JPS63203016A - Method for deciding number of errors - Google Patents

Abstract

PURPOSE:To attain the correction or errors in real time by a small capacity of exclusive processor even when number of errors is large by applying the decision of quantity between number of errors K included in a code word and an integral number t' (a positive integer smaller than maximum error correctable number). CONSTITUTION:First, syndrome is calculated and the number of errors K is decided prior to the decoding processing. In this embodiment, in the case of t'=4 and number of errors K having a relation of K<=4, a quadruple error correction processing is applied, and in the case of K>=5, the octuple error correction processing is applied respectively. In the quadruple error correction processing or the like, an exclusive processor applying it in real time is formed by a comparatively small circuit scale. The frequency of occurrence of an error is large with a smaller K and in most cases, K<=4 exists. Thus, it is rare to apply the octuple error correction processing and the correction of real time is attained in most cases. In case of K>=t'+2=6, erroneous decision of K<=4 might be arisen in the decision of number of errors, but in this case, erroneous correction takes place.

Description

DETAILED DESCRIPTION OF THE INVENTION (Field of Industrial Application) The present invention relates to a method for determining the number of errors in error correction codes used in storage devices such as optical disks, digital communications, and the like.

(Prior Art) FIGS. 5 and 6 each show a Reed-Solomon code (
FIG. 2 is a schematic diagram of a decoding algorithm for R8 code (abbreviated as R8 code).

In FIG. 5, code length n=30. Number of information symbols = 28.
FIG. 6 shows an R8 code with a minimum code amount distance d mxn = 3 and a maximum number of errors that can be corrected t = 1, where n = 120. k
=104. dmin=17. This is a decoding algorithm for R8 code with t=8.

R8 in Figure 5 (30, 28, dmin=3.t weight: 1)
To decode the received word R, (i=ol 1, 2...2
9) Two more syndromes S. , calculate S engineering. Here, it is assumed that the code generating polynomial 〇(x) is G(x)=(x+1)(x+α). (However, α is the primitive light of the finite field GF.) At this time, So,
Sl is calculated using the following formula.

S if there is no error in the code word. Since =S = 0, this determination is made, and if the number of errors is =O, no correction is performed.

Next, when the number of errors is 1, So and Sl are 5o=ex and 51=exα8, respectively, so the error position X is determined as α”=S1/So.

If actually = 1, then X determined in this way will be the number of positions that exist as code words. That is, O≦X≦
n-1=29.

If 0≦X≦n-1, it is determined that =1, and the error pattern eX (=S, ) is applied to the X-th received word symbol Rx.
Correction is performed by adding (exclusive OR operation). If 0 ≦

In this way, when decoding a code with small t, the number of errors K can be determined relatively easily during the decoding process, so
There is no problem even if the number of errors is not determined prior to decoding.

Next, RS (120, 104, d m1n=
The decoding of 17°t fold 8) will be described.

Since it is a t-fold 8-fold code, if the number of errors is K=8, it can be correctly corrected, but an 8-fold error correction process is performed considering correction up to a maximum of 8. Decoding begins with S from the received word R1 (i = 0, 1, 2...119). -Calculate 16 syndromes of 5XS.

Next, an error locator polynomial σ(X) and an error numeric polynomial η(x) are determined from this syndrome using an algorithm such as the Euclidean algorithm.

Next, a solution of σ(x)=O is found by the Chen search method or the like. When the number of errors K=8, exactly σ(x)=O solutions are found, and the value becomes the number of positions existing as code words. That is, O≦ja”” j7≦n-1
(=119).

In this case, the error pattern e, ~ej7 for each position is
is obtained from σ(X) and η(X), and e, respectively, for each received word symbol R1° to RJ7. ~Add eJ7 (
Correction is performed by performing an exclusive OR operation).

If there is even one error position found as a solution to σ(x)=O that is not greater than or equal to O and less than or equal to n-1, then the number of errors is K or more than 9, and the maximum number of correctable errors is t
(=8) or more errors, so no correction will be made.

In this way, R8 (120, 104, dmin=17.
Decoding of t-fold 8) can also be done by performing multiple error correction processing without having to judge the number of errors prior to decoding.
8 errors can be correctly corrected.

(Problem to be Solved by the Invention) However, in the case of decoding a code with relatively large t, such as the conventional example RS (120,104°=4−dmin=17.t=8), The amount of calculation for the t-fold error correction process, which is the decoding process, becomes extremely large (the amount of calculation increases in proportion to t2), and if this correction process is performed using a general-purpose microcomputer, the processing time will increase due to errors. For example, in an optical disk, real-time correction is possible for K=2 to 3 or less, but real-time correction is not possible when K is larger than that.

In order to enable real-time correction even for larger K, it is possible to create a processor dedicated to error correction processing, but in this case, if t is large, the circuit size of the dedicated processor will be very large. There was a problem that it became large, difficult to implement, or expensive.

Therefore, the number of errors is judged by t times (t times is a positive integer smaller than t), and when K≦t', t' times error correction processing is performed, and when K≧t'+1, An effective method is to perform processing according to the number of errors K, such as performing t-fold error correction processing (see "Error correction method" filed on the same day as the present invention). In this case, it is desirable to select t' to be approximately 4, which is a value that makes it possible to realize a dedicated processor capable of real-time correction with a relatively small circuit scale, and at the same time makes it difficult to perform real-time correction with a general-purpose microcomputer.

An object of the present invention is to provide a method for determining the number of errors, which complements the number of errors with a certain positive integer t', which is necessary for classifying the processing according to the number of errors K. It is something to do.

Another object of the present invention is to provide a method for determining the number of errors that can be corrected in real time even when the number of errors is relatively large, and that can be implemented using a dedicated processor with a small circuit scale.

Furthermore, it is an object of the present invention to provide a method for determining the number of errors that can easily determine the magnitude of the number of errors and an integer t' by using only remainders and additions between syndromes. .

(Means for Solving the Problems) In order to achieve the above object, the present invention decodes a 1 (1 is a positive integer) multiple error correction code, and the number of errors is K≦t'(
(t-fold is a positive integer smaller than t), t'-fold error correction processing is performed, and when K≧t'+1, t-fold error correction processing is performed. Information including 2t test symbols (n symbols) is received, and of the 2t syndromes calculated from the received words, 2t'+1 are arranged in the order shown below to determine the value of the determinant. If it is 0, it is determined that there are t' or less errors among the n symbols of the received word, and if it is not 0, it is determined that there are t'+1 or more errors.

(Function) Therefore, according to the present invention, by calculating the value of the determinant and determining whether the value is O or not, the magnitude of a certain integer t' is determined by the number of errors included in the code word. This has the advantage that the judgment can be made and the judgment result can be used for case classification according to the size of K in code processing.

(Embodiment) FIG. 1 is a determinant for determining whether the number of errors of the t-fold error correction code of the present invention is larger or smaller than a certain positive integer t'(t-fold<t). This determinant is 2t'-2t' in total
There are different types, but when K crab≦t', the value of all 2t-2t' is O, and when K crab=t'+1, the value is 2t-2
The value of all t' is not 0. When K≧t′+2, any determinant has probability 1/(q−1) and 01(q−2
)/(q −1) becomes non-zero. However, q is the number of elements of a finite field that constitutes a code word; for example, if the code word is on GF(2''), q=2''=256.

Therefore, if the value of the determinant in Fig. 1 is O, ≦t',
By determining that ≧t′+1 unless it is 0, K
If ≦t'+1, the determination can be made correctly.

If , ≧t'+2, the value of the determinant will be 0 with a probability of about 1/(q-1), so with this determination method, if ≧t'+2, the value of the determinant will be 0. With probability of (q-1) ≦
This results in an erroneous determination of t'. However, the phenomenon in which 2t-2t' determinants become 0 for ≧t'+2 is a stochastically independent event, so for example, if two determinants are selected and both of them are If we decide to judge ≦t' only when In the method for determining the number of errors, the number of errors can be determined with higher accuracy by increasing the number of determinants used for determination as necessary.

FIGS. 2 and 3 show what happens when the determinant shown in FIG. 1 is expanded when t'=3 and 4, respectively, as specific examples. When t'=3, the form is the sum of 10 products of four syndromes, t'=4
In the case of , the result is the sum of 26 products of 5 syndromes.

FIG. 4 shows a decoding algorithm in which the number of errors is determined prior to the decoding process using the method of determining the number of errors of the present invention with t'=4. The code is 2 of the conventional example.
R8 (120, 104, dmi
n=17. t = 8). In the error number determination, if it is determined that K≦4, quadruple error correction processing is performed with K2
If it is determined to be S, eight-fold error correction processing is performed. 4
For heavy error correction processing, a dedicated processor that can perform such processing in real time can be created with a relatively small circuit scale. In this case, it is preferable that the calculation for determining the number of errors, that is, the calculation shown in FIG. 3, is also performed by a processor dedicated to quadruple error correction.

The smaller K is, the higher the frequency of error occurrence is, and the frequency of errors is almost ≦
It is 4. Therefore, 8-fold error correction processing is rarely performed, and real-time correction can almost always be performed.

In the case of K≧t'+2=6, in determining the number of errors, K
≦4 may be incorrectly determined. In that case, σ(x
) = O is often not greater than O and less than n-1,
The process will move on to 8-fold error correction processing, but the number may be greater than or equal to 0 and less than or equal to n-1, in which case an error correction will occur. In order to reduce the probability of this miscorrection, it is possible to increase the number of determinants used for determining the number of errors to improve the accuracy of determining the number of errors, or if the solution of σ(X)=O is greater than or equal to O and less than or equal to n-1. Not only whether there is one, but also the number of solutions of σ(x)=O and σ
It is conceivable to use whether or not the orders of (X) match in the error correction prevention determination (see ``Error correction prevention method J'' filed on the same day as the present invention).

It should be noted that the hardware of the method for determining the number of errors of the present invention can be easily designed using a logic circuit, and the result of determining the number of errors of the present invention can be used for purposes other than decoding processing. Yes, it goes without saying.

(Effects of the Invention) As shown in the above embodiments, the present invention provides that the number of errors included in a code word is a certain integer t'(t' is a positive number smaller than the maximum correctable error number t of the code word). The present invention provides a determination method for determining the magnitude with respect to an integer (an integer), and according to this determination method, determination can be easily performed by performing only multiplication and addition between syndromes.

Furthermore, in the present invention, the number of errors is calculated only by multiplication and addition between syndromes, so even if the number of errors becomes relatively large, the scale of the dedicated processor can be reduced and correction can be made in real time.

Furthermore, the present invention can reduce the probability of erroneous correction by increasing the number of row example expressions used to determine the number of errors.

[Brief explanation of the drawing]

Figure 1 shows the determinant for determining whether the number of errors in a t-fold error correction code is K, ≦t', or ≧t'+1.
As a specific example of the determinant in the figure, the determinant when t' = 3 is expanded. Figure 3 shows the determinant when t' = 4 as a specific example of the determinant in Figure 1. The expanded version, FIG. 4, is R8 (120, 104, dmin = 17. t = 8) using the error number judgment (t' = 4) according to the present invention.
) decoding algorithm, Figure 5 is one of the conventional examples,
Error correction code R8 (30, 28, dmLn=3.t=
Figure 6 shows a conventional example of the decoding algorithm of i), in which the decoding of an error correction code RS (120° 104, dmin 17. t multiplier 8) with a large number of error corrections t is divided into processing cases by determining the number of errors. This is a decoding algorithm that performs t-fold error correction processing from the beginning without performing t-fold error correction processing. Figure 1 Determinant for determining whether the number of errors in the heavy error correction code is K or t' or t'+1 Figure 2 (Example 1) Determinant when t' = 3 Expansion formula of S j+i Sj+i S4+s Sj+'s +S
j+2sjyu2 Sj+2 SJ*a +S, ya2S,
+2S, +, S, + S j+2 S j+s S r, 35444 +S,
. 3 Sj+3Sj, 3S, 3 Figure 3 (Example: "Sj Sj+z Sj+4s, ya. Sj Sj+Z Sj+s Sj+5 S, S,, S, yaisj+s Sj Sj+4Sj+4Sj*. S j Sj*4Sj+S SJ+s SJ, □S, xsj, 4S ,.6 Sj+, Sj+, Sj+5 Sj's Sj+z Sj+z SJ+2 Sj+sS,, 2S,
Yu2 Sj+4. s, +4S1 or 2 Sj+3 Sj+
3Sj+4SJ+z SJ+4 Sj+4 SJ+4S
;+x S;+3SJ+3Sj+3 Sj+3S; and 3 Sj+484.

Claims (1)

[Claims] (1) When decoding t (t is a positive integer) double error correction code, if the number of errors K is K≦t'(t' is a positive integer smaller than t), perform t' double error correction processing, In the case of K≧t′+1, when performing t-fold error correction processing, information including 2 check symbols (n symbols) encoded according to a predetermined generator polynomial is received, and the received word If the value of the determinant of 2t+1 of the 2t syndromes calculated from 2t+1 syndromes arranged in the order shown below is 0, then there are t' errors among the n symbols of the received word.
A method for determining the number of errors, characterized in that if it is not 0, it is determined that the number of errors is t'+1 or more. Determinant used for determination | ▲ There are mathematical formulas, chemical formulas, tables, etc. ▼ | However, j = 0, 1, 2...2t-2t'-1 (2
) Select any N determinants (2≦N≦2t−2t′N is a positive integer) among the above determinants,
If all N values of the determinant are 0, the number of errors among the received word n symbols is t' or less, and the value of one or more determinants is 0.
If not, it is determined that the number of errors is t'+1 or more.