JPS62248314A - Decoding method for error correction code - Google Patents

Abstract

PURPOSE: To enable error correction for both a random error, and a burst error, by performing an error correction operation in a range <=(d-1) of the sum of the even number of error blocks, and the total number of error symbols in those blocks, when an inter-code minimum distance in an error correction code system is (d). CONSTITUTION:As for the block consisting of continuous error symbol groups, all of the error symbol positions within said block are decided by finding the reference position (for example, a forefront symbol position within the block) for the block, therefore, it is possible to perform an erasure correction for all of the error symbols SIGMAa within (i)-number of blocks by detecting each reference position for (i) number of error blocks. In other words, in the range of (i)+SIGMAa<=(d-1) ((d) is the inter-code minimum distance), it is possible to detect each reference position for (i) number of error blocks, and to perform the erasure correction for the number SIGMAa of all of the error symbols within those blocks.

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 decoding method for an error correction code with a minimum distance between codes of d, in which the number of error blocks consisting of consecutive error symbols is i, and the number of error symbols in the j-th block among these error blocks is aj. By performing error correction operations within the range that satisfies the inequality j + Σa ≤ d - where j = 1, 2...i, it is possible to perform strong error correction for both random errors and burst errors. That is.

[Conventional technology]

For symbols in digital data, so-called read
Since encoding is performed using an optimal error correction code such as a Solomon (Reed 5oloa+on) code, (
In a code system in which check symbols of n-k) symbols (nSk is a positive integer) are added, the minimum distance between codes d
is (+1 for 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≧2t+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 2, it is assumed that 512 bytes of original data (original data not including redundant data) are allocated to one sector of the disk, and 128 bytes in the horizontal direction and 4 pronks 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 (1 block 145 bytes). 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, that is, exceeding the error detection and correction capability described above, occurs in such an l block, error correction becomes impossible.

Here, if the errors are continuous like a burst error, the positions of all error bytes can be roughly determined by detecting a reference position such as the start position of the consecutive error bytes, but burst errors and random If errors occur simultaneously, there will be a plurality of consecutive error bytes and isolated error bytes.

The present invention has been made in view of these circumstances,
The purpose of the present invention is to provide an error correction code decoding method that enables strong error correction even when both random errors and continuous errors (so-called burst errors) occur at the same time.

[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 for error correction codes, the number of error blocks each having one error symbol or two or more consecutive error symbols is calculated as 12. When the number of error symbols in a block of ≦i) is a, the error correction operation is performed within a range that satisfies the direct inequality.

[Function] - In other words, when the minimum distance between codes of the error correction code system is d, the number t of symbols that can detect and correct errors and the number S of symbols that can perform erasure correction are d. The inequality -1≧2t+s holds true, and this can also be thought of as detecting the positions of symbols and performing erasure correction on (t+s) symbols. Here, for an error block consisting of a group of consecutive error symbols, if the reference position of the error block (for example, the first symbol position in the block) is known, the positions of all error symbols in the error block can be determined, for example. By detecting each reference position for i error blocks, the above erasure correction can be performed for all error symbols in all error blocks. That is, within the range that satisfies the condition of i+Σaj≦d-1 j*l, it is possible to detect each reference position of i error blocks and perform erasure correction on the total number of error symbols Σa1 in these error blocks. becomes.

Here, two or more consecutive error symbols constituting one error block do not actually need to be consecutive one symbol at a time; In other words, in one error block, as long as the reference position of the error block (for example, the first symbol position within the block) is detected, the positions of all error symbols within the block are automatically determined. It is made up of a group of symbols determined by .

〔Example〕

Before explaining the error correction code decoding method according to the present invention, conventional error detection and correction will be explained.

Here, for example, as shown in FIG. 1, a Galois field GF (
Considering the Reed-Solomon code C(n, k) on q'), when the primitive light is α, the generator polynomial is (x-1) (X-α) (tα... αL-1
) However, in this case, the minimum distance d between codes is l+1,
The maximum value t, I of the number of symbols t that can be detected and corrected is t* - (J/2) - ((d-1)/2) However, [ ] is a so-called gala symbol, and (x) is It indicates the largest integer that does not exceed the real number X. This is the syndrome So, S
It is obvious that two simultaneous equations are established for + to 31-1, and the number of elements is t, error positions, and size tH.

Conventionally, unless the error position (erasure location run) is detected prior to error correction, the above t
It is only possible to correct up to seven errors, and if there are more than t0 errors, it is impossible to correct them.

In contrast, the present invention enables apparent error detection and correction even when there are more than tN errors. This method treats two or more consecutive errors (error symbols) as one error block, considering that when there are relatively many errors, there is a high possibility that so-called burst errors have occurred. For this error block, the positions of all error symbols in the block are determined by detecting one reference position (for example, the first symbol position in the block), and for these located error symbols, For example, when detecting each of the reference positions of i error blocks, the j-th (1≦3s%)
When the number of error symbols in the error block of is aJ, the total number of all error symbols for all error blocks is al+a, Jubeiken +a! 0 ΣaJ j+1, and these error symbols can be corrected by the erasure correction described above. Therefore, by detecting i positions and erasing corrections Σa, it is possible to detect errors in Σaj symbols apparently. Corrections can be made. In this case, the number of error blocks i
The following relationship should just hold between the total number Σaj of all error symbols and the minimum inter-symbol distance d: i+Σa4≦d−1. For example, when the distance d is 17, the maximum value 1M of the number t of symbols that can be detected and corrected in the conventional system is 8, but it is assumed that all error symbols are continuous (the number of error blocks 1), then i=1 and up to 15 error symbols can be corrected. Also, the number of error blocks is set to 2.
When the number of error symbols is 1, it is possible to correct up to 14 error symbols, and, for example, it is possible to perform apparent error detection and correction on one independent error symbol and 13 consecutive error symbols. In addition, the number of error blocks i can be arbitrarily set within a range that satisfies the above inequality, but in consideration of actual digital arithmetic processing, it is appropriate that i be about 2.

Here, the above-mentioned consecutive errors (error symbols) constituting one error block are, for example, in the case of the recording format shown in FIG. 2, consecutive errors of approximately j symbols in one block. Since the first error symbol position X is known, x+
1. It can be estimated that the symbol at the position x+2 . . . is also incorrect. In addition, due to interleaving etc.
For example, errors may occur every two symbols or every three symbols, and such cases are also included in the concept of consecutive error symbols constituting the error block of the present invention.

Next, a specific example of error correction for an error block consisting of a plurality of consecutive error symbols when the burst error occurs will be described. Here, in order to simplify the explanation, it is assumed that continuous error correction is performed when the number of consecutive error symbols in an error block is three.

The error symbol group tel in the error block at this time
If the symbol at the first position in is 88 and three consecutive symbols '3 Xl 8 ml+ e Tt*N are incorrect, then four syndromes S0,
For S +, S t, S s, S6= e,
+ eX◆, + exitS H=
(X Xe K + 11 ”' e g+1
+ Of “Rei” 11x*willS,=a”e,+
cx”+”e XI+ + α””e wetS z
−(It ” @ X + (X ”” 6 g+ 1
+ (X "" e z6g simultaneous equations will hold. Therefore, by solving this simultaneous equations, ct""(α"'(αXso+s+)+(
α”S1+1)1+αx++(αXS++Sg)+(α
If there are four syndromes So, St, St, Ss that satisfy the formula ``S1+53)=0, then the above three consecutive symbols e N+ eE+In eX4! are 1.
Afterwards, by error erasure correction processing, the above three consecutive error symbols eX+ eX+l+ e1
142 can be corrected.

Therefore, when random errors and burst errors coexist, each symbol position detection for consecutive multiple symbol errors caused by burst errors is
Detection of one reference position is sufficient, and (apparent) error detection and correction can be performed up to a number greater than the maximum value t0 of the number t of symbols that can be detected and corrected.

Note that the present invention is not limited to the above-mentioned example. For example, the error correction code is not limited to the above-mentioned Reed-Solomon code, 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. Furthermore, 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, prior to performing the above error detection and correction, the same normal (for random errors)
Error detection and correction may be performed, and when this normal error detection and correction is impossible, the apparent error detection and correction may be performed on the error blocks caused by random errors and burst errors.

〔Effect of the invention〕

According to the error correction code decoding method of the present invention, for any error block, an error block consisting of one error symbol caused by a random error, or an error block consisting of two or more error symbols caused by a guest error. However, it is possible to perform error correction by erasure correction operation on all error symbols by simply detecting one reference position for each, and when the number of code errors exceeds the number of symbols that can be corrected using conventional error detection. However, at maximum (when the number of error blocks is 1), it becomes possible to perform apparent error detection and correction for up to the number of errors that can be roughly corrected by erasure correction, and bursts occur at the same time as random errors. Powerful error correction can be realized for signal transmission systems (including recording and reproducing systems) that are prone to errors.

[Brief explanation of drawings]

FIG. 1 is a diagram illustrating an example of an error correction code used to explain the present invention, and FIG. 2 is a diagram illustrating an example of a data recording format on a magneto-optical disk.

Claims (1)

[Claims] In a method for decoding an error correction code in which digital data is encoded with an error correction code so that the minimum distance between codes is d, one error symbol or two or more When the number of error blocks consisting of consecutive error symbols is i, and the number of error symbols in the j-th (1≦j≦i) error block among these error blocks is a_j, then i+Σ＾i_j_=_1a_j≦d A method for decoding an error correction code, characterized in that an error correction operation is performed within a range that satisfies the inequality -1.