JPS62248313A - Decoding method for error correction code - Google Patents

Abstract

PURPOSE:To enable error correction for a random error, and a burst error, by executing the correction up to <=[(d-2)/2] symbol numbers when an inter- code minimum distance in an error correction code system is (d), and performing the error correction to <=d-2 symbol numbers, when the error correction is impossible. CONSTITUTION:Firstly, the same error correction as in a conventional method is performed. The correction, assuming the inter-code minimum distance as (d), is executed for the symbol up to an even number (t) that satisfies tr<=[(d-2)/2], and when the correction is impossible, the error correction for a continuous error due to the burst error, etc., is performed for the symbol up to a number (a) that satisfies a <=d-2. In this case, each position of error symbol group is decided by the detection of the position of an error symbol which becomes one reference, based on an assumption that errors (error symbol group) are continued according to a prescribed rule. And by applying the error correction on the symbol at each position, it is possible to perform the error coorection for up to (d-2)-number of the symbols.

Description

DETAILED DESCRIPTION OF THE INVENTION [Field of Industrial Application] The present invention relates to a method of decoding an error correction code, and particularly to a method of decoding an error correction code that can strongly correct both random errors and burst errors.

[Summary of the invention]

The present invention provides a method for decoding an error correction code with a minimum distance between codes of d, which is the upper limit of the error detection and correction ability ((d-
1)/2) (However, [ ] is the so-called Gala symbol, (x)
represents the largest integer not exceeding the real number X.)
Execute error detection and correction up to the following number of symbols t, and if correction cannot be performed, the number of consecutive symbols a - 2 or less a
By performing error correction up to this point, it is possible to perform powerful error correction not only for random errors but also for burst errors.

[Conventional technology]

For symbols in digital data, so-called read
By performing encoding using an optimal error correction code such as a Reed Solomon code, (n
-k) symbols (n is a positive integer) In a code system in which check symbols are added, the minimum inter-symbol distance d is (+1 to n-).

This distance d, the number of symbols that can be detected and corrected by detecting and correcting errors whose positions are unknown, and error erasure correction (erasure correction) which corrects errors whose positions are known.
It is generally known that the relationship d-1≧'lt+s holds between the number of possible symbols S.

For example, the number of test symbols (check symbols) in k-200 and n-216 Reed-Solomon codes is 16, and the distance d is 17, so error detection and correction of up to 8 symbols is possible. Or up to 1
Error erasure correction of up to 6 symbols is possible.

[Problem that the invention seeks to solve]

By the way, when recording data on a magneto-optical disk or the like, for example, a two-dimensional array data matrix as shown in FIG. Data is encoded using a Solomon code or the like, and data is sequentially read out in a direction perpendicular to this (vertical direction in the figure) and written onto a disk. In the example shown in Figure 3, it is assumed that 512 bytes of original data (original data that does not include redundant data) are allocated to one sector of the disk, and 128 bytes in the horizontal direction and 4 blocks in the vertical direction ( A total of 512 bytes of original data constitutes a two-dimensional array. A 4-byte CRC code is added to this 512-byte data, and an additional 16 bytes for each block (64 bytes per sector)
A check byte is added using a Reed-Solomon code, etc. Therefore, it is possible to detect and correct errors up to 8 bytes for each block of data (145 bytes per block). Note that the numbers in the figure indicate the data writing order.

If a disk on which data is recorded based on such a recording format is scratched or has dust attached, continuous errors, so-called burst errors, will occur, causing the 145-byte data in one block to be lost. However, an error of 9 bytes or more may occur. This corresponds to errors of 36 or more consecutive bytes on the disk, and on extremely high recording density media such as magneto-optical disks, even the slightest scratch or minute dust can cause a burst error of this magnitude. It's something you get. If an error of 9 bytes or more occurs in one block, that is, an error exceeding the error detection and correction capability described above, error correction becomes impossible.

The present invention was made in view of these circumstances, and provides a decoding method for error correction codes that can perform strong error correction not only for random errors but also for continuous errors, so-called burst errors. For the purpose of providing.

[Means for solving problems]

In order to solve the above-mentioned problems, the error correction code decoding method according to the present invention encodes digital data with an error correction code so that the minimum distance between codes is d.
In the decoding method of the error correction code, d-1(d
represents the above distance), the maximum integer number t of symbols less than or equal to 1H that does not exceed ) performs error detection and correction until it indicates the largest integer not exceeding X,
If this error detection and correction is not possible, the present invention is characterized in that continuous errors of a number a (t<a≦d-2) of symbols greater than t and less than or equal to d-2 are detected and corrected.

[For production]

1 above corresponds to the maximum number of symbols that can be detected and corrected when the minimum distance between codes of the error correction code system is d, and the position of the error symbol (error symbol or erasure) is detected in advance. If there is an error exceeding tI4 when there is no burst error, it becomes uncorrectable, but if a burst error occurs and a group of consecutive error symbols exists, the first position of the error symbol group If this is known, it becomes substantially possible to correct errors exceeding t and l by regarding the a number of consecutive symbols from this leading position as error symbols (erasures). Here, the above-mentioned continuous film or continuous error symbol group does not actually have to be continuous one symbol at a time, but also includes cases where they are chained under a predetermined rule in relation to interleaving, etc. In other words, it is a symbol group in which the positions of the remaining error symbols can be automatically determined by detecting the position of one reference error symbol.

〔Example〕

An error correction code decoding method according to an embodiment of the present invention will be briefly described with reference to the flowchart of FIG. 1. First, in step SL, normal error detection and correction as in the conventional method is performed.

This error detection and correction is performed on up to t symbols that satisfy t≦((d-1)/2), where d is the minimum distance between codes. It is determined whether or not error detection and correction has been effectively completed, that is, whether correction is possible or not. If No (correction is not possible), the process proceeds to step S3. In step S3, burst errors such as those described above are detected. Error correction for continuous film is performed on up to a number of symbols satisfying a≦d−2. In this case, errors (error symbol group) are continuous according to a predetermined rule. Based on the assumption that each position of the error symbol group is determined by detecting the position of one reference error symbol,
By performing error correction on the symbols at each of these determined positions, it is possible to perform error correction on up to d-2 symbols. Note that if the determination in step S2 is YES (correction has been completed effectively) or if the error correction in step S3 has been completed effectively, the error-corrected data is sent to the next data processing unit, etc. All you have to do is transfer it and finish the operation.
If error correction in step 3 is not possible, for example, a request to retransmit the data may be issued to the disk device or the like, or information indicating that the data is uncorrectable may be sent to the next data processing section.

Next, the operation in each step in FIG. 1 will be explained in more detail.

First, in step S1 of FIG. 1, normal error detection and correction for so-called random errors is performed. That is, as an example, a Galois field GF in which a check symbol (check symbol) of a symbol is added to n- for the information data of a symbol as shown in FIG.
Considering the Reed-Solomon code C(n,,k) on (q“), when the primitive light is α, the generator polynomial is
(x-1) (x-α) (x-α two...
Shiridashi, j! −n−, in which case the minimum intersymbol distance Md is z+1,
The maximum value 1 of the number of symbols t that can be detected and corrected is tll-(1/2)-((d-1)/2), which means that for the syndrome So, S+ ~5t-1, one The simultaneous equations are established, and the number of elements is 1.1 error positions,
This is obvious from the fact that the size is t and the number of pieces.

Conventionally, unless the error position (location of erasure) is detected prior to error correction, the above t
It is only possible to correct up to t errors, and if there are more than t errors, correction is impossible.

On the other hand, in the present invention, if there are more than the 114 errors mentioned above, that is, if it is determined that the above-mentioned normal error detection and correction is impossible in step S2 of FIG. It is determined that a so-called burst error has occurred, and the position of a reference l symbol among the continuous errors (error symbol group) caused by this burst error is detected, for example, the start position of the error symbol group. By estimating the positions of all error symbols and performing erasure correction on these estimated error symbol positions, the number of symbols that can be detected and corrected is apparently increased. There is.

Here, continuous errors caused by the above-mentioned burst errors etc. appear as continuous errors of about one symbol each in one block in the case of the recording format shown in FIG. If position i is known, it can be estimated that the symbols at positions ill, i+2, . . . are also incorrect. In addition, due to interleaving and the like, errors may occur, for example, every two symbols or every three symbols, and such cases are also included in the concept of continuous errors in the present invention.

Next, we will explain a specific example of error correction when the burst error occurs. To simplify the explanation, we will use a Reed-Solomon code on the Galois field GF (2") to correct the check symbol. It is assumed that the number of symbols is 4, the minimum inter-symbol distance d is 5, and continuous error correction of 3 symbols is performed.

The generating polynomial of this Reed-Solomon code is G (x)
= (x-1) (x-α) (x-α2) (x-α3
), and α in this formula is #A (primitive light) of the primitive polynomial P(x)−X@+x44X”+X”+1. At this time, the first position in the error symbol group (e) The symbol of is 64, and three consecutive symbols @! + e i*l+ e is! When it is assumed that is wrong, the four syndromes S @, S
For I, S z, Ss, 36” @, +
6! Il+6! *zS
l-α'64+α"'61.1+α""6i+!31m
cr"s t+ α"directly" e ill +
α”◆4@ is!Szma”e6+ako! +26
,,, +α””e is! The simultaneous equations will hold true. Therefore, by solving this simultaneous equation, α08 (αi1(α5Syu+S t)+
+5t))+α1゛1(α'St+S)+(α'Sg
+5i)=0,°,αko”'S*+(α3+α2+α)
α■Sl+(α"+α-1-1)αmu St+5s-0, rearranging this, α35*23, +(z bulk L11+99 S, +
The formula for α five orders rII S, +5, , Q is obtained.

The above four syndromes Syu, S that satisfy this formula
If +, St, Ss exist, three consecutive symbols 414n'I! +1+'! ! It turns out that +fi is an error, and the rest is error correction (erasure correction).
By processing, the above three consecutive error symbols e!
＋ ' io1+ '' You can correct ``5''.

In other words, in general, in an error correction code with a minimum inter-code distance d, as described above, the number of symbols that can detect and correct errors, the number of symbols that can perform erasure correction (S), and the distance d are The relationship d-1≧2t+3 holds true between them, but if continuous errors occur due to burst errors, etc., in other words, once the position of one error symbol serving as a reference is known, the positions of the remaining error symbols can be determined. is automatically determined, if one error detection and correction is performed, the rest can be corrected by error erasure correction, which corresponds to setting t to 1. Therefore, one symbol by error detection and correction, and three symbols that satisfy (1-1≧2+3, that is, ≦d-3), for a total of a symbols, that is, a symbols that satisfy a≦d-2. It is possible to correct errors up to symbols.

For this number a, the maximum value t of the number t of symbols that can be detected and corrected normally (for random errors),
For example, when the above-mentioned path 1IIId is 17, the above-mentioned value t is 8, but the maximum value of the above-mentioned a (d-2) is 15, which can be almost doubled. Recognize.

Therefore, when continuous errors occur due to burst errors, etc., error detection and correction (apparent) up to d-2, which is greater than the maximum value t, 4 of the number of symbols t that can be detected and corrected, is performed. It can be carried out.

Note that the present invention is not limited to the above-mentioned example. For example, the error correction code is not limited to the Reed-Solomon code described above, but can also be applied to a so-called BCH code, etc.
It can also be easily applied to cases where multiple error correction coding is applied to two or more sequences. Further, it goes without saying that the number of information symbols, the number of check symbols, etc. of the error correction code sequence are not limited to the above-mentioned example. Furthermore, instead of performing the above-mentioned normal error detection and correction, the number of error symbols is detected in advance, and according to this number, normal error detection and correction (for random errors) and the above-mentioned apparent error detection for burst errors are performed. Correction may be performed alternatively.

〔Effect of the invention〕

According to the error correction code decoding method of the present invention, it is possible not only to perform error detection and correction with the same correction ability as conventional methods for normal random errors, but also to detect and correct errors that exceed the number of symbols that can be detected and corrected due to burst errors, etc. If a number of consecutive errors occur, it becomes possible to perform apparent error detection and correction for up to the number of errors that can be roughly corrected using erasure correction. It is possible to realize powerful error correction for recording/reproducing systems (including recording/reproducing systems).

[Brief explanation of drawings]

FIG. 1 is a flowchart for explaining the general operation of an embodiment of the present invention, FIG. 2 is a diagram showing an example of an error correction code for explaining the embodiment, and FIG. 3 is a diagram for recording data on a magneto-optical disk. FIG. 2 is a diagram for explaining an example of a format.

Claims (1)

[Claims] In an error correction code decoding method in which digital data is encoded with an error correction code so that the minimum distance between codes is d, the value obtained by subtracting 1 from the distance d ( The number of symbols t that is less than or equal to the maximum integer not exceeding 1/2 of d-1), that is, t≦[(d-1)/2] However, [x] is the error detection and correction up to the maximum integer not exceeding x. If this error detection and correction is not possible, detect and correct continuous errors up to the number of symbols a that is less than or equal to the value (d-2) obtained by subtracting 2 from the distance d (i.e., a≦(d-2)). A method for decoding an error correction code, characterized in that: