JPS63286026A - Error correction method - Google Patents

Abstract

PURPOSE:To correct the error of both a burst error and a random error without requiring complicated error correction calculation by applying a data table where a residue group of either of both the errors and its residual group are made correspondent by 1:1 to other kinds of error patterns with expansion. CONSTITUTION:In the coderection of a data error in case of the decoding of a digital data or the like received by wired/radio communication, a 1st table where the error pattern group whose burst error is correctable and a residue group being the result of the error pattern by a generation polynomial generated by the received code are made correspondent by 1:1, and a 2nd table where the error pattern group whose random error is correctable and the residue group being the division of the error pattern by the generation polynomial are made correspondent, are generated. A residue polynomial being the result of division of the received code in polynomial expression by the generation polynomial is read from one of the 1st and 2nd tables to correct the error, and when the residue polynomial is not included in one table, it is read from the other table to correct the error, and when the residue polynomial is included in both the tables, the error is corrected as one of the error.

Description

DETAILED DESCRIPTION OF THE INVENTION [Field of Industrial Application] The present invention relates to a method for correcting code errors in received data in digital data transmission.

[Conventional technology]

When transmitting digital data, more specifically when decoding digital data received via wired or wireless communication or read from a recording medium, it is necessary to correct data errors that occur during transmission or reading. It is. Conventionally, this error correction has been performed using random error correction codes, which aim to correct errors that occur independently in each code in the received code;
It is broadly divided into two types: cases using burst error correction codes, which aim to correct errors that occur densely in a certain range; and cases using burst error correction codes.

[Problem that the invention seeks to solve]

By the way, random errors that can be corrected using the random error correction code mentioned above and burst errors that can be corrected using the burst error correction code have different possibilities of occurring depending on the data transmission format, so generally they are used differently depending on the type of data transmission. It is true. On the other hand, in order to deal with both, a method called double encoding, that is, a method of performing processing on both at the same time, can be applied, but double encoding requires complicated processing and time. Therefore, it has conventionally been difficult to process random error correction and burst error correction at the same time.

The present invention was made in view of these circumstances, and
The purpose of the present invention is to provide an error correction method that can simultaneously correct burst errors and random errors.

Means for Solving Problems] The present invention provides a method in which the coset of the error pattern of a burst error correction code is a part of the set of all cosets (at least A
(below), and by expanding the data table that has a 1:1 correspondence between one of the error pattern types and its coset to apply to other types of error patterns, two types of error patterns can be used. We are trying to correct errors.

〔Example〕

DESCRIPTION OF THE PREFERRED EMBODIMENTS The present invention will be described in detail below based on drawings showing embodiments thereof.

FIG. 1 is a block diagram of a wireless transmission circuit in which the error correction method according to the present invention is implemented. In the figure, 1 is an antenna, and 2 is a transmit/receive changeover switch that selectively connects the antenna 1 to the transmitting system or the receiving system. be.

The transmission system includes a ps code converter 5 that converts transmission data from parallel to serial. FS modulator 4 which modulates the serial data from this PS code converter 5. It is comprised of a wireless transmitter 3 for transmitting the output of this FS steel transformer 4 from an antenna 1.

On the other hand, the receiving system includes a radio receiver 6. It is comprised of an sp code converter 8 that converts the serial output of the FS demodulator 7 into parallel signal reception data.

FIG. 2 shows an example in which the PS code converter 5 and SP code converter 8 in FIG. 1 are integrated into a microcomputer.

9 in FIG. 2 is a microprocessor (μ-cpu>), which outputs the output signal SO to the FS modulator 4, and also outputs the FSt
A signal Sr from the ltm unit 7 is input. This microprocessor 9 generates check bits and encodes the transmitted data and received data that are input/output to the parallel input/output circuit 12 using the method of the present invention described later when transmitting, and also detects errors and corrects errors associated with the received data when transmitting. However, the data table used for error correction at this time is R.
Stored in OM10. Note that 11 in the figure is a RAM for temporarily storing various data during processing by the microprocessor 9.

Next, the principle of the present invention will be explained with reference to FIGS. 3 and 4.

FIG. 3 is a schematic diagram showing a set of error patterns. In burst error correction, a code word (
There are 2n error patterns, which is the same as the number of error patterns (there are 2n), and the length that can be corrected for burst errors for the set G3 is b (however, n- is ≥ 2b, and k is the number of check points m from the code length n). , i.e. =n-m), and 2
- is shown as street set 01.

On the other hand, among other error patterns to be corrected, that is, for example, a set of 2-pin random errors, a portion that does not belong to set 01 is defined as set G2.

FIG. 4 is a schematic diagram showing correctable error patterns (error syndromes). In the figure, the set of error syndromes for all error patterns is 03',
If the original burst error syndromes for the aforementioned set 01 are the set G1', and the error syndromes for the set G2 are the set G2', then the sets G1, G, l
has a perfect 1:1 correspondence, and sets G2 and G2' have a 1:1 correspondence except for the part G4 of set 02' that overlaps with G and l. In other words, although there is a possibility that the set G4 may be incorrectly corrected, it is possible to significantly reduce the size of the set 04 by appropriately setting the conditions for correctable random errors, that is, the set G2'. Furthermore, by predetermining which of burst errors and random errors should be given priority in correction, it is possible to give priority to correction of one of the errors.

Hereinafter, implementation of the method of the present invention will be specifically explained.

The set of code words F (x) is defined as (F(x)'t = ((fn-+, fn-2.-1+
, fa) 1 (however, rn-+, rn-:+,
``'fl, fn is a value of 0' or 1'') In polynomial expression, (F(x)) = (frl-H・Xn' +rn-
2・Xn-2'+----+f 1-X' +FO-X
O). On the other hand, the code word is divided into the original data D (x) and the code for error correction, that is, the check bit R (x), each of which is (D (x)) = (dx-+ ・X' + d
'x-2・X''-2+...-+d, XI +do -X
01(R(x)) = (rn-y-1・Xn-'
+ rn− to −2・Xn− to −2+−+r 1 ・X'
+ro ・XO), and similarly the generator polynomial G(
χ) is (G (x)) - (X n-' + g
4- x-1・X' to 1→...10g+・X'
+go, XOl, and in the Galois set (Mob, 2), D
Remainder R(x) when (x)・Xn- is divided by G (x)
becomes F (x).

Therefore, F (x) is divisible by G (x).

These relationships also hold for the error syndrome in the case of reception, and (F(x)) is transformed into an error pattern (E(
x)l, the relationship between (E(x)l and error syndrome (R'(X)) is exactly the same.

As a specific example, (n, k, b) = (27,1
6,5), that is, a 5-bit burst error correction code, and the generating polynomial is Q (x), −X II + X 10 + X
The case of 9+X7→-X6+XE+X+1 will be explained below.

FIG. 5 shows the set G1 of 5-bit burst errors in FIG. 3, with the first bit positions 05 to 1B <16
The vertical axis shows the error bit pattern (remaining 4 digits).
The data itself corresponds to the sets G and I, and is a hexadecimal representation of a 1-bit error syndrome value.

Similarly, Figure 6 shows the part of the set of 2-bit random errors excluding the part belonging to set G, with the previous error pit position on the vertical axis expressed in hexadecimal from 06 to IB, and the horizontal axis as the hexadecimal representation. The subsequent error pit position is shown in hexadecimal representation from 1 to 16. This corresponds to set G2', and the data in the table is a hexadecimal representation of the error syndrome.

Now, FIG. 7 is a rearranged version of FIG. 6, and specifically shows the procedure for correcting a 5-bit burst error.

In other words, the three digits of the hexadecimal representation of the error syndrome are arranged in ascending order, with the 3rd and 2nd digits on the vertical axis and the 1st digit on the vertical axis, and the data itself indicates that the 3rd and 2nd digits are 5-bit burst errors. The first position of the error bit is indicated by the I-th digit, and the subsequent 4-bit error pattern is indicated by the asterisk (*) indicating that it belongs to the error syndrome set G4 in FIG.

Corresponding to the error syndrome shown in FIG. 7, burst errors are corrected.

On the other hand, Figure 8 is a reverse rearrangement of Figure 6, and like Figure 7, the error syndrome is arranged in three hexadecimal digits, and the data itself is the first two digits of the 2-bit random error. indicates the first error bit position, and the last two digits indicate the subsequent error pit position, and the underlined data belongs to set G in FIG.

According to FIG. 8, it is possible to correct the error syndrome in the received code as a random 2-bit error. However, regarding the errors belonging to the underlined set G4, as mentioned above, if they are random 2-bit errors, they can be correctly corrected, but if they are other errors, the 5-bit burst shown in Figure 7 above can be corrected. It will be corrected as an error.

However, as shown in Table 1, < (n, ni, b) = (
27,16°5), the number of errors belonging to the set G is as small as 20, and poses almost no problem in practice.

Table 1 Tables such as those shown in FIGS. 7 and 8 are stored in advance in the RO old O, and the received data St is error-corrected and decoded. This is shown in the flowchart of FIG.

First, the received data SI is arranged in bit order and F' (x
). Next, the error syndrome R'(χ) is calculated. If this R' (x) is 0, it means that there is no error, but if R' (x) is not 0, it means that an error is included.

And the error pattern E(χ) corresponding to R'(x)
is taken out from the table stored in ROM10.

At this time, correction is impossible if R' (x) is not in the table, but if it is, read the corresponding E (x) and perform XOR (exclusive OR) with this and the received code F' (to). is encoded into the original code F (x).

As a result, the burst error in the set G1 shown in FIG. 3 can be corrected 100%, and at the same time, the burst error in the set G2 in FIG.
Among the random errors, the error syndrome set 02' in FIG. 4 is 100% correctable, and the set G in FIG. 4 is correctable if it is a random error.

In the above embodiment, priority is given to correcting 5-bit burst errors and 2-bit random errors are also corrected, but other combinations are also possible. Further, although the above embodiments are applied to wireless transmission, it goes without saying that optical transmission, wired transmission, etc. are also possible.

〔Effect of the invention〕

As described above, according to the present invention, error syndromes and error patterns are stored as a table on a storage means such as 120M by superimposing a random error pattern in addition to the original burst error correction pattern.
Both errors can be corrected without performing complicated error correction calculations, and erroneous corrections are also reduced.

[Brief explanation of the drawing]

Fig. 1 is a block diagram of a wireless transmission circuit to which the method of the present invention is applied, Fig. 2 is a block diagram of a case where the code converter is configured with a microprocessor, and Fig. 3 is a block diagram of a wireless transmission circuit to which the method of the present invention is applied. A schematic diagram showing the relationship between sets,
Fig. 4 is a schematic diagram showing the relationship between correctable error patterns (error syndromes), Fig. 5 is a table showing 5-bit burst error patterns, Fig. 6 is a table of 2-bit random error patterns, and Fig. 7 is a table showing the relationship between correctable error patterns (error syndromes). , a table of error syndromes and error patterns for 5-bit burst errors, and FIG. 8 shows error syndromes and error patterns for 2-bit random errors. FIG. 9 is a flowchart showing the error correction procedure. Note that the same reference numerals in each figure indicate the same or corresponding parts.

Claims (1)

[Scope of Claims] 1. In an error correction method when decoding a digital reception code, error patterns capable of burst error correction and a coset obtained by dividing the error pattern by a generator polynomial generated from the reception code are 1. : The first associated with 1
and a second table that associates error patterns that can be corrected with random errors and remainders obtained by dividing these by the generator polynomial, and divide the received code expressed as a polynomial by the generator polynomial. read out the remainder polynomial from one of the first and second tables and correct the error; if the remainder polynomial is not included in one of the tables, read it from the other table and correct the error; An error correction method characterized in that when a polynomial is included in both of the tables, it is corrected as an error in one of the tables.