JPS61257024A - Decoding method - Google Patents

Abstract

PURPOSE:To decrease the error rate after decoding by decoding earlier a code having a large minimum distance. CONSTITUTION:The entire decoding error probability Pepsilon0 as to C1 and C2 decod ing of two kinds of 2-dimension arranging codes C1, C2 is expressed in equation I. A data is stored in a RAM 2, the C2 decoding is executed by a C2 decoder 4 according to a command of a control circuit 5 and the C1 decoding is executed by a C1 decoder 3 after the end of the C2 decoding. Since the C2 code is decoded at first, the error rate Pepsilon after the C2 decoding is expressed in equation II. Then the decoding is applied continuously as the C2 and C1 decodings, the error rate after the decoding is expressed in equation III. That is, as to the decoding error probability Pepsilon0 and PepsilonK expressed in equations I, III, when the code length of the codes C1, C2 is nearly the same, even when the power of the major them P of the probability is the same, the coefficient expressed in equation III is smaller. That is, the error rate is suppressed lower when the decoding is applied from the larger code.

Description

DETAILED DESCRIPTION OF THE INVENTION [Field of Industrial Application] The present invention relates to a method for decoding an error correction code to improve the reliability of memories such as digital audio and the main memory of a computer.

[Conventional technology]

Conventionally, when two types of two-dimensional constellation codes are combined and decoded as a product code, the product code inherently has a high degree of redundancy, so it is necessary to devise a decoding method that has a correction ability greater than the guaranteed minimum distance. Since this is expected, the code with the smaller distance is first decoded, and then the code with the larger distance is decoded.

For example, the literature [Bengami, Sujihara, Namekawa, “Decoding of two-dimensional codes by estimating residual erasure”, Institute of Electronics and Communication Engineers Technical Report, 1t
83-13.1983), it is better to decode codes with larger distances first, but the above example uses iterative decoding to highlight the erasure and then performs EE decoding at the end. (erasure/error decoding), special decoding is required, two types of codes C1*C2 for two-dimensional equipment.
'1 decoding and C2 decoding are not performed once.

In addition, decoding that performs erasure correction at the end of something with a distance of 2, such as a simple parity or crossword code, is trivial (t
rivlal) and the effect of the correction is small, so it will not be discussed here. FIG. 3 shows an operation flowchart of a conventional decoder.

Next, the operation will be explained.

Now, a code with a small distance will be called a 01 code, and a code with a large distance will be called a 02 code.

In conventional decoding, as shown in the 70-chart in Figure 2, when the data store and initial settings are completed, 01 decoding is performed, and then C
2 decoding and sequential decoding were performed and the decoding results were output. In this case, if the error probability of the communication path is p, then C1
The probability pQ of an error remaining uncorrected after decoding is Plx = f (p) ・=-(
It is represented by 11.

On the other hand, when the C2 code is decoded alone, the error probability after correction is 2g2=g(p)...
...It is expressed as (2). Therefore, the decoding error probability Pg0 of the entire C1 decoding and C2 decoding is Pgo=g・(f(p))...
It is expressed as (3).

[Problem to be solved by the invention] As described above, the conventional decoding method first decodes the code C1 with the smaller distance,
Since the code C2 having a larger distance is then decoded, there is a problem in that the residual WA area of the product code cannot be reduced to a small size.

This invention was made to solve the above-mentioned problems, and aims to provide a decoding method that decodes the C2 code having a large distance first to reduce the residual error. .

[Means for solving problems]

In the decoding method according to the present invention, in order to reduce the error rate after decoding, decoding is performed before codes with a large minimum distance.

[Effect]

The decoding method according to the present invention decodes the code with a large minimum distance first, so that the error rate after decoding can be reduced.

〔Example〕

An embodiment of the present invention will be described below with reference to the drawings. In the figures, the same parts as in Figure 3 are indicated by the same reference numerals. In Figures 1 and 2, 1 is an address data and control signal bus, 2 is a RAM (random access memory), and 3 is a C1 decoder. 4 is a C2 decoder, and 5 is a control circuit.

Next, the operation will be explained. As shown in the operation flowchart of FIG. 2, the data is first stored in the RAM 2, and then cz decoding is executed by the C2 decoder 4 according to a command from the control circuit 5, and after that, C1 decoding is performed. Container 3 C
1 decryption is performed.

In the present invention, as shown in FIG. 2, since the C2 decoder is decoded first, the error rate P8 after C2 decoding is expressed by equation (4).

pg□=g0) ・・・・・・(4
)Next, KC1 decoding is executed, but since C1 decoding alone results in equation (1) mentioned above, if C2 decoding and C1 decoding are sequentially decoded, the error rate after decoding is given by equation (5).

Pε=f−(gω)) ・・・・・・(5
) That is, the decoding error probability Pεo of the entire decoding of the conventional method
For the decoding error probability Pgk of equation (3) and equation (5) according to the present invention, if the code length of C1*C2 is about the same, even if the power of P of the main term of the probability is the same, the coefficient is the same as that of equation (5). is small.

In other words, it is possible to suppress the error wealth by decoding starting from the code having a large distance. This will be confirmed below using actual parameters.

c, the sign is the Galois field a F ((32,
28,5) Using RS (Read-8olomon) code and assuming C2 code, TeG F (2') (7)
(32, 26, 7) Rllwo use il.

First, when 01 code is decoded using the conventional method, the decoding error probability P
M1 is =4.8389ip'=462.097p' However, AI(n) is the code length and the number of RS codewords with a weight of 1.

Next, the error probability pz when using the 02 code as input for decoding is Pz
=466.94p'. Next, in C2 decoding, the decoding error probability PM2 is = 1
, 554 P' Also, the error detection probability Pτ2 is = 4494.1p'', and the uncorrectable probability Pfo is Pfox4496X(466,94p')' = 2.1.
372X10,p...(6)C2
When decoding is performed first, the decoding error rate PM2 in C2 decoding is given by =1.554p'. tab detection probability PT2 is PT2=449
It becomes 4.1 p. Therefore, the error rate py as input of C1 is Py=
4496.0 p". The decoding error rate PMI of C1 decoding is = 4.8389
1 pY5 Error detection probability PTI is = 462.096 pY5 Therefore, uncorrectable probability Pfk is Pfk = 466.9 (4496, Op')' = 4.24
4×10 p (7).

In other words, when comparing the conventional decoding method (6) and the decoding method (7) of the present invention, there is a reliability difference of about one order of magnitude in the uncorrectable probability, and it is better to decode the one with the larger minimum distance first. It can be seen that the results are good. But right now the distance is 5 and 7. Although the explanation has been given using an example where the distances are relatively close to each other, a combination of distances such as 3 and 9 is even more effective. Moreover, if erasure correction is used in subsequent decoding using decoding information etc. that was decoded first, further improvement can be achieved, but since the principle is the same in both cases, the explanation will be omitted.

〔Effect of the invention〕

As explained above, according to the present invention, as a method of reducing the residual error probability of the two types of codes C1yc2 in a two-dimensional arrangement, the C2 code having a large distance is decoded first, so that the residual part S is small. This has the effect of greatly improving the reliability of information.

[Brief explanation of drawings]

FIG. 1 is a block diagram showing the hardware of the present invention;
FIG. 2 is a flowchart of the operation of the decoder of the present invention, and FIG. 3 is a flowchart of the operation of the conventional decoder. In the figure, 1 is an address/data/control signal bus, 2 is a RAM, 3 is a C1 decoder, 4 is a C2 decoder,
5 is a control circuit.

Claims (3)

[Claims] (1) In a decoding method in which two types of codes C_1 and C_2 in a two-dimensional arrangement are decoded as a product code and the residual error probability that causes a difference in error control ability after decoding is reduced, the codes C_1 and C_2 are 1. A decoding method characterized in that when decoding is performed in multiple steps, such as decoding and C_2 decoding, a code with a larger minimum distance is first decoded to reduce residual errors. (2) When decoding an error control device using a plurality of RS codes on the Galois field GF (2^8) in which the codes C_1 and C_2 have different minimum distances from each other, the code with the larger minimum distance is The decoding method according to claim 1, characterized in that decoding is performed before decoding. (3) G of the codes C_1 and C_2 having a distance from each other
(32, 26, 7) RS code on F(2^8) and (3
2, 28, 5) The decoding method according to claim 1, wherein when decoding is performed using the RS code, the code of the distance T is first decoded.