficients v(L-1, i, j) (However, in K-L-2tL-1, ap-v(Ftt◆p
, i, j)), let the next coefficient of the (2tL-1)-order polynomial equation %() be v (k, i, j). That is, for the (L - 2tt,) elements of the above region 1,
The 2tL parities generated by the code generation polynomial GL(X) are expressed as elements v(0, i, j), v(1, i, j), −, v(2
tL-1, i, j).

This operation is performed for all i such that 0≦i<M, 0≦j<N,
Do this for j (end of procedure) Similarly, when j is fixed, (M-2 of region 1 of set V is divided into one element v(k, 2tmj), I/( k, 2tM+1.j),
..., v(k, M-1, j), 2tw parities generated by code generation polynomial G(X) are expressed as elements v(k, 0.j), v of region 2 (k, 1.j), −, v(k,
2tM-1,j).

Repeat this operation for all cases where 0≦k<L, O≦j<N, j
(End of procedure) 1ii Ball surface Similarly, when i is fixed, (N-2ts) elements v(k, i, 2t,), v( k, i, 2tH+1),
−, v(k, i, N-1), 2ts parities generated by the code generation polynomial GN (X),
Elements of region 2 v(k, i, O), v(k, i, 1), ”・,
Let v(k, i, 2tH-1).

This operation is performed for all 0≦k<L and O≦i<M for i. (End of procedure) The direction in which k increases is the "Z axis", and the direction in which i increases is the "Y axis".
axis”, and the direction of increase of j is expressed as “X-axis J, V coordinates (0, 0
, 0) will be called the "origin".

By executing steps Ez, y, and Ex, the rectangular parallelepiped V has M×N codes R5(L, L−2t and 2jL) in the Z-axis direction.
+1) Code RS of L×N tree in Y-axis direction (M, M72tm
, 2tv+1) L×M codes RS(N, N
−2tN, 2tN+1). The structure of this code is shown in FIG.

Now, the L×M×N symbols of the rectangular parallelepiped V are arranged in a series in an appropriate order and transmitted sequentially. This sequence, to which symbol errors have been added in the transmission path, is reconfigured on the receiving side into a rectangular parallelepiped V' with lengths M and N on each side.

Each side length is 1M, N is a 3-bit cell LxMxN
A rectangular parallelepiped F consisting of V is prepared, and decoding of the rectangular parallelepiped V' is performed by the following procedure. (L×M× of rectangular parallelepiped F
It is assumed that cell N is initialized to 000. ) First, the following decoding procedure DDx, DDY.

DD2 performs first-stage error correction and position detection of uncorrectable errors.

11 Supervision 1" 1 onward N elements v' (k, i, o), =-, v' (k, i, N-) in the x-axis direction at the locus m (k, i, j) of L V'
1) is the corresponding N elements v (k, i, 0) , ---, v (k, i, N-1) of the original rectangular parallelepiped V
R5(N, N-2tN, 2ts+1
) where errors may have been added to the code.

For the L×M codes that may have errors in the rectangular parallelepiped V' (N, N-2tN, 2tN''1), set in advance a natural number nx that satisfies 0<n, ≦t, and 4. and 0≦
All k such that k<L, O≦i<M.

%(ttt-nx) or less error corrections are attempted L×M times for i.

In other words, if error correction of one code specified by i is successful, the erroneous symbol in that code is corrected.

"Succeeding in error correction" means Reed-5olomo
This is a case in which the decoding is successful in the usual sense in decoding an n code. In other words, there may be errors in the N elements v (k, i, O) , · -, v (k, i, N-1) in the X-axis direction of V' specified by i. Assuming the code R5 (N, N-2tN, 2tN+1), 1) 2tN syndromes are all 0. 2) The positions and values of (tN-nX) or less errors were calculated.

This refers to the case where either one of the following holds true.

On the other hand, if error correction is not possible (that is, Rimo 2 also does not hold), an error has been detected, and the position (k, i, O) corresponding to the code on the rectangular parallelepiped F, =.
Add 001 mod 2 to N cells of (k, i, N-1) in bit units. (End of procedure) Decoding procedure DDY Set a natural number ny such that 0〈nY≦tY in advance, and
For all ≦k<L, O≦j<N, for j, the code R5 (M, M-2tM, 2tM''1) of the L×N tree in the Y-axis direction is (t, -n,) Correct less than 1 error.

If error correction is successful, the corresponding symbol on V' is corrected.

"Succeeding in error correction" means: 1) All 2tM syndromes are 0. 2) The positions and values of (tv-ny) or less errors were calculated.

This refers to the case where either one of the following holds true.

If error correction is not possible (an error is detected), 010 is added to M cells at positions corresponding to the code on the rectangular parallelepiped F.
Add mod 2 to each bit. (End of procedure) Decryption procedure DD! Set in advance a natural number 12 such that 0×n2≦tL, and O
For all i, j such that ≦i<M, O≦j<N, there are at most (tL-nz) numbers for the code R5 (L, L-2tL, 2tL÷1) of the M×N tree in the Z-axis direction. Correct any errors.

If error correction is successful, the corresponding symbol on V' is corrected.

"Successful error correction" means: 1) All 2tL syndromes are 0. 2) The positions and values of (tL-nz) or less errors can be calculated.

This refers to the case where either one of the following holds true.

If error correction is not possible (an error is detected), 100 bits are added to L cells on the rectangular parallelepiped F that correspond to the code.
Add mod 2 to the unit. (End of procedure) Now, assume that "all uncorrectable errors have been detected at each stage of the decoding procedure DDK, DDy, and DDz."

(This will be referred to as ``Assumption 1.'') This results in [Define the location of any remaining errors as (k, i.

j), the corresponding cell of the rectangular parallelepiped F (k.

The value of i, j) is always 111.'' (We will call this "Proposition 1.") On the other hand, just because the value of cell (k, i, j) of rectangular parallelepiped F is 111, the coordinates (k, i.

j) is not necessarily incorrect.

The position (k, i) where the cell value of F is 111.

j) will be called "intersection J ((:ross Po1nt, abbreviated as cp). From this, Proposition 1 becomes as follows.

"All remaining errors are CP." Next, the following decoding procedure ocxyz is used to correct errors that could not be corrected in the first stage error correction.

Decoding procedure DCxyz For all intersection CPs, X for each CP.

Three types of error correction are attempted in each direction of the Y and Z axes.

However, in the X-axis direction, Ilx such that ta < n was used (t
s - error correction for errors below X), and in the Y-axis direction, IY such that my < ny was used (tit
- Y) error correction, in the Z-axis direction, Dt using mz such that 112 < nz, -
mz) or less error corrections are performed respectively. This is procedure DDx.

DD, , means that corrections are made with a higher ability than DD.

If the coordinates of a certain CP are (k, i, j), then among the three correction results in the x, y, and z axes that intersect with it,
If the correction is successful in at least two directions, each result is reasonable, and the results match, the matching result is considered correct and adopted, and CP (k, i, j)
At the same time, all CP values existing on at least two axes with matching results are set to 0.
00 (that is, erase CP).

The definition of ``correction is successful in both directions, each result is reasonable, and the results match'' is as follows.

“Successful correction” means CP(k, i, j
), N elements v'(k, i, 0), ・-, v'(k, i, N-1
) as a code R5 (N, N-2tN, 2tN◆1) that has (possibly) an error. 1) All 2t syndromes are 0. 2) There are fewer than (tH-ax) errors. I was able to calculate the position and value.

The same applies to the Y and Z axis directions, where either one of the following holds true.

``Results are reasonable'' means: 3) When the correction is successful and 2), all calculated positions are CP.

In addition, in case 1) where all the syndromes are O, the result is unconditionally considered to be "rational."

This judgment is based on the contrapositive of Proposition 1, ``There is no error at a position that is not CP.''
If an error is detected at a position other than P, this means that the error correction is considered to be an erroneous correction and is not adopted. Furthermore, in case 1), it is asserted that there is no error on that axis, and even if there is CP on the axis, it does not contradict Proposition 1.

“The results match in two directions” means (k, i
, j), it is assumed that "error correction was successful" in two directions, the X-axis and the Y-axis, and that "the results were reasonable" in both directions.

The decoding result on the X axis is expressed as X(k, i, 0), +++, X(k, i, j),
−,
..., Y(k, M-1, j). At this time, if the decoded values match at the only locus m(k, i, j) where the two axes, the X axis and the Y axis, intersect, i.e. , 4) Express the case of X(k, ij) −Y(k, i, j) as ``
The results match."

At the coordinates (k, i, j) of a certain cp, there can be the following four combinations of axes in which "error correction is successful in at least two directions, and the results are both reasonable and consistent."

(x, y) (y, z) (Z, It is. The fourth set is the X axis,
This is a case where the results on both the Y-axis and the two axes match.

At this time, in each combination, correction of errors on the X axis and Y axis, erasure of CP, correction of errors on Y@ and Z glaze, correction of errors on CP, correction of errors on ZM and X axis, and erasure of CP on Xi and Y axes. , corrects the error on the X axis, and erases the CP. (
(procedure) In this procedure o c xyz, the coordinates of a certain cp (k.

Although "error correction was successful and both results were reasonable" in the two directions in i, j), "
The case where the results do not match is, for example, a case where 1) holds true for the X-axis, 2) holds true for the Y-axis, and the error correction position is exactly (k, i, j). It is.

At this time, since the syndrome is 0 in X-axis decoding, X (k, i, j) = v' (k, i, j),
In Y-axis decoding, v” (k, i, j) is incorrect, so Y
(k, i, j) ≠v' (k, i, j), and 4
) does not hold true.

Such a case may occur when at least one of the X-axis and Y-axis decoding is incorrectly corrected.

The feature of this procedure DCXY2 is that it employs decision logic based on majority voting. The procedure DDX as described above,
Since the correction ability is higher than that of D Dv and D Dz, the risk of erroneous correction increases accordingly. This risk is reduced by majority decision.

Also, note that this procedure DCXY2 not only performs error correction, but also reduces the CP generated by procedures DDx, DDy, and DDz, which greatly contributes to the effectiveness of the following procedures. .

4 encoding order DExY□ X-axis direction code R5 (N, N-2tH, 2ts"
1) is erasure correction up to 2tN, code R5(M, M-2tM, 2tM in the Y-axis direction)
” 1) has the ability to correct up to 2tM erasures, and the code R5 (L, L-2t2tL◆1) in the Z-axis direction has the ability to correct up to 2tL erasures. All coordinates (for k, i, j> ° [, X, Y, Maximum 2ts in each direction of the Z axis,
Erasure correction is performed up to 2tM and 2tL, and the CP at the corrected position is also erased.

By repeating this erasure correction for the entire V' not just once but several times, the CP can be successively reduced. The stopping condition for repetition is St) C on any axis in the intersecting x, y, and z directions.
All coordinates of F where P exists (k.

i, j), respectively 21. on each axis. +1゜2tw”
l, 2tL◆One or more CPs exist.

or, S2) CP does not exist in F.

Assume that one of the following holds true. (End of procedure) The above multiple procedures can be performed not only in the order mentioned above, but also in various modifications. For example, repeat DCxyz several times, omit DCxyz and perform DEXYZ in a circular manner, or (D For example, CXY!=D Ex-yz) is repeated several times.

Here, a procedure that is an extension of the procedure DCxyz will be described.

In the procedure DCxy□, the coordinates (k, i,
In j), the condition for adoption of the results was that the results matched in at least two axial directions. The coordinates of a certain cp (k
, i, j), consider the case where there is only one axis in which r error correction is successful and the result is "rational". At this time, even if the decoding result for that axis is correct, the decoding result must be discarded because there are no other similar axes.The next step D is to save such a single axis.
It is CXYz-A.

In the procedure DCxY□-8 Procedure DCxyz, if there is only one axis for which "error correction was successful and the result is reasonable", the number of CPs on that axis is equal to the correctable code of that axis. If the number of errors is less than the number of errors, the decoding result is accepted as correct.

That is, at the coordinates (k, i, j) of a certain cp, if the X axis is such an axis, then SX) <X
(number of cp on H)≦tH−+*If the XY axis is such an axis, sy) (number of CP on y axis)≦t
If the M-myZ axis is such an axis, 5□)
(Number of cp on Z axis)≦1. If -2 holds, in each case, the decoding result is accepted as correct. (End of procedure) The validity of this procedure D CXYZ-A is clear from Proposition 1. That is, if the number of CPs on a certain axis is NCP, proposition l guarantees that the number of errors on that axis is less than or equal to NCP. Therefore, if the NCP is less than or equal to the number of correctable errors in the code of that axis, error correction can be performed without error correction.

In this way, in order for the present decoding method to avoid erroneous corrections, it is highly dependent on Proposition 1, and hence Assumption 1, being satisfied. Needless to say, the assumption l is just an assumption, and the procedure DD.

In reality, an uncorrectable error may be overlooked at each stage of DDY and DDz, and this error may not occur at the intersection CP. It is necessary to reduce the probability of this oversight as much as possible, and for that purpose, it is better to increase nx+'Y and nZ. The probability of missing is minimized when jH”nx + jM”ny *L,, -nz,
That is, in each stage of the procedures D Dx , D Dy , and D Dz, only error detection is performed without correction (specifically, only determination of whether the syndrome is 0 or not) is performed. However, in this case, DDx, DDy, DD
Not only are errors that could be corrected at each stage of z left as they are, but the number of CPs generated increases significantly, making it impossible to expect the effectiveness of the erasure correction procedure DExyz. Therefore, it is desirable that nX, nY, and n be appropriate values.

In this way, an error may be overlooked and may exist at a location other than the intersection CP. At this time, decoding procedure D
If Exyz is executed, a new error will occur due to incorrect correction. Therefore, it is conceivable to detect erroneous corrections in erasure correction by introducing a match test of decoded values at intersections similar to that performed in procedure DCxyz. This expansion is the next step D E xyz
”'A.

Encoding procedure D E XYZ-A In the procedure DExyz, the coordinates of a certain cp (k.

Among the decoding results of erasure correction on three axes that intersect at
.

Also, in this case, CP(k, i
, j) are also deleted. ) The stopping conditions for how many times this procedure is repeated for all of V' are: 5l-A) The number of CPs that can be erased for all of V' is 0.

or 52) CP does not exist in F.

Assume that one of the following holds true. (Procedure) An example of a specific code, decoding procedure, and configuration of a decoding device according to this method will be shown.

L=36. M=34. N±32, GL(X
)=(X a') ・(X −atsuGM (X)
-(X-a') ・(X-a')GN(X)-(X
−a 0) ・(X −a′). At this time,
tL=t,=t,=1, and the rectangular parallelepiped V is 36X 34X
The size is 32, and the code R of the 34X32 tree is in the Z-axis direction.
5 (3B, 34.3) 36X32 in the Y-axis direction Tree code R5 (34, 32, 3) 36X34 in the X-axis direction
The book code R5 (32, 30, 3) is configured. Each axis code has the ability to correct up to one error or correct up to two erasures.

The total number of symbols of this code is 3fix x 34 x 32-39168 symbols The amount of information that can be transferred is 34 x 32 x 30-32640 symbols The coding rate (ratio of parity symbols to the entire code) is 1- (32640/39168) #0.167.

FIG. 2 shows an example of the configuration of a decoding device that decodes 39188 symbols to which errors have been added through a transmission path.

The human-powered symbol series S is sequentially written into the three-dimensional memory V'.

V' is a three-dimensional memory with a size of 38 x 34 x 32 bytes, and by specifying the Z-axis coordinate and the Y-axis coordinate i, 32 bytes of data v' (k
, f, O) s= , v' (k, i, 31) is accessible, and likewise the coordinate k of the Z and X axes.

By specifying j, 34 bytes of data v in the Y-axis direction
' (k, o, j) , ・= , v' (k, 33.j
) can be accessed and similarly the coordinates i of the Y and X axes.

By specifying j, 36 bytes of data v in the X-axis direction
' (0, i, j) , ..., v' (35, i, j
) shall be accessible.

The rectangular parallelepiped F consisting of 3-bit cells that stores CP is also 3
It is assumed that a three-dimensional memory with a size of 6 x 34 x 32 bytes allows similar access.

The error detector DDx sets tH=nX=1 and performs only detection without error correction.

For all 0≦k<L, O≦i<M, for i, X
Axial code RS (32, 30, 3) 32 bytes
Data v' (k, i, 0) , ---, v' (i, i, 3
1) is read from ■′, and the value α0. Syndrome S using α1. Calculate XI stz, and if So, l≠0 or SIX≠0, set 0 to the cells at the coordinates (k, i, 0), ..., (k, f, 31) of the rectangular parallelepiped F.
Add mod 2 to 01 to the bit vehicle position.

Similarly, for error detection DDY, t,=nY=1, and 0≦
Syndrome S with code RS (34, 32, 3) in the Y-axis direction for all k<L, 0≦i<N.

7. If either one of S1a is not 0, 0 is added to the cell at the coordinates (k, o, j), ..., (k, 33.j) of the rectangular parallelepiped F.
10 is added by zod2 in bit units.

Similarly, for error detection DDz, tL=l'12=1,
For all i and j such that 0≦i<M, 0≦j<N,
Syndrome S with axial sign RS (3[i, 34.3). If either z or stz is not O, add 1 to the cell at coordinates (0, i, j), ..., (35, i, j) of the rectangular parallelepiped F.
Add mod 2 to 00 bit by bit.

If the memory elements constituting v' and F are sufficiently fast, error detectors DDK, DDy, and DDz can be operated in parallel.

In the error corrector DCXY2, m x = my = mz = 0, and for all CP coordinates (k, i, j), X, Y
, Z axis direction. Needless to say, it is possible to successfully correct errors in at least two directions.
and the results are both reasonable and consistent, then the results are accepted as correct, and in that case, V′
Error correction and erasure of F's CP are performed.

If we use the above procedure D If so, the result of that axis is accepted as correct.

The error corrector DCxyz sequentially scans all the cells in %F, and if the cell is a CP, the coordinates of the CP (k, i, j
) corresponding to the coordinates of V' (k, t.

3-axis data intersecting at j) (36-1)” (34-1) +32-100 bytes
e is read from V', codes for each axis are constructed, and three types of single error correction are attempted. Based on the results, for the axis for which it is determined that the correction has been correctly performed, the correction result is written in V' and 0000 data is written in F.

As mentioned above, each axis code has the ability to perform erasure correction for up to two codes. Therefore, the erasure corrector DExyz sequentially scans all cells of F, and if the cell is cp, cp
The coordinates (k, i, j) of v′ corresponding to the coordinates (k, i, j) of
3IIIl data intersecting at j) (35-1) + (34-1) ◆32-100 bytes
e is read from V', a code for each axis is constructed, erasure correction is performed for the axis where the number of CPs is 2 or less, and the result is written. When erasure correction is repeated several times for the entire V', the process ends when the following stopping conditions are met.

S1) C on any axis in the intersecting X, Y, and Z directions.
At all coordinates (k, i, j) of F where P exists, three or more PCs exist on each axis.

or S2) cp does not exist in F.

[Effects of the Invention] When the decoding method of the present invention is applied to a three-dimensionally constructed Reed-5olomon code, a low-performance code with a small number of parities is used in each axis direction, and the code as a whole is It is possible to achieve a higher correction ability than a two-dimensional product code which has the same conversion rate and more parities in each of the two axes directions.

For example, in the example, each axis direction is Reed-5ol.
3 configured with the minimum number of parities of 2 as an amon code
Dimension code R5 (36, 34, 3), R5 (34, 32, 3)
, R5 (32, 30, 3), by using this decoding method, R5 (69, 63, 7), R5 ( 69,83,7) and
It has been confirmed that the correction ability is higher than R5 (92, 84, 9), which has eight parities each, and R5 (92, 84, 9).

Furthermore, it is clear from the explanation of the real 7i cage example that this decoding method can be used to decode a Reed-5olomon code configured three-dimensionally with parity of 2 or more in each axis direction. The code is Reed-5
Codes other than the Olomon code can also be applied.

[Brief explanation of drawings]

FIG. 1 is a configuration diagram of a three-dimensional rectangular parallelepiped code, FIG. 2 is a diagram showing an example of the configuration of a decoding device.

Claims (1)

[Scope of Claims] 1) In the form of a rectangular parallelepiped, each side having lengths L, M, and N, M×N individual symbols parallel to the side of length L, parallel to the side of length M. The existence of errors is detected individually in the decoding of a code that has a three-dimensional shape as a whole, consisting of L × N individual codes parallel to a side of length N and L × M individual codes parallel to a side of length N. An error correction code decoding method characterized by detecting a point CP where three independent codes intersect. 2) Shape of a rectangular parallelepiped with side lengths L, M, and N.M×N individual symbols parallel to the side of length L, L×N individual symbols parallel to the side of length M sign, and L× parallel to the side of length N
In a code that is composed of M individual codes and has a three-dimensional shape as a whole, at least two of the decoding results of the individual codes in three directions intersecting a certain point are individually correct. Error correction characterized in that, when it is determined that the decoding results in at least two directions match, if the values at the intersection of the decoding results in at least two directions match, the whole or part of the decoding results in at least two directions are adopted as correct. Code decoding method. 3) Regarding the result of decoding a certain single code constituting the code of the three-dimensional shape, when the position of the obtained error is any of the intersection points CP, the decoding result is determined to be correct. 2. The error correction code decoding method according to claim 1. 4) Regarding the result of decoding a single code constituting the code of the three-dimensional shape, if the position of the obtained error is at any of the intersection points CP, the decoding result is correct. Regarding the decoding result of a certain single code, which is said to be, the decoding result of the single code is determined to be correct if the number of intersection points CP existing on this single code is less than or equal to a certain preset value. The error correction code decoding method according to claim 3, characterized in that: 5) Individual codes in three directions intersecting at the intersection point CP are individually decoded, and at least one of the three obtained decoding results is correct in the sense of the method according to claims 2 and 3 above. When there is either the decoding result in two directions, or the only decoding result that is correct in the sense of the method according to claim 4, writing the decoding result in the corresponding position of the rectangular parallelepiped. The error correction code decoding method according to claim 1, characterized in that: 6) In the method according to any one of claims 1 to 5, after adopting the decoding result of a single code determined to be correct and writing the decoding result in the corresponding position of the rectangular parallelepiped, A decoding method for an error correction code, characterized in that an intersection point CP that exists in the above is not considered to be an intersection point CP in subsequent decoding. 7) An error correction code decoding method characterized in that, for the decoding result of the method according to any one of claims 1 to 6, the intersection point CP is regarded as the erasure position, and erasure correction is performed on each individual code. . 8) In the method of claim 7, the error correction is characterized in that the intersection point CP that exists on a single code that has been successfully erased is not the intersection point CP in subsequent erasure correction for another single code. Code decoding method. 9) The error correction code decoding method according to claim 7 or 8, wherein erasure correction is repeated over the entire rectangular parallelepiped. 10) The error correction code decoding method according to any one of claims 1 to 9, characterized in that a code is constructed in which lengths L, M, and N of each side of the rectangular parallelepiped are equal.