JP2579616B2 - Decoder - Google Patents

Description

DETAILED DESCRIPTION OF THE INVENTION [Technical Field of the Invention] The present invention relates to an (n, k, d) error correction code for simultaneously correcting erasure information and error information (n: code length, k: information length, d: (Minimum distance).

(Prior art)

Conventionally, erasure information and error information are corrected simultaneously (n, k,
d) FIG. 1 shows a flowchart of an error correction code decoding method. First, a syndrome polynomial S (Z) and the number of flags Nx are calculated from n pieces of code information and N pieces of flags indicating the number of pieces of erasure information (step 1,
2). As an example, GF (2 ⁸⁾ (Galois field) on the (32, 24,
9) Consider RS (Reed-Solomon) code.

In general, the generator polynomial G (Z) is Then, the syndrome polynomial A (Z) becomes Given by Here, α is the root of a primitive polynomial, and the primitive polynomial is given by, for example, Z ⁸ + Z ⁴ + Z ³ + Z ² +1. The parity check matrix H is Therefore, Si (i = 0, 1,..., 7) is given by Si = H · V ⁷ (4). Here, V is code information, and T is a transposed matrix. Therefore, when there is no error, Si = 0 (i = 0, 1,..., 7)
Becomes

Returning to FIG. 1, it is checked whether the syndrome polynomial S (Z) is 0 (step 3). If S (Z) = 0, the input information is output as it is without error, and the flag is reset. Is ended (step 8).

On the other hand, when S (Z) ≠ 0, the flag number Zx is Nx ≧ d
It is checked whether (= 9) (step 4). If Nx ≧ d, it is determined that decoding is impossible and only error detection is performed, a flag is set, and the operation is terminated (step 9).

When Nx <d, the decoder operates as a decoder that corrects Nx erasure information and ne error information that satisfy the inequality Nx + 2ne <d. At this time, the algorithm for simultaneously correcting the erasure error is, for example, Y.SU
GIYAMA et al. `` An Erasures-and-Errors Decoding Algorith
m for Goppa Codes '' IEEE Transactions on Imformatio
n Theory 1976-3. Then, when the error position is normally obtained (steps 5 and 6), the magnitude of the erasure and the error are calculated to correct the erasure information and the error information, and the flag is reset (step 7). If the error position is not found normally, a flag is set as error detection. (Step 9). Here, the flag is used as error detection information.

In such a conventional decoding method, the decoding result is as shown in FIG. In FIG. 2, the vertical axis represents the number of erasure information in one codeword, and the horizontal axis represents error (Err).
or) Number of information. In the figure, C indicates a state where decoding is correctly performed, D indicates a state where an error can be detected but cannot be corrected, and M indicates a state where a correction or error is erroneously detected. In addition, ○ indicates a state where the information is not incorrect in the lost information, and ● indicates a state where the information is incorrect in the lost information. The error correction capability obtained from such a decoding result can be calculated from the erasure and error occurrence probabilities.

As an example, the calculation is performed on FIG. FIG. 3 is a decoding block diagram of a two-stage encoded code, 11 is an input terminal for code information, 12 is a C1 decoder that outputs decoded information (data) and check information (flag), 13 Is the information of C1 code
A de-interleave circuit that rearranges information in the order of C2 code information,
14 is a C2 encoder, which is a deinterleave circuit 13
The erasure / error correction is performed based on the decoded information and the check information from, and the decoded information and the check information are sent to the output terminals 15a and 15b, respectively.

Here, it is assumed that (32, 30, 3) RS is used as the C1 code, and (32, 24, 9) RS is used as the C2 code. In order to improve the detection capability of the C1 code, only detection without correction is performed. Then, the detection and oversight probability Pdf1, Pdt1, Pm1 of each information are Becomes

Here, P is the symbol error rate, Pdf1 is the probability of erasure information having no error in the data (（in FIG. 2), and Pdt1 is the probability of erasure information having error in the data (● in FIG. 2). , Ai (n) are the number of RS code words of code length n and weight i,
It is given by the following equation.

Here, d = 3 and q = 2 ⁸ = 256.

Next, the probability of error detection (D in FIG. 2) by the C2 decoder 14
As shown in FIG. 2, the main term of Pd2 was 9 disappeared (circled 8).
Number, ● mark 1), 0 errors, Given by In this case, the symbol error rate P (usually 10 ⁻²
If the degree is worse, the part with a larger number of erasures becomes the main term of the detection probability, and the error correction capability rapidly deteriorates.

Further, when the correction is performed by the C1 decoder 12, if the symbol error rate P becomes worse from around 10 ⁻² , the error is lost with 0 errors.
More than one case was the main term.

As described above, in the conventional decoding method, as the detection probability of the erasure information increases, that is, as the number of flags from the C1 decoder 12 increases, and when there is much erasure information with no error in the data, the symbol error rate is poor. However, the correction capability deteriorates rapidly, or a sufficient correction capability cannot be obtained.

[Summary of the Invention]

The present invention has been made in order to eliminate the above-mentioned drawbacks of the conventional device.
By judging whether or not the number of flags exceeds the correction capability in the order of the number of corrections, it is determined whether to correct lost or error information or to detect error detection information based on the determination result. It is another object of the present invention to provide a decoder capable of improving error correction capability.

(Example of the invention)

Hereinafter, an embodiment of the present invention will be described with reference to the drawings. FIG. 4 shows a decoder according to an embodiment of the present invention, in which a case where two kinds of flags F1 and F2 are used in the order of higher reliability is shown. 21 is a calculating means for calculating the syndrome polynomial S (Z) and the number of flags Nx1 and Nx2 of each of the flags F1 and F2. Nx2 is a predetermined value d11, d21 respectively
Determining means 30 for determining whether or not (≦ d) or more is a decoding means, which corrects a predetermined number of erasure information and error information based on the determination result of the determining means 22.
In the decoding means 30, 23a is Nx1 + 2ne1 when the judgment result of the judgment means 22 is S (Z) ≠ 0 and Nx1 <d11.
<First error position detecting means for calculating ne1 error positions satisfying d12, 23b determines that the above-mentioned determination result is S (Z) ≠ 0, Nx1 ≧
When d11 and Nx2 <d21, satisfy Nx2 + 2ne2 <d22
ne 2 second error position calculating means for calculating 2 error positions, 2
4 is an error correction means for calculating the magnitude of the error at the error position obtained by the first and second error position calculation means 23a and 23b, and correcting the erasure information and the error information;
(Z) = 0 is a flag setting / resetting means for resetting a flag when no error or error correction is performed, and setting a flag when detecting error detection information without error correction. And the above calculation means 2
1, C2 shown in FIG. 3 by the judgment means 22 and the decoding means 30
A decoder 14 is configured.

Next, the operation of this embodiment will be described with reference to the flowchart of FIG. Here, as described above, two types of flags are used.
F1 and F2 are used, and the reliability of the flag F1 is higher.

Calculation of syndrome polynomial S (Z), number of flags Nx1, Nx
The calculation up to 2 and the determination of S (Z) are the same as in the past. (Steps 31-33).

If S (Z) ≠ 0, it is first checked whether the flag number Nx1 of the flag F1 with high reliability is Nx1 ≧ d11 (step 34). Here, d11 ≦ d. If Nx1 <d11, decoding is performed to correct Nx1 pieces of erasure information and ne1 pieces of error information that satisfy Nx1 + 2ne1 <d12 (≦ d) (step 41). If Nx1 ≧ d11, it is checked whether or not Nx2 ≧ d21 (≦ d) (step 35). If Nx2 <d21, Nx2 erasure information satisfying Nx2 + 2ne2 <d22 (≦ d) and ne2 The decoding for correcting the error information is performed (step 36). If Nx2 ≧ d21, a flag is set as error detection (step 40).

If the error position is found normally in this way,
The magnitude of the erasure and error is calculated to correct the erasure and error information (steps 37 and 38). If the error position is not found normally, a flag is set as error detection information (step 39). Here, the case where the error position was not found normally means that the basic equation could not be solved as described in the above-mentioned document, or that the basic equation was solved but the error position was not included in the code word. And so on.

Next, the operation and effect of the present embodiment will be described in detail with reference to the decoding of the two-stage encoded code shown in FIG. d11 = d12 = d2
Let 1 = d. Assuming that the flag described in the conventional example is a flag F1, the detection and miss probability of each information is (5) (6)
It is given by equation (7). Here, the flag F1 is set to (32, 30,
3) Highest reliability because RS code is decoded only for detection. Next, as a highly reliable flag F2, one piece of error information is corrected with the C1 code and the flag is added without adding a flag.
If a flag is added when more than one error information is detected, the main term of the detection and oversight probability Pdf2, Pdt2, Pm2 of each information is, assuming that the error is random, Given by Here, P is the symbol error rate, Pdf2 is the probability that the code data is not erroneous but becomes lost data with the F2 flag added, and Pdt2 is the probability that the F2 flag is added and the code data becomes erroneous lost data. is there. The probability of the decoding result when the two types of flags F1 and F2 are separately used and decoded by the conventional decoding method shown in FIG.
FIG. 7 and FIG. Here, FIG. 6 shows the minimum order when the flag F1 and FIG. 7 use the flag F2, and the coefficients are omitted.

As can be seen from FIGS. 6 and 7, when the flag F1 having high reliability is used, the probability of occurrence decreases as the error information increases, as compared with the case where the flag F2 having low reliability is used. (P ≒ 10 ^-2 ). In contrast, the probability of occurrence increases as the amount of lost information increases.

Therefore, the erasure information having a high probability of occurrence is mainly corrected by using the flag F1 having high reliability (step 41 in FIG. 5). If the number of flags in the flag F1 is too large to exceed the correction capability, the reliability is corrected. It will be described below that the error correction capability and the error detection capability can be improved as a whole by correcting the erasure information and the error information by using the low flag F2 (step 36 in FIG. 5). From FIG. 2 and FIG.
Main terms of the error detection probability PdF1 when using the erasure information number 9, in the case of error information number 0 is PdF1arufaP ^9. The main term of the error correction probability PmF1 is that the number of lost information is 8, and the number of error information is 1
In the case of a PmF1αP ^11. Note that the above-mentioned probability Pdf,
The equations used to calculate Pdt and Pm are the symbol error rate P
Is sufficiently small, and a numerical value which is a coefficient to be multiplied by the symbol error rate P can be ignored in this case.

On the other hand, in the case of using only the flag F2, from FIG. 2 and FIG. 7, the primary term of the error detection probability PdF2 is lost information number 1, if the number of error information is 4, is PdF2arufaP ¹⁰ . Error correction probability
Main terms of PmF2 is lost information number 0, if the number of error information is 5, it is PmF2αP ^10.

According to this embodiment, when the number of flags F1 is 8 or less, F1
And if the number of flags F1 is 9 or more,
Decrypt using F2. Therefore, the probability when the erasure information, which was the main term of the error detection probability PdF1, is 9 and the number of error information is 0, is as follows. It will be moved, correctable and will, what was in proportion to P ⁹ in the flag F1 is now proportional to P ^18, is improved.

On the other hand, consider the probability when the number of lost information, which is the main term of PdF2, is 1 and the number of error information is 4, when only the flag F2 is used. The main term of the error information probability Pm2 in the case of the flag F2 is 1
This is the case where error correction is performed and error correction is performed, and this is error detection with the flag F1. In the present invention, the flag F1
In the case where decoding is possible, the number of lost information as seen by the flag F1 is 9, which corresponds to the number of error information 0, and the breakdown of the lost information is (○, ●, ●, ●). Here, ○ is proportional to P, and ● is proportional to P ² , so PdF2 in this embodiment is improved because it is proportional to P ¹⁴ when ○ is 4 and ● is 5 You.

Similarly PmF2 is error information number 5 in flag F2 is lost in the flag 1 Information Number 9 (OOOO ●●●●●) to be improved will be proportional to P ¹⁴ since.

Therefore, error detection in the case of decoding by using the flag F1 alone, whereas erroneous correction probability is proportional to P ⁹ are proportional to P ¹⁰ each case of using the flag F2 alone,
Error detection in the present embodiment, erroneous correction probability is proportional to P ^14, respectively, it can be seen that the improved error correction capability. As described above, the occurrence probability using the flag F1 shown in FIG. 6 includes the equations (11), (12), and a part of the equation (10) when the flag F2 is used. 7 excludes the case where the error information is corrected by the flag F1, and it can be seen that the error information has a higher error correction capability than decoding by the flag F2 alone.

Furthermore, by calculating the occurrence probability of each of the number of lost information and the number of error information in detail and setting d11, d12, d21, and d22 finely, the error correction capability and the error detection capability can be further improved.

In this embodiment, since the number of times of decoding is one, the decoding time does not become long, and d11 = d12 = d21 = d22 = d, so that the circuit scale of the decoder can be almost the same as before.

In the above embodiment, the RS code is used as the correction code. However, any error correction code that can simultaneously correct erasure information and error information can be applied in the same manner as in the above embodiment.

In the above embodiment, two types of flags are used.
It goes without saying that the same applies to the case where more than two types of flags are used. For example, when three types of flags are used, if (32, 28, 5) RS is used as the C1 code, no error is detected as a decoding result, and one error correction, two error corrections, and error detection are performed.
Since two states are obtained, when all errors are detected without performing error correction as the flag 1, when one error correction is performed as the flag 2 and when two or more error corrections are detected, the flag 3 is used.
Can set three types of flags when 1 and 2 error corrections are performed.

〔The invention's effect〕

As described above, according to the present invention, using two or more types of erasure flags, it is determined whether the number of flags exceeds the correction capability in ascending order of the number of corrections. Since the correction or the error detection is performed, there is an effect that the error correction and the detection capability can be improved.

[Brief description of the drawings]

FIG. 1 is a diagram showing a flowchart of a conventional decoding method,
FIG. 2 is a diagram showing a result of decoding a (32, 24, 9) RS code by a conventional decoding method, FIG. 3 is a block diagram of a two-stage coded code, and FIG. FIG. 5 is a block diagram of a decoder according to an embodiment, FIG. 5 is a flowchart of a decoding method by the decoder, and FIG. 6 is a diagram showing the minimum order of the probability of the decoding result when decoding is performed using the flag F1. FIG. 7 is a diagram showing the minimum order of the probability of the decoding result when decoding is performed using the flag F2. 21: calculation means, 22: determination means, 30: decoding means.

Claims (1)

(57) [Claims] 1. An (n, k, d) error correction code (n: code length, k: information length, d: minimum) that simultaneously corrects erasure information and error information having m (≧ 2) or more types of flags. Distance), the number of flags Nx1, Nx2,
, Nxm, and whether or not the syndrome polynomial S (Z) is 0, and the number of flags Nxi (i = 1, 2,..., M) is a predetermined value di1 (≦ d, i =
(2,..., M) or more; and if the syndrome polynomial is S (Z) = 0, the input information is output as it is without error, and the syndrome polynomial is S (Z). Z) ≠ 0 and the number of flags Nxi (i = 1, 2,..., M) is a predetermined value di1 (≦ d, i = 1, 2,.
m) is determined in order from the smallest i, and if the determined result is Nxi <di1, a predetermined value di2 (≦ d, i = 1, 2,..., m) is obtained from the input information. Nxi + 2 · nei <di
Decoding means for performing decoding for correcting Nxi pieces of erasure information and nei pieces of error information satisfying 2 and outputting error detection information when S (Z) ≠ 0 and Nxi ≧ dm1. A decoder characterized by the above-mentioned.