KR20150023087A - Concatenated BCH coding method, coding apparatus, and reliability based decoding method - Google Patents

Abstract

The present invention relates to a concatenated BCH coding method, to a coding apparatus, and to a reliability based decoding method. The present invention concatenates multiple sub symbols in parallel on a row and a column. The present invention includes the following steps: receiving a message from outside; setting total side of the message, the number of matrix sub symbols (krB, kcB), index numbers (mr, mc), and error correction capabilities (tr, tc) in a range which satisfies an equation of {(-1-mrtr)×krB>=N, (-1-mctc)×kcB>=N}; and concatenated-BCH-coding the message by using the set parameters (N, krB, kcB, mr, mc, tr, tc).

Description

[0001] The present invention relates to a concatenated BCH coding method, a coding apparatus, and a reliability based decoding method,

The present invention relates to a method of encoding a message to detect a communication error, and more particularly to a concatenated BCH coding method, a coding apparatus, and a reliability-based decoding method.

2. Description of the Related Art [0002] Recently, various encoding methods for encoding data in order to reduce errors occurring in data transmission processes of optical communication, digital broadcasting, and memory devices have been used. Among them, a BCH (Bose-Chaudhuri-Hocquenghen) coding method having excellent coding performance is widely used.

FIG. 1 shows the structure of a conventional single BCH code. Referring to FIG. 1, in a single BCH code 101, the size (L2) of a shortened message is excessively set to be close to half the size (L1) of a BCH code. A short message is an unused message. Therefore, as shown in FIG. 1, if the size (L2) of the short message is large, parity is used inefficiently. Generally, when designing a BCH code on GF (2 ^m ), the size (L1) of the BCH code is (2 ^m - 1) bits. Therefore, when a message having a size of 2 ^m bits is to be BCH encoded, a BCH code having a size of (2 ^{m + 1} - 1) bits is designed on GF (2 ^{m + 1} ) It is inevitable to overshoot the half of the size of the BCH code.

2 shows a structure of a conventional concatenated BCH (Concatenated BCH) code. 2, the concatenated BCH code 201 includes a plurality of sub-codes 211 to 215 concatenated in a row, a plurality of sub-codes 221 to 215 concatenated in a column, 225). Also in the concatenated BCH code 201, the shortened messages are arranged so that their sizes (L2 ', L2 ") are close to half of the sizes (L1', L1") of the subcodes 211 to 215 and 221 to 225 And the performance between the plurality of row sub-codes 211 to 215 and the plurality of column sub-codes 221 to 225 is the same, and all message blocks have the same size . That is, it has a message block that evenly divides the entire message.

In this manner, when a message is subjected to concatenated BCH coding in the conventional manner, the sizes of the messages of the plurality of row sub-codes 211 to 215 and the plurality of column sub-codes 221 to 225 are the same. That is, although each parity of the row sub-codes 211 to 215 has an error correcting capability of t bits in a code having a size of (2 ^{m + 1} - 1) bits, And is utilized for securing a t-bit error correcting capability in a code having a size close to (2 ^m ) bits.

As shown in FIGS. 1 and 2, according to the structure of the conventional BCH codes 101 and 201, although the unicast message portion is large enough to be similar in size to the actual message portion, it is not used but a parity bit ). As a result, the parity of the BCH code 101 is inefficiently used. Further, in the case of the concatenated BCH code 201, since the plurality of sub-codes 211 to 215 and 211 to 215 are utilized as constituent codes, this inefficiency becomes larger.

The present invention provides a concatenated BCH coding method in which a size of a shortening message is minimized and an encoding apparatus for executing the concatenated BCH encoding method.

The present invention is also intended to provide a reliability-based decoding method with improved performance.

According to an aspect of the present invention,

A method of coding an encoding apparatus by concatenating a plurality of sub-codes in rows in parallel, the method comprising: receiving a message from outside; Equation ({

_{- 1 - m r t r)} × k r B ≥ N} to the extent not satisfied, the number of the total size (N) of the message, the row sub-code (k _r ^B), index (m _r) and an error correction capability (t _r ); And performing concatenated BCH coding of the message using the set parameters (N, k _r ^B , m _r , t _r ).

In order to solve the above problems,

A method for encoding a plurality of sub-codes in parallel by concatenating a plurality of sub-codes in a coding apparatus, the method comprising the steps of: receiving a message from outside; Equation ({

_{- 1 - m c t c)} × k c B ≥ N} to the extent not satisfied, the number of the total size (N), open sub-code of the message (k _c ^B), index (m _c), and error correction capability (t _c ); And provides a concatenated BCH encoding method comprising the step of using the established parameters ^{_{(N, k c B, m}} c, t c) concatenated BCH code the message.

In order to solve the above problems,

A coding method for encoding a plurality of sub-codes in parallel by concatenating a plurality of sub-codes in a row and a column, the method comprising: receiving a message from outside; The mathematical expressions {(

- 1 - m _r t _r ) x k _r ^B ≥ N, (

_{- 1 - m c t c)} × k c B ≥ N} to the extent not satisfied, the total size (N) of the message, the number of the matrix sub-code (k _r ^B, k _c ^B), the index (m _r , m _c ) and error correction capabilities (t _r , t _c ); And concatenating the message with the set parameters N, k _r ^B , k _c ^B , m _r , m _c , t _r , and t _c .

In order to solve the above problems,

Receives a message from the outside,

- 1 - m _r t _r ) x k _r ^B ≥ N} and the equation {(

- of _{m c t c) × k c} B ≥ N} to be the total size (N), line parameter to {row index (m _r), a row error correction capability (t _r) of the message, line satisfy the sub-codes 1 (K _r ^B )} and column parameters {column index (m _c ), column error correcting capability (t _c ), number of column sub-codes (k _c ^B )}; And a coding unit for receiving a signal output from the parameter setting unit and performing concatenated BCH coding.

In order to solve the above problems,

A method for decoding an encoded code, the method comprising the steps of: (a) determining a position of a failed row and a column by performing a syndrome check on the code; (b) extracting low-confidence bits in the failed row and column; And (c) performing a decoding after inverting a predetermined number of bits among the extracted bits.

As described above, according to the present invention, the size of the short message included in the concatenated BCH code is minimized.

Therefore, the performance of the concatenated BCH code is improved because parity is utilized very efficiently.

Further, when the reliability-based decoding method according to the present invention is applied to code decoding, the performance is greatly improved as compared with the case where the reliability-based decoding method is not applied.

FIG. 1 shows the structure of a conventional single BCH (Bose-Chaudhuri-Hocquengen) code.
2 shows a structure of a conventional concatenated BCH (Concatenated BCH) code.
FIG. 3 shows the structure of a single BCH code according to the present invention.
FIG. 4 shows an embodiment of a concatenated BCH code structure according to the present invention.
FIG. 5 shows another embodiment of the concatenated BCH code structure according to the present invention.
6 is a flowchart illustrating a concatenated BCH coding method according to the present invention.
7 is a block diagram illustrating an example of a concatenated BCH coding apparatus according to the present invention.
FIG. 8 is a flowchart illustrating a reliability-based decoding method according to the present invention.
FIG. 9 is a graph showing the effect of the decoding method shown in FIG.

Hereinafter, embodiments of the present invention will be described in detail with reference to the accompanying drawings so that those skilled in the art can easily carry out the present invention. Like reference numerals in the drawings denote like elements.

FIG. 3 shows the structure of a single BCH code according to the present invention.

Referring to FIG. 3, a single BCH code 301 is composed of a short message, a message, and a parity. Here, the total size of a single BCH code 301 is represented by (

- 1) If la bits, the size of the parity bits is (m × _r t _r), the size of the message {(

- 1) - (t _r x m _r )} bits. That is, if the sum of the size of the message and the size of the parity is (

- 1) bits. Here, m _r represents an exponent, and t _r represents an error correction capability of the BCH code 301. The index (m _r ) is calculated by the following equation (1).

[Equation 1]

m _r = ceiling (log ₂ N / k _r ^B )

Here, N denotes the total size of the BCH code, and k _r ^B denotes the number of row sub-codes.

Thus, the size of the unicast message of the single BCH code 301 according to the present invention is configured to be close to zero. Therefore, the parity can be utilized more efficiently than in the prior art.

FIG. 4 shows an embodiment of a structure of a concatenated BCH code according to the present invention. Referring to FIG. 4, the concatenated BCH code 401 includes a plurality of sub-codes 411 to 417 concatenated in a row and a plurality of sub-codes 421 to 425 concatenated in a column. Each of the plurality of sub-codes 411 to 417 connected in a row is composed of a message and parity, and some sub-codes, for example, a sub-code 417, further include a short message 431. Each of the plurality of sub-codes 421 to 425 connected to the column is composed of a message and parity, and some sub-codes, for example, the sub-code 425, further include the short message 431 and 432.

Specifically, for each of the plurality of sub-codes 411 to 417 connected in a row, the total size of the sub-code is set to (

- 1) bits, the parity size is ( _tr x m _r ) bits and the size of the message is {

- 1 - (t _r m _r )} bits. Also, for each of the plurality of sub-codes 421 to 425 connected to the column, the total size of the sub-code is represented by (

- 1) bits, the parity size is (t _c × m _c ) bits and the size of the message is {

- 1 - (t _c m _c )} bits.

Here, m _r and m _c represent exponents, and t _r and t _c represent error correction capability of the concatenated BCH code 401. The exponents (m _r , m _c ) can be calculated using Equation (1) above.

As described above, the size of the short message of the sub-codes 417 and 425 of the concatenated BCH code 401 according to the present invention is configured to be almost zero or very small.

That is, the plurality of sub-codes 411 to 417 and 421 to 425 included in the concatenated BCH code 401 do not all have message sizes of the same size, but some have different sizes of messages. In other words, some of the plurality of sub-codes 417 and 425 include the short message 431 and 432, and the portions 411 to 416 and 421 to 424 do not include the short message 431 and 432.

The concatenated BCH code 401 shown in FIG. 4 is reduced in size as compared with the concatenated BCH code 201 shown in FIG. 2, while the number of row sub-codes 411 to 417 is larger . That is, the number of row sub-codes 411 to 417 of the concatenated BCH code 401 shown in FIG. 4 is 7, whereas the number of row sub-codes 211 to 215 of the concatenated BCH code 201 shown in FIG. Is five.

As described above, since the size of the short message included in the plurality of sub-codes 411 to 417 and 421 to 425 is greatly shortened, parity can be utilized very efficiently.

FIG. 5 shows another embodiment of the structure of the concatenated BCH code according to the present invention. Referring to FIG. 5, the concatenated BCH code 501 includes a plurality of sub-codes 511 to 517 connected in a row and a plurality of sub-codes 521 to 525 connected in a column. Each of the plurality of sub-codes 511 to 517 and 521 to 525 connected by a matrix includes a short message 531 and 532, a message, and a parity.

Specifically, for each of a plurality of concatenated sub-code in the row (511-517), the overall size of the BCH ^code, - if (1 bit LA, the size of the parity (t _r m × 2 ^m) ") Bit, and the size of the message consists of {(2 ^{m '} - 1 - t _r m') - short message} bits. In addition, the heat for each of the plurality of concatenated sub-code of (521-525), the overall size of the BCH code ^"when (La 1-bit, the size of the parity (t _c m × 2 ^m)") bit, and , The size of the message consists of {(2 ^{m "} - 1 - t _c m") - short message} bits.

Here, m 'and m' denote exponents, and t _r and t _c denote the error correction capability of the BCH code. Exponents m 'and m''can be calculated using Equation (1).

As described above, the sizes of the short messages 531 and 532 of the plurality of sub-codes 511 to 517 and 521 to 525 of the concatenated BCH code 501 according to the present invention are very small. Therefore, parity can be utilized very efficiently.

In addition, the concatenated BCH code 501 shown in FIG. 5 is reduced in size as compared with the concatenated BCH code 201 shown in FIG. 2, and the number of row sub-codes 511 to 517 is larger. In other words, the number of row sub-codes 511 to 517 of the concatenated BCH code 501 shown in FIG. 5 is 7, while the number of row sub-codes 211 to 215 of the concatenated BCH code 201 shown in FIG. Is five.

6 is a flowchart illustrating a concatenated BCH coding method according to the present invention. Referring to FIG. 6, the concatenated BCH coding method includes first through third steps 611 through 631.

In the first step 611, the encoding device (701 in Fig. 7) receives a message from the outside.

7, the coding apparatus (701 in FIG. 7) sets the total size N of the entire message, the row parameters (row index (m _r ), row error correction capability (t _r), the number of the row sub-code (k _r ^B)} and the heat parameters of {row index (m _c), a row error correction capability (t _c), the number of the row sub-code (k _c ^B)} .

&Quot; (2) "

(

- 1 - m _r t _r ) x k _r ^B ≥ N

&Quot; (3) "

(

- 1 - m _c t _c ) × k _c ^B ≥ N

The total size N of the entire message is divided by the number (k _r ^B ) of the row sub-codes (411 to 417 in Fig. 4 and 511 to 517 in Fig. 5) Is N / k _r ^B ┐ or └N / k _r ^B ┘, and individual messages are GF (

) And has a correction capability of t _r bits.

Further, the total size (N) of the entire message is divided by the number (k _c ^B ) of the column sub-codes (421 to 425 of FIG. 4 and 521 to 525 of FIG. 5) The size of the message is ┌N / k _c ^B ┐ or └N / k _c ^B ┘, and individual messages are GF

) And has a correction capability of _tc bits.

the message block (B _{i, j} ) is generated by dividing the messages constituting the i-th row sub-codes into k _r ^B ,

The value of ┌N / k _r ^B ┐ or └N / k _r ^B ┘.

( _Tc , < / RTI >< RTI ID = _0.0 &

, k _c ^B ), the jth column code is coded.

Using Equation 2, given the total size N of the entire message and the error correction capability t _r , the number of selectable row sub-codes (411 - 417 in FIG. 4, 511 - 517 in FIG. 5) If the error is given a number (k _r ^B) of the k _r ^B) a can be obtained, the total size of the entire message (N) and the row sub-code of (411-417, 511-517 of Fig. 5) in the range of 4 It is possible to obtain a range that the correction capability ( _tr ) can take. The total sum of the sizes of the messages included in the sub-codes (411 to 417 in Fig. 4 and 511 to 517 in Fig. 5) connected to the row is at least larger than the message size N to be encoded. Otherwise, the number of rows in the sub-code (411-417, 511-517 of Fig. 5 in Fig. 4) (k _r ^B), and error correction capability (t _r) sub-code of the line (411 of Figure 4 in accordance with the 417, 511 to 517 in Fig. 5) can not be designed. What is important here is that the exponent (m _r ) is determined by the exponential expression {m _r =? Log ₂ (N / k _r ^B )} to prevent excessive shortening.

It is possible to prevent excessive shortening of the column sub-codes (421 to 425 in Fig. 4, 521 to 525 in Fig. 5) in the same manner as described above. Note that the coding of the sub-codes (421 to 425 of FIG. 4 and 521 to 525 of FIG. 4) connected to the columns requires that the sub-codes (421 to 425 of FIG. 4) in the case of parallel concatenation (521 to 525 in Fig. 5) are the same as the message size (N) of the entire sub-codes (411 to 417 in Fig. 4 and 511 to 517 in Fig. 5) In the case of serial concatenation, the message size of all the sub-codes (421 to 425 of FIG. 4 and 521 to 525 of FIG. 4) connected to the column is (N '= N + k _r ^B m _r t _r ) . That is, in the case of the serial concatenation, the size of the message of the sub-codes (421 to 425 in FIG. 4, 521 to 525 in FIG. In the case of serial concatenation, sub-codes (421 to 425 in Fig. 4, 521 to 525 in Fig. 5) Even parity is used as a message. For this reason, in the case of serial concatenation, the size of a block including the parity of sub-codes (411 to 417 in Fig. 4 and 511 to 517 in Fig. 5) This problem can be solved by defining the sub-code concatenated with the j-th column through Equation (4) as follows.

&Quot; (4) "

Where f (x) is f (x) = (x - 1) mod k _c ^B +1, and B _{i , j} and R _j ^c are the parity of the sub-codes (421 to 425 of FIG. 4, 521 to 525 of FIG. 5) .

Also important in designing an irregular concatenated BCH code is that sub-codes (411 to 417 in Fig. 4, 511 to 517 in Fig. 5) and row The total parity of the codes (421 to 425 in Fig. 4, 521 to 525 in Fig. 5) should not exceed the parity availability (P).

&Quot; (5) "

k _r ^B m _r t _r + k _c ^B m _c t _c ≤ P

P is defined by the following Equation 6 by the target code rate R and the total size N of the entire message.

&Quot; (6) "

P = └N / R┘ - N

By performing encoding as described above, it is possible to more efficiently utilize the parity by the unequal concatenated BCH encoding. This coding scheme is not limited to the sub codes (421 to 425 in Fig. 4, 521 to 525 in Fig. 5) and the sub codes (511 to 512 in Fig. It can be applied to only one side. (M =? Log ₂ (N / k (k)) related to the size of the fields of all the sub-codes (411 to 417 and 421 to 425 of FIG. 4, 511 to 517, and 521 to 525 of FIG. ^B )?), All of the sub-codes (411 to 417 and 421 to 425 of FIG. 4, 511 to 517 and 521 to 525 of FIG. 5) may be designed on different fields according to their respective numbers. However, in such a case, the sub-codes (421 to 425 in Fig. 4, 521 to 525 in Fig. 5) and the sub codes (511 to 512 in Fig. The same decoder can not be shared, and the complexity of the entire decoder may increase.

In a third step 631, the received message is subjected to BCH coding using the total size (N) of the set message, row parameters and column parameters.

A method of BCH coding a message will be described as a practical example.

First, it is assumed that the total size (N) of the entire message is 32,768 bits (4 kB).

When the number (k _r ^B ) of row sub-codes (411 to 417 in Fig. 4, 511 to 517 in Fig. 5) is determined in the case of utilizing Equation 2, available row sub- , error correction capability of the error correction capability (t _r) to be obtained and, conversely, the row sub-code (411-417, 511-517 of Fig. 5) of Fig. 4 in the range of 511-517 in Fig. 5) (t _r (K _r ^B ) of row sub-codes (411 to 417 in Fig. 4, 511 to 517 in Fig. 5) can be obtained.

For example, it is assumed that coding is performed by utilizing row codes and column codes each having 16 error correction capacities of 10 (t _r = t _c = 10) in the conventional method. In the conventional method, since a message of 32768 bits must be uniformly divided into 16 messages, the total size of messages of the individual configuration codes is 2048 bits. Therefore, the sub-code (411-417 and 421-425, 511-517 and 521-525 of Fig. 5 in Fig. 4) are designed on the GF (2 ^12), each of the parity is 12 * 10 (= m _r × t _r = m _c x tc). The number of row sub-codes (411 to 417 in Fig. 4, 511 to 517 in Fig. 4) and the number of row sub-codes (421 to 425 in Fig. 4, 521 to 525 in Fig. 411 and 417 and 421 to 425 in FIG. 4, and 511 to 517 and 521 to 525 in FIG. 5) is 32, the parity of 3840 (12 × 10 × 32) bits is required in the conventional method.

However, the present invention is applied as follows.

Assuming that the number (k _r ^B ) of the row sub-codes (411 to 417 in FIG. 4 and 511 to 517 in FIG. 5) is 16, the index (m _r ) . Substituting this number into Equation 2 results in (2 ¹¹ - 1 - 11 × t _r ) × 16 ≥ 32768. When the inequality is summarized, the range of error correction capability (t _r ) is obtained as a negative number. Therefore, at this time, row encoding can not be performed unlike the conventional method. That is, since there is no restriction condition as in Equation (1) in the past, excessive shortening is made near half of the message.

Therefore, since unequal concatenated BCH coding can not be performed using the 16 row sub-codes, a method of using 17 row sub-codes (m _r is the same as before) is applied. If the number of lines in the sub-code (411-417, 511-517 of Fig. 5 in Fig. 4) (k _r ^B) so that it is 17, similarly to the above by the equation (1) index _(r m) is 11. (K _r ^B ) and exponent (m _r ) of the row sub-codes (411 to 417 in FIG. 4 and 511 to 517 in FIG. 5) and the total size (N) In summary, it can be seen that the error correction capability (t _r ) is 10 or less. Here, the error electrostatic capacity (t _r ) must be a positive integer.

The sizes of the messages included in the sub-codes (411 to 417 and 421 to 425 in FIG. 4, 511 to 517 and 521 to 525 in FIG. 5) are reduced and the error correction capability (t _r = t _c = 10 It is necessary to set the parameters so as to have the following parameters. The amount of parity for this is 3740 bits (11 x 10 x 34). That is, the size of the parity according to the present invention has the error correcting capability of all the constituent codes even if the parity size is reduced to 100 bits compared with the conventional parity size (3840 bits). In addition, since the size of the sub-codes (411 to 417 & 421 to 425 in Fig. 4, 511 to 517 & 521 to 525 in Fig. 5) becomes smaller, the error correction capability is improved.

7 is a block diagram illustrating an example of a concatenated BCH coding apparatus according to the present invention. Referring to FIG. 7, the concatenated BCH coding apparatus 701 includes a parameter setting unit 711 and an encoding unit 721.

The parameter setting unit 711 receives a message input from the outside and calculates the total size of the entire message (N in FIG. 4 and FIG. 5) and the row parameters (FIGS. 4 and 5 the outputs by setting the _r m, _r t, k _r ^B), and the thermal parameters (of FIGS. 4 and _{5 m c, t c, k} c B). 4 and 5) and row parameters (m _r , t _r , k _r ^B in Figs. 4 and 5) and column parameters (m _c , t in Figs. 4 and 5) _c , k _c ^B ) has been described in detail with reference to FIG. 6, so that a description thereof will be omitted in order to avoid redundant explanations.

4 and 5) and the line parameters (m _r , t _r , k (see FIGS. 4 and 5), the total size _r ^B ) and column parameters (m _c , t _c , k _c ^{B in} FIGS. 4 and 5) to perform concatenated BCH coding. The method of performing the concatenated BCH coding is a known technique, and a detailed description thereof will be omitted. The encoding unit 721 outputs the encoded signal to the memory (not shown).

The memory may be a NAND flash memory. The memory may further include a NAND flash memory and a controller for controlling operations of the NAND flash memory.

The encoding unit 721 may further include a decoder for decoding the encoded signal stored in the memory.

In addition to the concatenated BCH coding function, the coding unit 721 may further include a hamming coding function and a RS (Reed Solomon) coding function. Alternatively, the coding unit 721 may perform Hamming coding or RS coding alone have.

The signal output from the encoding unit 721 may be transmitted to a receiver (not shown) that receives the signal through wire communication or wireless communication.

As described above, the encoding apparatus 701 according to the present invention minimizes the short message. Therefore, the parity is utilized very efficiently, and the performance of the concatenated BCH code is improved.

FIG. 8 is a flowchart illustrating a reliability-based decoding method according to the present invention. Referring to FIG. 8, the reliability-based decoding method includes first through third steps 811 through 831.

In a first step 811, a syndrome check is performed on the rows and columns of the code in the process of decoding the encoded code to determine the number of failed rows and columns Locate the location. The code is composed of a plurality of rows and a plurality of columns as shown in Fig. Therefore, a syndrome check is performed on the plurality of matrixes. If there are no failed rows and columns, the reliability-based decoding process is terminated.

In a second step 821, low-confidence bits are extracted from the failed row and column. That is, only the bits corresponding to the common portion of the failed row and column are read multiple times to obtain reliability information, and a plurality of low reliability bits are retrieved and extracted based on the reliability information.

The executes after which the decoding in Step 3 (831), predetermined number of bits of the extracted bits (N _s bits), the reverse (flip).

If the decryption is successful in the decryption process, the decryption process is terminated. If the decryption fails in the decryption process, the third step 831 is repeatedly executed a predetermined number of times. At this time, if the predetermined number of times is exceeded, the reliability-based decoding process is terminated. The predetermined number of times may be arbitrarily set by the designer according to the characteristics of the code, and may indicate when the plurality of bits with low reliability are all inverted.

FIG. 9 is a graph showing the effect of the decoding method shown in FIG. Referring to FIG. 9, when the reliability-based decoding method 911 according to the present invention is applied to code decoding, the performance is significantly increased compared with the case 921 in which the reliability-based decoding method is not applied, %]. While the present invention has been particularly shown and described with reference to exemplary embodiments thereof, it will be understood by those of skill in the art that various changes and modifications may be made without departing from the scope of the present invention. It will be appreciated that embodiments are possible. Accordingly, the true scope of the present invention should be determined by the technical idea of the appended claims.

Claims (16)

A method for encoding a plurality of sub-codes in parallel by concatenating a plurality of sub-codes in a row,
Receiving a message from outside;
Equation ({

_{- 1 - m r t r)} × k r B ≥ N} to the extent not satisfied, the number of the total size (N) of the message, the row sub-code (k _r ^B), index (m _r) and an error correction capability (t _r ); And
And performing concatenated BCH coding of the message using the set parameters N, k _r ^B , m _r , and t _r . The method according to claim 1,
Wherein the exponent m _r is calculated using the equation {m _r = ceiling (log ₂ N / k _r ^B )}. The method according to claim 1,
The actual messages of the plurality of sub-

). ≪ / RTI > A method for encoding a plurality of sub-codes in parallel by concatenating a plurality of sub-codes in a column,
Receiving a message from outside;
Equation ({

_{- 1 - m c t c)} × k c B ≥ N} to the extent not satisfied, the number of the total size (N), open sub-code of the message (k _c ^B), index (m _c), and error correction capability (t _c ); And
Concatenated BCH encoding method comprising the steps of: using the established parameters ^{_{(N, k c B, m}} c, t c) concatenated BCH code the message. 5. The method of claim 4,
Wherein the exponent m _c is calculated using the equation {m _c = ceiling (log ₂ N / k _c ^B )}. 5. The method of claim 4,
The actual messages of the plurality of sub-

). ≪ / RTI > A coding method for encoding a plurality of sub-codes by concatenating rows and columns in parallel in an encoding apparatus,
Receiving a message from outside;
The mathematical expressions {(

- 1 - m _r t _r ) x k _r ^B ≥ N, (

_{- 1 - m c t c)} × k c B ≥ N} to the extent not satisfied, the total size (N) of the message, the number of the matrix sub-code (k _r ^B, k _c ^B), the index (m _r , m _c ) and error correction capabilities (t _r , t _c ); And
Wherein concatenated BCH coding is performed on the message using the set parameters N, k _r ^B , k _c ^B , m _r , m _c , t _r , and t _c . The method according to claim 1,
Said index (m _r, m _c) is, using the equation of _{[{m c = ceiling (log} 2 N / k c B)}, {m r = ceiling (log 2 N / k r B)}] And calculating the concatenated BCH coding. The method according to claim 1,
The actual messages of the plurality of sub-

) And GF (

). ≪ / RTI > The method according to any one of claims 1, 4, and 7,
Wherein each of the plurality of sub-codes comprises one of a Hamming code, a Bose-Chaudhuri-Hocquengen code, and a Reed Solomon (RS) code. The method according to any one of claims 1, 4, and 7,
Wherein the encoding method is also applied to a method of serial concatenating the plurality of sub-codes. Receives a message from the outside,

- 1 - m _r t _r ) x k _r ^B ≥ N} and the equation {(

- of _{m c t c) × k c} B ≥ N} to be the total size (N), line parameter to {row index (m _r), a row error correction capability (t _r) of the message, line satisfy the sub-codes 1 (K _r ^B )} and column parameters {column index (m _c ), column error correcting capability (t _c ), number of column sub-codes (k _c ^B )}; And
And a coding unit for receiving a signal output from the parameter setting unit and performing concatenated BCH coding. 13. The method of claim 12,
Wherein the encoding unit outputs the encoded signal and transmits the encoded signal to the NAND flash memory. 13. The method of claim 12,
Wherein the parameter setting unit and the encoding unit are provided in a transmitter that transmits a signal through a communication channel. A method for decoding an encoded code,
(a) performing a syndrome check on the code to determine positions of failed rows and columns;
(b) extracting low-confidence bits in the failed row and column; And
(c) reversing a predetermined number of bits among the extracted bits and then performing decoding. 16. The method of claim 15, wherein in step (b)
Wherein the reliability-based decoding method further comprises the steps of: obtaining reliability information by performing multiple read operations on only bits corresponding to the common portion of the failed row and column; and retrieving and extracting the reliability- .

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