JPH0659032B2 - Decryption method - Google Patents

Description

The present invention relates to a method of decoding an error correction code for improving reliability of memories such as a digital audio and a main memory of a computer.

[Conventional technology]

Conventionally, when two types of two-dimensional arrangement codes are combined and decoded as a product code, the product code is inherently high in redundancy, and therefore, by devising the decoding method, it is possible to have a correction capability of a minimum distance or more guaranteed. As expected, the code with the smaller distance was decoded first, and then the code with the larger distance was used for decoding.

For example, reference [Inoue, Kasahara, Namerikawa "Decoding 2D Codes by Estimating Residual Erasure" IEICE Technical Report, it83
-13, 1983], it is better to decode a code with a larger distance first, but the above example uses iterative decoding to raise the erasure and finally EE decoding (erasure. It is a very special type of decoding that performs error decoding).
The two types of two-dimensionally arranged codes C ₁ and C ₂ are not C ₁ decoding and C ₂ decoding once.

In addition, decoding for erasure correction of a distance 2 such as simple parity or crossword code is performed by trivial (tr
ivial) and the correction effect is small, so it is not described here.
FIG. 3 shows an operation flow chart of a conventional decoder.

Next, the operation will be described.

Now, a code with a smaller distance is a C ₁ code, and a code with a larger distance is C ₂
I will call it a code.

In the conventional decoding, as shown in the flow chart of FIG. 3, when the data store and initial setting are completed, C ₁ decoding is performed, and then C ₂ decoding and sequential decoding are performed and the decoding result is output. In this case, if the error probability of the channel is p, the error probability Pε ₁ that remains uncorrected after C ₁ decoding is represented by Pε ₁ = f (p) (1).

On the other hand, when the C ₂ code is decoded alone, the error probability after correction is represented by P ε ₂ = g (p) (2). Therefore, the decoding error probability Pε _{0 for the} entire C ₁ decoding and C ₂ decoding is expressed by Pε ₀ = g · {f (p)} (3).

[Problems that the invention is trying to solve]

As described above, in the conventional decoding method, the code C ₁ with a smaller distance is decoded first, and then the code C ₂ with a larger distance is decoded, so that the residual error of the product code does not easily become small. There was a problem.

The present invention has been made to solve the above problems, and an object of the present invention is to provide a decoding method in which a C ₂ code having a large distance is first decoded to reduce a residual error. To do.

[Means for solving problems]

The decoding method according to the present invention is designed such that decoding is performed before a code having a large minimum distance in order to reduce an error rate after decoding.

[Action]

In the decoding method according to the present invention, a code having a large minimum distance is decoded 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 FIG. 3 are shown with the same reference numerals. In FIGS. 1 and 2, 1 is an address data and control signal bus, 2 is a RAM (random access memory), and 3 is C ₁ decoder, 4 is a C ₂ decoder, and 5 is a control circuit.

Next, the operation will be described. As shown in operation flow chart of FIG. 2, the C ₂ decoder 4 first by data instructions stored control circuit 5 to the RAM 2, C ₂ decoding is performed, by C ₁ decoder 3 following its termination C ₁ decryption is performed.

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

Pε ₂ = g (p) (4) Next, C ₁ decoding is executed, but if C ₁ decoding alone is the same as equation (1) already described, if C ₂ decoding and C ₁ decoding are performed successively, The error rate after decoding is given by Eq. (5).

Pε _k = f · {g (p)} (5) That is, the decoding error probability Pε ₀ (3) of the entire conventional decoding
C ₁ and C ₂ between the equation and the decoding error probability P ε _{k of} equation (5) according to the present invention.
If the code lengths of P and P are the same, the coefficient of Eq.

That is, the error rate can be suppressed smaller by decoding from a code having a larger distance. This is confirmed below with actual parameters.

(32,28,5) RS (Reed on Galois field GF (2 ⁸ ) as C ₁ code
-Solomon) code and (32,26,7) RS code on GF (2 ⁸ ) is used as C ₂ code.

First, when decoding the C ₁ code by the conventional method, the decoding error probability P _M1
Is The error detection probability P _T1 is However, Ai (n) is the number of RS code words of code length n and weight i.

Next, the error probability P _Z with the C ₂ code as the input for decoding is P _Z = 466.94p ³ . Next, in C ₂ decoding, the decoding error probability P _M2 is The error detection probability P _T2 is The uncorrectable probability P _f0 is P _f0 = 4496 × (466.94p ³ ) ⁴ = 2.1372 × 10 ¹⁴ p ¹² (6) Decoding error rate in C ₂ decoding if C ₂ decoding is performed first
P _M2 Given in. The error detection probability P _T2 is P _T2 = 4494.1p ⁴ . Therefore, the error rate P _Y as the input of C ₁ is P _Y = 4496.0p ⁴ . The decoding error rate P _{M1 for} C ₁ decoding is The error detection probability P _T1 is Therefore, the uncorrectable probability P _fk is P _fk = 466.9 (4496.0p ⁴ ) ³ = 4.244 × 10 ¹³ p ¹² …… (7).

That is, comparing the conventional decoding method (6) with the decoding method (7) of the present invention, the difference in reliability of about one digit occurs in the uncorrectable probability and the one with the smallest minimum distance is decoded first. It turns out that is good. However, the combination of the distances of 3 and 9 described in the example of the case where the distances of 5 and 7 are relatively close to each other is more effective. Further, if the erasure correction is used for the subsequent decoding by using the decoded information which has been previously decoded, the effect of improvement can be obtained, but the principle is the same, and the description thereof is omitted.

[Effects of the Invention] As described above, according to the present invention, as a method of reducing the residual error probability of two types of two-dimensionally arranged codes C ₁ and C ₂ , C ₂ code with a large distance is decoded first. As a result, the residual error is reduced and the reliability of information is greatly improved.

[Brief description of drawings]

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

 ─────────────────────────────────────────────────── ─── Continuation of front page (72) Inventor Kazuhito Endo No. 1 Baba Institute, Nagaokakyo City, Kyoto Prefecture Mitsubishi Electric Corporation Electronic Products Development Laboratory (72) Inori Sadano Ishida No. 1, Nagaokakyo Baba Institute, Kyoto Mitsubishi (72) Inventor Hideo Yoshida 325 Kamimachiya, Kamakura City, Kanagawa Mitsubishi Electric Corporation

Claims (3)

[Claims] 1. A decoding method for decoding two types of two-dimensionally arranged codes C ₁ and C ₂ as a product code and reducing a residual error probability which causes a difference in error control capability after the decoding. _1, C ₂ and C ₁ decoding, when the decoding is divided into C ₂ decoding such as a plurality of times, the decoding method characterized by executing the decoding from a large code minimum distance. _{2. When} the error control apparatus performs decoding by using a plurality of RS codes on the Galois field GF (2 ⁸ ) of the codes C ₁ and C _{2 having} different minimum distances from each other, the minimum distance becomes large. The decoding method according to claim 1, wherein the decoding is performed prior to the decoding of the code. 3. A (32,26,7) RS code on GF (2 ⁸ ) of the codes C ₁ and C ₂ having a distance from each other, and (3
2. The decoding method according to claim 1, wherein when decoding is performed using the RS code, the code of the distance 7 is decoded first.