WO2014046395A1 - Encoding/decoding method and apparatus using complementary sparse inverse code - Google Patents

Abstract

The present invention relates to an encoding/decoding method and an apparatus using complementary sparse inverse code. The encoding method includes the steps of: creating a message block generated as a successive message block created from n number of bits of fixed length by deleting the data of the bits up to the bit in which the first "1" appears from a previous message block formed from n number of bits of fixed length and n number of bits of fixed length from the original message data, and continuously filling the successive data of the previous message block from the original message data up to the number of bits of the deleted data, or filling with 1 bits in the case where there are not enough successive data bits; creating a first matrix of size n x n in which the k-th row (column) has each bit of a message block created from n number of bits arranged into n number of columns (rows), and the remaining rows are composed so that only one "1" exists in each row and each column wherein the first column (row) in which a "1" exists is excluded from the k-th row (column); obtaining an inverse matrix of the first matrix and generating a second matrix by applying a modulo 2 modulus operation to the inverse matrix; and generating code words by using the message block or the second matrix in order to transmit the code words.

Description

Encoding / Decoding Method and Device Using Complementary Low Density Inverse Code

The present invention relates to a method and apparatus for encoding / decoding using complementary low density inverse code, wherein a matrix is generated from a message block of fixed length from original message data, and the inverse of the generated matrix and the transmitted data The present invention relates to a method and apparatus for encoding / decoding using a complementary low density inverse code that can easily encode and decode a message using a density of.

In general, in many communication apparatuses and recording / reproducing apparatuses, bit error rates (BERs) of digital transmission information are reduced by transmitting a code sequence encoding an input information sequence.

In recent years, for example, researches in communication fields such as mobile communication and space communication, and broadcasting fields such as terrestrial or satellite digital broadcasting have been actively conducted. Accordingly, code theory aimed at improving error correction encoding and decoding has been actively conducted. Research on this is being done steadily.

As an example of the theoretical limit of code performance, the Shannon limit imposed by C.E.Shannon's communication coding theorem is known. One of the aims of the study of sign theory is to develop codes that show performance close to this Shannon limit.

However, conventionally developed coding methods are not efficient in the decoding and encoding stages, and a problem arises in that the calculation becomes complicated.

Accordingly, the need for a coding method in which the decoding process can be significantly reduced from the encoding stage and the data decoding performance is significantly improved in the decoding stage is also increasing.

The present invention solves this problem. The present invention generates a message block having a fixed length from original message data, generates a matrix using the message block, and obtains an inverse matrix of the generated matrix. Then, by encoding using an inverse matrix to which the operation of modulus 2 is applied, an encoding method using a complementary low density inverse code capable of significantly reducing the calculation used for encoding is provided. Its purpose is to.

In addition, the present invention provides a complex calculation process by generating data encoded by the encoding method into a matrix and decoding the data based on the density of each row or column in the generated matrix. It is an object of the present invention to provide a complementary decoding method using a sparse inverse code that can be omitted to significantly improve decoding performance.

Furthermore, an object of the present invention is to provide a complementary encoding / decoding apparatus using a low density inverse code for executing the complementary encoding / decoding method.

According to an encoding method using a complementary low density inverse code according to embodiments of the present invention, the method includes: generating a message block having n bits of fixed length from original message data; A k-th row in which each bit of the message block of n bits is arranged in n columns or a k-th column in which each bit of the message block of n bits is arranged in n rows (column), and when the message block is arranged in the k-th row, each row except for the k-th row, a column in which '1' first appears in the k-th row, and one 'in each column Generate a first matrix of size nxn consisting of remaining rows configured to have only 1 ', and in the case where the message block is arranged in the kth column, the kth column and the first' 1 'in the kth column Generating a first matrix having an nxn size consisting of each column except the other columns and the remaining columns configured to have only one '1' in each row; Obtaining an inverse matrix of the first matrix and generating a second matrix by applying a modulus operation of 2 to the inverse matrix; And generating and transmitting a codeword using the second matrix.

In an embodiment of the present invention, in the generating of the message block, data up to the first bit of the '1' in the previous message block having a fixed length of n bits is deleted, and the original message data is deleted from the original message data. The number of bits of deleted data is filled with the subsequent data of the previous message block to produce a subsequent message block of n bits of fixed length. In this case, when the number of bits of the erased data is not completely filled from the subsequent data of the previous message block from the original message data, the subsequent message block may be filled with bit '1' and the fixed length of the subsequent message block may be of a fixed length. Generate to have n bits.

In another embodiment of the present invention, in the generating of the message block, the data up to the first bit of the '1' in the previous message block having n bits of fixed length is deleted, and the deleted data is deleted. Fill a bit '1' by the number of bits in to create a subsequent message block of n bits of fixed length.

In the embodiments of the present invention, when the original message data is divided into a plurality of partial original message data, the partial original message data is fixed using at least one of the methods of claims 2 to 4. Create a subsequent message block of n bits of length.

In addition, when the original message data is divided into a plurality of partial original message data, n is a fixed length by filling the number of bits of data deleted in the previous message block from neighboring partial original message data with subsequent data of the previous message block. If a subsequent message block consisting of three bits is generated, and all the number of bits of data deleted in the previous message block are not filled from neighboring partial original message data, the non-filled data is filled with bit '1' to have a fixed length. Generates a subsequent message block of n bits.

Meanwhile, the length of the original message data and the length of the message block may be the same.

In the embodiments of the present invention, when the message blocks are all composed of only '0', one bit consisting of '0' or '1' is generated as the codeword.

In another embodiment of the present invention, when the first occurrence of '1' in the message block in the step of generating the first matrix is the kth bit, the message block satisfies 1 ≦ t ≦ k. To the tth row or tth column.

In an embodiment of the present invention, in the step of generating the first matrix, if the first bit of the '1' in the message block is the kth bit, the message block satisfies 1 ≦ t ≦ k Arranged in a row or t-th column, and '1' present in the remaining rows or columns except for the t-th or t-th column except for a column or row in which '1' first appears in the t-th or t-th column , The first matrix is generated such that '1' is present in each row and each column in the order of the rows or the columns.

Here, when the k-th block of the first bit of the '1' is arranged in the t th row of the first matrix, the t th column of the k th row is '1' and the k th column is '0' And the remaining columns of the kth row are configured in the same manner as the message block, and from the first row to the (k-1) th row, a zero matrix of size (k-1) × 1, (k-1) × ( k-1) a unit matrix of size and (k-1) × (nk) zero matrix are arranged in order, and from (k-1) to nth rows, the matrix of size (nk) × k A second matrix is generated by arranging the unit matrix of size (nk) × (nk) in order. In addition, when the message block having the k-th bit where '1' first appears is arranged in the t th column of the first matrix, the t th row of the k th column is arranged as '1' and the k th row is '0' The remaining rows of the k-th column are configured in the same manner as the message block, and from the first column to the (k-1) th column, a zero matrix of size (k-1) × 1, (k-1) × (k-1 ) The unit matrix of size and (k-1) × (nk) zero matrix are arranged in order, and from the (k-1) th column to the nth column, (nk) × k matrix and (nk) A second matrix is generated by arranging unit matrices of size × (nk) in order.

In embodiments of the present invention, when generating the codeword (codeword) using the second matrix, when the message block is composed of n bits, the length of the codeword may be n ² or 1. . Specifically, when the message block having one or more bits 1 is composed of n bits, the length of the codeword is n ² , and the message block having all bits 0 is composed of n bits. The length of the codeword is one.

In addition, in generating a codeword using the second matrix, a codeword having a length of n ² is generated by sequentially connecting the first to nth rows of the generated second matrix. Alternatively, n ² length codewords may be generated by sequentially connecting the first to nth columns of the generated second matrix.

According to the decoding method using the complementary low density inverse code (sparse inverse code) according to an embodiment of the present invention, receiving a transmission message; Measuring a length of the received transmission message; Comparing the measured lengths of the transmission messages; As a result of the comparison, when the measured transmission message length is n ² , the transmission message is divided into n blocks, and each block of the n blocks is arranged in rows or columns in order to form a third matrix having an size of n × n. Generating; In the case where the third matrix is generated by arranging each block of the n blocks in order, a row having the highest density among the n rows of the generated third matrix is selected. Selecting a column having the highest density among the n columns of the generated third matrix when the third matrix is generated by arranging each block of the n blocks in order; Generating partial decoded message data based on the selected row or column; And decoding using the generated partial decrypted message data.

In embodiments of the present invention, as a result of the comparison, when the measured length of the transmission message is '1', the data is generated as partial decoded message data composed of n '0' lengths of message blocks.

In embodiments of the present invention, selecting a row or column having a relatively highest density among the n rows or n columns of the generated third matrix may be determined by the n. Select the row or column that contains the most relatively '1' among the rows or columns.

Here, when there are two or more rows or columns including '1' among the n rows or columns, the first row or column is selected based on the first row or the first column.

In embodiments of the present invention, in the case of generating the third matrix by arranging each block of the n blocks in a row in the order of generating the third matrix, each of the n rows is one '1'. If it contains only ',' the row containing '1' in the kth column is selected.

In another embodiment of the present invention, in the case of generating the third matrix by arranging each block of the n blocks in sequence in the step of generating the third matrix, each of the n columns is one '1'. If it contains only, select the column that contains '1' in the kth row.

In embodiments of the present invention, if the selected row or column is a d-th row or column in the step of generating partial decoded message data based on the selected row or column, distant consecutive (d-1) '0's. Data consisting of '1' and '1' in order may be generated as partial decrypted message data.

In embodiments of the present invention, in the decoding using the generated partial decoded message data, the generated partial decoded message data is sequentially combined with previously generated decoded message data.

In embodiments of the present invention, if the length of the decoded message is greater than or equal to the length of the original message data in the decoding using the generated partial decoded message data, the length of the original message data is equal to. Decrypt the message.

An encoding apparatus using a complementary low density inverse code according to embodiments of the present invention includes a message block generation unit generating a message block of n bits having a fixed length from original message data; A k-th row in which each bit of the message block of n bits is arranged in n columns, or a k-th column in which each bit of the message block of n bits is arranged in n rows, If the message block is arranged in the k-th row, the k-th row, and each row except for the column where '1' first appears in the k-th row, and the remaining one configured to have only one '1' in each column When a first matrix of size nxn is formed, and the message block is arranged in the k-th column, the k-th column, each column except for the first '1' in the k-th column, and each row A first matrix generator configured to generate a first matrix having an nxn size consisting of remaining columns configured to have only one '1'; A second matrix generator which obtains an inverse of the first matrix and generates a second matrix by applying a modulus operation of 2 to the inverse matrix; A codeword generator for generating a codeword using the second matrix; And a transmission unit for transmitting the generated codeword to the outside.

Decoding apparatus using a complementary low density inverse code (sparse inverse code) according to an embodiment of the present invention includes a transmission message receiving unit for receiving a transmission message; A transmission message length measuring unit measuring a length of the received transmission message; A transmission message length comparison unit comparing the measured transmission message lengths; As a result of the comparison, when the measured transmission message length is n ² , the transmission message is divided into n blocks, and each block of the n blocks is arranged in rows or columns in order to form a third matrix having an size of n × n. A third matrix generator for generating; In the case where the third matrix is generated by arranging each block of the n blocks in order, a row having the highest density among the n rows of the generated third matrix is selected. A selection unit for selecting a column having the highest density among the n columns of the generated third matrix when the third matrix is generated by arranging each block of the n blocks in order; ; A partial decoded message data generation unit configured to generate partial decoded message data based on the selected row or column; And a decoder which decodes the generated partial decoded message data.

According to the encoding / decoding method and apparatus using the complementary low density inverse code with the block size as described above, the following effects are obtained.

First, the original message data is truncated into at least one message blocks of a certain size, and subsequent message blocks after the first message block delete data up to the first bit with a '1' in the previous message block, and the deleted data. Fills the subsequent message block by the number of bits of the original message with the subsequent data bits of the previous message block, or the subsequent data bits of the previous message block by the number of bits of the deleted data in the message block. If not filled, the next message block is filled with '1' to generate the subsequent message block, or the subsequent message block is filled with '1' by the number of bits of the deleted data in the message block. Significantly reduce errors with respect to the effectiveness of decoding performance. Cattle can be.

Second, when the input data (message block) consisting of n bits is arranged in a specific k row or a specific k column and arranged in the kth row, the kth row and the column where '1' is present in the kth row for the first time Generating a low density first matrix of size nxn consisting of each row except the other rows and the remaining rows configured to have only one '1' in each column, and wherein the k-th column and the Encoding and decoding are avoided by generating a low density first matrix of size nxn consisting of each column except for the first '1' in the kth column and the remaining columns configured to have only one '1' in each row. Can be reduced.

Third, the input data is arranged in a specific row or a specific column, and an identity matrix and a zero matrix are arranged to generate a low density first matrix having an nxn size including the input data. The calculation process is reduced.

Fourth, the rules appearing in the second matrix provide a source description of decoding, reduce the computational burden of decoding, and improve the effectiveness of decoding.

Fifth, by utilizing the inverse matrix rule of the first matrix or the second matrix of input data, unit matrix, and zero matrix, the computational burden on the inverse matrix is reduced and plays an important role in the effect of the decoding technique and performance.

Sixth, in the encoding step, the codewords generated by concatenating the rows or columns of the matrix are received to improve the decoding function in simple encoding and decoding.

Seventh, by selecting the row or column associated with the data by using the row or column having the highest density, the decoding process can be made very simple and very efficient.

1 is a block diagram illustrating an encoding apparatus using a complementary low density inverse code according to embodiments of the present invention.

2 is a flowchart illustrating a coding method using a complementary low density inverse code according to embodiments of the present invention.

3 is a block diagram illustrating a decoding apparatus using a complementary low density inverse code according to embodiments of the present invention.

4 is a flowchart illustrating a decoding method using a complementary low density inverse code according to embodiments of the present invention.

Hereinafter, a method and apparatus for encoding / decoding using a complementary low density inverse code according to embodiments of the present invention will be described in detail. As the inventive concept allows for various changes and numerous modifications, particular embodiments will be illustrated in the drawings and described in detail in the text. However, this is not intended to limit the present invention to a specific disclosed form, it should be understood to include all modifications, equivalents, and substitutes included in the spirit and scope of the present invention. In describing the drawings, similar reference numerals are used for similar elements. In the accompanying drawings, the dimensions of the structure is shown to be larger than the actual size for clarity of the invention, or to reduce the actual size to understand the schematic configuration.

In addition, terms such as first and second may be used to describe various components, but the components should not be limited by the terms. The terms are used only for the purpose of distinguishing one component from another. For example, without departing from the scope of the present invention, the first component may be referred to as the second component, and similarly, the second component may also be referred to as the first component. On the other hand, unless otherwise defined, all terms used herein, including technical or scientific terms, have the same meaning as commonly understood by one of ordinary skill in the art. Terms such as those defined in the commonly used dictionaries should be construed as having meanings consistent with the meanings in the context of the related art and shall not be construed in ideal or excessively formal meanings unless expressly defined in this application. Do not.

1 is a block diagram illustrating an encoding apparatus using a complementary low density inverse code according to embodiments of the present invention, and FIG. 2 illustrates an encoding method using a complementary low density inverse code according to embodiments of the present invention. It is a flowchart for doing so.

1 and 2, the encoding apparatus 100 using the complementary low density inverse code according to the embodiments of the present invention may include a message block generator 110, a first matrix generator 120, and a second matrix. It includes a generator 130, a codeword generator 140 and the transmitter 150.

The message block generation unit 110 generates a message block consisting of n bits having a fixed length from the original message data (S110). For example, the length of the message block is specified according to a user setting or initialization setting value.

If the original message data is 100 bits and the length of the message block is fixed to 30 bits, the message block may be set to 30 bits and the remaining bits set to 70 bits, with three message blocks and 10 each having a length of 30 bits. It may be divided into residual bits having a length of bits. In addition, three message blocks each having a length of 30 bits and a dummy bit may be filled in the remaining 10 bits, and thus may be composed of a message block having a length of 30 bits.

In the embodiments of the present invention, the message block generator 110 extracts the original message data by a predetermined length and transfers the corresponding message block to the first matrix generator 120. Subsequently, the message block generation unit 110 deletes the data up to the first '1' bit in the message block, and fills the deleted data with the subsequent data bits of the message block in the original message. Here, the message block may be configured in order of the data remaining in the message block first, followed by the complementary bits.

Further, when the number of bits of the deleted data in the message block cannot be filled with subsequent data bits of the message block in the original message, the subsequent message block is configured by filling the unfilled data with '1'.

Alternatively, the message block may be generated using bit '1' without using the original message data as many as the data bits deleted from the message block. The subsequent message block thus ensures that the number of bits as truncated is always followed by subsequent data in the message block from the original message data, or by using only bit '1' to always have a preset length.

For example, if the length of the message block is set to 5 for '001011010' having a length of original message data of 9, the first message block is '00101', and a first matrix is generated using the first message block. do.

The second message block, which is a subsequent message block of the first message block, has two bits remaining in the first message block after deleting '001', which is data up to the first '1' bit in the first message block. '101' can be obtained by sequentially taking the number of bits' 1010 'deleted from 01' and subsequent data '1010' of the first message block in the original message data, and the two bits remaining in the first message block are obtained. When sequentially combined with the '01', a second message block '01101' having a set length of 5 is obtained.

The third message block, which is a subsequent message block of the second message block, deletes three bits '101' in the second message block when the first message block '01' is deleted from the second message block. Two bits must be added to '. In this case, '1010' may be obtained by sequentially combining '0' remaining in the original message data with '101' remaining in the second message block to fill as many bits as deleted bits in the second message block. However, the third message block '10101' may be obtained by adding bit '1' to the end since the set message block does not satisfy 5, which is the length of the set message block. In other words, if the 'last one bit' 1 'is not replenished in the third message block, there is no remaining data (bit) of the original message data, so that subsequent message blocks cannot be filled from the original message data. In such a case, subsequent message blocks are filled with '1'.

The fourth message block deletes '1' until the first bit in which the '1' appears in the third message block, and bits '0101' remaining in the third message block and subsequent data of the third block message in the original message data. Since there are no more bits, the number of bits that do not satisfy the set block message length is filled as '1'. Therefore, the fourth message block becomes '01011'.

The fifth message block sequentially combines the bits '011' remaining after deleting '01' to the first bit where '1' appears in the fourth message block, and the additional two bits '11'. The block becomes '01111'.

Therefore, a fifth message block is generated from the first message block for the original message data '001011010' having a total length of nine. In summary, the message blocks are generated as shown in Table 1 below.

Table 1

On the other hand, the bit '1' can be used to compensate for the deleted bits without using the original message data.

Specifically, when the length of the original message block is set to the length of the message block, for the original message data '001011010', the first message block is the same as the original message data, and the second message block is the first '1' in the first message block. After deleting '001' until the bit where 'appears, and complementing the remaining bits' 011010' and '1' by the deleted bit in the first message block, the second message block is' 011010111 'and the third message block. Deletes the bit until the first '1' appears in the second message block, that is, '01', and complements the remaining bits '1010111' and the deleted bit with the bit '1' in the second message block, '101011111', and the fourth message block deletes '1' until the first bit where '1' appears in the third message block, and bits '1 011111' and bits deleted by the remaining bits in the third message block. 'To get' 010111111 'as the fourth message block. The fifth message block deletes '01' until the first bit in which the '1' appears in the fourth message block, and complements the bit '1' by the remaining bits '0111111' and the number of deleted bits in the fourth message block. 5 Get message block '01111111'.

Therefore, when the length of the original message data is set to the length of the message block, the first message block is generated from the fifth message block. In summary, the message blocks are generated as shown in Table 2 below.

TABLE 2

In addition, when the original message data is divided into a plurality of partial original message data, various methods of generating a message block for each partial original message data may be applied simultaneously or separately. For example, a message block may be generated using the same method for each of the partial original message data having a smaller number of bits than the original message data, and each partial original may be generated according to the type of bits constituting the partial original message data. Different message data may be used to generate a message block using a different method.

Further, when the original message data is divided into a plurality of partial original message data, n is a fixed length n by filling the number of bits of data deleted in the previous message block from neighboring partial original message data with subsequent data of the previous message block. Create a subsequent message block of bits. And when the number of bits of data deleted in the previous message block is not completely filled from neighboring partial original message data, the subsequent message block of n bits having a fixed length is filled by filling the non-filled data with bit '1'. Can be generated. That is, the plurality of partial original message data may be used to interwork with each other to generate a message block.

Meanwhile, the length of the original message data and the length of the message block may be the same. In other words, the original message data is used as the message block. In this case, when generating the message block, since there is no original message data to supplement the subsequent message block with respect to the bit deleted from the previous message block, the subsequent message block can be filled with bit '1'.

On the other hand, if the message block generator 110 is all made up of only '0', the message block generator 110 is a codeword generator 140 for one bit consisting of '0' or '1' Generate as codeword in.

In embodiments of the present invention, the first matrix generator 120 may include a k-th row in which a message block composed of n bits received from the message block generator 110 is arranged in n columns of each bit; In operation S120, a first matrix having an nxn size is formed of each row except for a column in which '1' is present in the k-th row, and the remaining rows configured to have only one '1' in each column (S120).

In addition, when the message block is arranged in the kth row, the first matrix generator 120 determines that '1' exists in the remaining rows except for the kth row. Except for the column in which '1' appears, the first matrix may be configured such that one '1' exists in each row and each column in the order of the rows or the columns.

In other embodiments of the present invention, the first matrix generator 120 k-th arranges each bit into n rows of a message block composed of n bits received from the message block generator 110. A first matrix of size nxn consisting of a column, the k-th column, each column except for the first '1' in the k-th column, and the remaining columns configured to have only one '1' in each row. Can be generated.

Further, when the message block is arranged in the kth column, the first matrix generator 120 may indicate that the first matrix is present in the remaining columns except for the kth column, where '1' is the first in the kth column. Except for the rows where 1 'appears, the first matrix may be configured such that there is one' 1 'in each column and each row in the order of the columns or the rows.

That is, the first matrix generator 120 may arrange the message blocks received from the message block generator 110 in a specific row or in a specific column.

For example, when the message block generator 110 transmits '00101' to the first message block from the message block generator 110 to the first matrix generator 120, the first matrix generator 120 transmits the first message block to the first message block. Each row in the order of the columns or the order of the columns, except for the column in which the first '1' appears in the first row in the second row to the nth row, which are remaining rows except the first row. And the first matrix can be configured such that '1' is present in each column.

That is, the first matrix generator 120 generates a first matrix configured as in Equation 1 below with respect to the first message block '00101'.

Equation 1

Subsequently, when the second message block is '01101' and the third message block is '10101', the first matrix generator 120 generates a first matrix as shown in Equations 2 and 3 below. .

Equation 2

Equation 3

After obtaining the inverse of the first matrix generated by the first matrix generator 120, the second matrix generator 130 generates a second matrix by applying a modulus operation of 2 (S130). ). In this case, when the first matrix generator 120 generates a first matrix, the second matrix generator 130 also generates a second matrix.

For example, when the first matrix generator 120 generates the first matrices of Equations 1 to 3, the second matrix generator 130 is the first matrix of Equations 1 to 3 Second matrices of Equations 4 to 6 are generated.

Equation 4

Equation 5

Equation 6

In an embodiment of the present invention, the first matrix generator 120 may satisfy the message block with 1 ≦ t ≦ k when the bit in which the first '1' appears in the message block is the kth bit. Can be arranged in t rows or t columns. In this case, the first matrix generator 120 may include '1' existing in the remaining rows or columns except for the t th row or the t th column, or a column in which '1' appears first in the t th row or the t th column. Except for rows, the first matrix may be generated such that one '1' exists in each row and each column in the order of the rows or the columns.

In this case, when the message block having the k-th bit where '1' first appears is arranged in the t-th row of the first matrix, the second matrix generator 130 selects the t-th column of the k-th row by '1'. ', Arranging the k th column to' 0 'and the remaining columns of the k th row are configured in the same manner as the message block, and the first to the (k-1) th rows are (k-1) × 1 in size. The zero matrix, the unit matrix of size (k-1) × (k-1) and the zero matrix of size (k-1) × (nk) are arranged in order, and the (k-1) to nth rows A second matrix may be generated by arranging a (nk) × k sized matrix and a (nk) × (nk) sized matrix in order.

Similarly, when the message block having the k-th bit where '1' first appears is arranged in the t-th column of the first matrix, the second matrix generator 130 sets the t-th row of the k-th column to '1', the first. The k rows are arranged as '0', and the remaining rows of the k th column are configured in the same manner as the message block, and from the first column to the (k-1) column, a zero matrix of size (k-1) × 1, ( Unit matrix of size k-1) × (k-1) and zero matrix of size (k-1) × (nk) are arranged in order, and (nk) × A second matrix may be generated by arranging a k matrix having a size k and a unit matrix having a size of (nk) × (nk) in order.

As described above, according to the method of constructing the first matrix, the second matrix can be generated by a simple rule without performing the inverse matrix and the law operation of 2 as the law.

In the embodiments of the present invention, the codeword generator 140 uses a second matrix of size n × n generated by the second matrix generator 130 to generate a codeword of length n ^2. ) Is generated (S140). In embodiments of the present invention, the codeword generator 140 generates a codeword of length n ² by arranging the first to nth rows of the generated second matrix in order on one line. can do. For example, the codeword generator 140 may generate a codeword of '0100000100100010001000001' for the second matrix of Equation 4, and generate a codeword of '0100010101001000001000001' for the second matrix of Equation 5. can do.

When the message block is arranged in the k-th column, the codeword generator 140 generates a codeword having a length of n ² by connecting the first to nth columns of the generated second matrix in order.

Meanwhile, when the message block composed of all zeros is input from the message block generator 110 to the codeword generator, the codeword generator 140 may have a value of '0' or '1'. It becomes a codeword and transmits one bit to the transmitter 150.

Meanwhile, when only one bit is transmitted from the message block generator 110, the codeword generator 140 transmits the received one bit to the transmitter 150. do.

Therefore, the codeword generated by the codeword generator 140 may have a length of n ² or 1.

The transmitter 150 transmits the codeword generated by the codeword generator 140 to the outside (S150).

As such, the encoding apparatus 100 using the low density inverse code cuts the original message data into singular or plural blocks of a predetermined size, and subsequent message blocks after the first message block have a '1' first in the first message block. Deleting data up to bits, filling the number of bits of the deleted data with bits of subsequent data of the message block in the original message data, and failing to fill the number of bits of the deleted data in the message block, Subsequent message blocks are generated by filling the unfilled data with '1' or by supplementing the bit number of the deleted data with bits '1'. In this way, the computational burden and decoding performance of encoding are greatly improved, and errors can be significantly reduced.

3 is a block diagram illustrating a decoding apparatus using a complementary low density inverse code according to embodiments of the present invention, and FIG. 4 illustrates a decoding method using a complementary low density inverse code according to embodiments of the present invention. It is a flowchart for doing so.

3 and 4, the decoding apparatus 200 using the complementary low density inverse code according to the embodiments of the present invention includes a transmission message receiver 210, a transmission message length measurement unit 220, and a transmission message length comparison. The unit 230 includes a third matrix generator 240, a selector 250, a partial decoded message data generator 260, and a decoder 270.

In the embodiments of the present invention, the decoding apparatus 200 using the low density inverse code receives predetermined information from the encoding apparatus 100 and performs a decoding process. In this case, the decoding apparatus 200 may include information on a row or column into which input data is inserted, information on a length of original message data, a length of a message block, and a length of a decoded message (to be decoded to a specific point in time). Information about the length of the message) and information about the length of the transmission message may be acquired in advance or received from the encoding apparatus 100.

The transmission message receiving unit 210 receives a transmission message transmitted from the outside. At this time, the transmission message receiving unit 210 may receive a transmission message having a specific length. For example, the transmission message receiving unit 210 may receive a transmission message having a length of n ² bits or 1 bit (S210).

The transmission message length measuring unit 220 measures the length of the transmission message transmitted from the transmission message receiving unit 210 (S220), and the transmitted message is based on the measured length of the transmission message in the third matrix generator 230. Alternatively, the partial decoded message data generator 250 is transmitted.

On the other hand, if the decoding apparatus 200 already knows the information on the length of the transmission message without measuring the transmission message length, the transmission message length comparison unit 230 does not go through the transmission message length measurement unit 220, the transmission message It is determined whether is one bit (S230), and the comparison result. The transmitted message may be delivered to the third matrix generator 240 or the partial decoded message data generator 260.

The transmission message length comparison unit 230 determines whether the length of the transmission message is 1 bit (S230).

As a result of the comparison in the transmission message length comparison unit 230, if the transmission message length is 1, the transmission message length comparison unit 230 transmits the partial message data generation unit 260. In this case, when the length of the message block is n, the partial decryption message data generation unit 260 generates a partial decryption message composed of '0' by the length (size) of the message block. For example, when the length of the message block is 5 bits, the partial decoded message data generator 260 generates '00000' as partial decoded message data.

On the other hand, if the length of the transmission message in the transmission message length comparison unit 230 is n ² , the transmitted message is transferred to the third matrix generator 240.

The third matrix generator 240 divides the transmission message into n blocks, and arranges each block of the n blocks in rows or columns in order to generate a third matrix having an size of n × n. At this time, the third matrix generator 240 divides the third matrix into n blocks of n ² length transmission messages, and then generates a third matrix including first rows to nth rows, A third matrix including the nth column may be generated (S240).

For example, if the transmitted message received by the transmission message receiving unit 210 is 010101110, the message length transmitted by the transmission message length measuring unit 220 is measured as 9, and the comparison message transmitted by the transmission message length comparing unit 230 is transmitted. Since the length of the message is not 1, the message is transmitted to the third matrix generator 240 and the third matrix generator 240 generates a as a third matrix.

Equation 7

The selector 250 selects a row having the highest density among the n rows of the generated third matrix. That is, the selector 250 selects the row having the highest density, and if there are several rows having the same maximum density, the selector 250 selects the highest density row that appears first. In the embodiments of the present invention, the selector 250 selects a row that includes the largest number '1' among the n rows. For example, when the third matrix is the matrix of Equation 5, the selector 250 selects the second row including the most '1' (S250).

In addition, the selector 250 selects the earliest row when there are two or more rows including '1' relatively largely among the n rows. That is, the selector 250 selects the first row based on the first row. For example, when the density of the second row and the fifth row is equally high, the selector 250 may select the second row.

In addition, when the n rows of the third matrix each include only one '1', the selector 250 selects a row including '1' in the k-th column (cloumn). That is, in the decoding apparatus 200 that receives the information of inserting the input data into the k-th row from the encoding apparatus 100, the selector 250 has n rows in the third matrix, each of which has one '1'. When it contains only, select the row that contains '1' in the k th column (cloumn).

In addition, when the third matrix generator 240 generates a third matrix in which transmission messages are arranged in column order, the selector 250 has the highest density among the n columns of the generated third matrix. You can choose high heat. In this case, the selector 250 differs only in selecting a high-density column instead of selecting a high-density row instead of selecting a high-density row in the case where the third matrix is generated based on the row. Since the details are the same, detailed descriptions will be omitted.

The partial decryption message data generator 260 generates partial decrypted message data based on the row or column selected by the selector 250 (S260).

In the embodiments of the present invention, when the row selected by the selector 250 is the d-th row, the partial decoded message data generation unit 260 first sequentially (d-1) zeros and one next. Generates data composed of '1' in this order as partial decoded message data. Similarly, when the column selected by the selector 250 is the d-th column, the partial decoded message data generating unit 260 first consists of (d-1) '0's and then one' 1 'in sequence. Generate data as partial decrypted message data.

For example, when Equation 4 is the third matrix generated by the third matrix generator 240, the selector 250 selects the third row, and the partial decoded message generator 260 performs the partial decoded message. Is '001', and when Equation 5 is the third matrix generated by the third matrix generator 240, the selector 250 selects the second row, and the partial decryption message generator 260 partially selects the second row. The decoding message is '01', and when Equation 6 is the third matrix generated by the third matrix generator 240, the selector 250 selects the first row and the partial decryption message generator 260. The partial decryption message in becomes '1'.

As mentioned above, when the length of the transmission message is 1 bit, the partial decryption message data generation unit 260 generates the partial decryption message data having zero length as the length of the message block.

The decoder 270 decodes the partial decoded message data generated by the partial decoded message data generator 260 (S270).

For example, the decoder 270 generates a decrypted message by concatenating the current partially decoded message S260 sequentially next to the previous partially decoded message using the generated partial decoded message data. (S270). In other words, the decoder 270 may decode the generated partial decoded message data by sequentially combining the generated partial decoded message data in order with the previously generated decoded message data.

For example, in the case of the third matrix generated by the third matrix generator 240 in Equation 4, the selector 250 selects the third row, and the partial decoded message generator 260 performs the partial decoded message. Is '001', and when the decoding message is '001' in the decoder 270 and the third matrix generated by the third matrix generator 240 in Equation 5 is selected, the selector 250 is the second. The partial decryption message is' 01 'in the partial decryption message generator 260, and the decryption message' 00101 is connected by the current partial decryption message '01' to the previous decryption message '001' in the decryption unit 270. 'Get. Next, in the case of the third matrix generated by the third matrix generator 240 in Equation 6, the selector 250 selects the first row, and in the partial decoded message generator 260, the partial decoded message is' 1 ', and the decryption message' 001011 'is obtained by concatenating the current partial decryption message' 1 'to the previous decryption message' 00101 '.

On the other hand, if the length of the message decrypted by the decryption unit 270 is greater than or equal to the length of the original message data, the message is decrypted by the length of the original message data, and exceeds the length of the original message data of the entire decoded message The decoded bits are finally excluded from the decoded message.

For example, when the original message is '00111010', the decoding unit 270 outputs '00111010' except the last bit '1' as the final decrypted message when the decoding message is '001110101'. .

As described above, the decoding apparatus 200 using the low density inverse code selects the most complex, highest density row or column in a matrix, and constructs original message data or original message data using the order of the selected rows or the columns. The partial decrypted message data can be restored. Very simple calculations and rules can be used to decode the message, and even if noise is included, there is no significant effect on the highest density of the row or column containing the message data. Can also be significantly reduced. Furthermore, since the decoding is performed by a codeword formed by matrices using a message block of a constant size, the error rate can be significantly reduced. In addition, when the message block is composed of '0', only one bit is received and thus easily decoded, thereby reducing the computational burden.

The above-described embodiment is merely an example of the structure and process of an encoding / decoding method and apparatus using a basic low density inverse code, but is not limited thereto. Those skilled in the art will understand that the present invention can be easily modified in other specific forms without changing the technical spirit or essential features of the present invention. Therefore, it should be understood that the embodiments described above are exemplary in all respects and not restrictive.

[Description of the code]

100: encoding apparatus 110: message block generating unit

120: first matrix generator 130: second matrix generator

140: codeword generation unit 150: transmission unit

200: decoding apparatus 210: transmission message receiving unit

220: transmission message length measurement unit 230: transmission message length comparison unit

240: third matrix generator 250: selector

260: partial encoded message data generation unit

270 decryption unit

Claims (42)

1. Generating from the original message data a message block of n bits of fixed length;

   A k-th row in which each bit of the message block of n bits is arranged in n columns or a k-th column in which each bit of the message block of n bits is arranged in n rows arranged in (column),

   If the message block is arranged in the k-th row, the k-th row, and each row except for the column where '1' first appears in the k-th row, and the remaining one configured to have only one '1' in each column Create a first matrix of size nxn of rows,

   When the message block is arranged in the k-th column, the k-th column includes each column except for the first row of '1' in the k-th column, and the remaining columns configured to have only one '1' in each row. generating a first matrix of nxn size;

   Obtaining an inverse matrix of the first matrix and generating a second matrix by applying a modulus operation of 2 to the inverse matrix; And

   Generating and transmitting a codeword using the second matrix, wherein the encoding method uses a complementary low density inverse code.
2. The method of claim 1, wherein generating the message block

   In the previous message block having a fixed length of n bits, the data up to the first '1' bit is deleted, and the number of bits of the deleted data is filled from the original message data with subsequent data of the previous message block, thereby fixing the data. A method of encoding using a complementary low density inverse code, characterized by generating a subsequent message block of length n bits.
3. The method of claim 2, wherein generating the message block

   When the number of bits of the deleted data is not completely filled from the subsequent data of the previous message block from the original message data, the non-filled data is filled with bit '1' so that the subsequent message blocks have n fixed lengths. A coding method using complementary low density inverse code, characterized in that it is generated to have a bit.
4. The method of claim 1, wherein generating the message block

   In the previous message block consisting of the n bits of the fixed length, the data up to the first bit of '1' is deleted, and the number of bits of the deleted data is filled with the bit '1' to the number of bits of n bits of fixed length. An encoding method using a complementary low density inverse code, characterized in that it generates a subsequent message block.
5. The method according to any one of claims 1 to 4,

   When the original message data is divided into a plurality of partial original message data,

   Complementary low density inverse code (sparse inverse) characterized in that for each of the partial original message data to generate a subsequent message block of a fixed length n bits using at least one of the method of claim 2 to claim 4 coding method using code).
6. The method according to any one of claims 1 to 4,

   When the original message data is divided into a plurality of partial original message data,

   From the neighboring partial original message data, the number of bits of data deleted in the previous message block is filled with subsequent data of the previous message block to produce a subsequent message block of n bits of fixed length,

   If not all the bits of the data deleted from the previous message block are filled from neighboring partial original message data, the non-filled data is filled with bit '1' to generate a subsequent message block of n bits of fixed length. A coding method using a complementary low density inverse code, characterized in that the.
7. The encoding method according to claim 1 or 4, wherein the length of the original message data and the length of the message block are the same.
8. The method of claim 1,

   If the message blocks are all composed of only '0', a coding method using a complementary low density inverse code, characterized in that one bit consisting of '0' or '1' is generated as the codeword. .
9. The method of claim 1, wherein generating the first matrix

   A complementary low density inverse code characterized by arranging the message block in a t th row or a t th column satisfying 1 ≦ t ≦ k when the first bit of the '1' in the message block is the k th bit; coding method using sparse inverse code.
10. The method of claim 1, wherein generating the first matrix

    If the first bit of the '1' in the message block is the k th bit, the message block is arranged in the t th row or the t th column satisfying 1≤t≤k,

    '1' present in the remaining rows or columns except for the t th row or the t th column is in the order of the rows or the columns except for the column or the row in which the first '1' appears in the t th row or the t th column A coding method using a complementary low density inverse code, characterized in that the first matrix is generated such that one '1' exists in each row and each column.
11. 11. The method of claim 10, wherein generating the second matrix

    If the message block in which the first bit of the '1' is the k-th is arranged in the t th row of the first matrix,

    The t-th column of the k-th row is arranged as '1', the k-th column is arranged as '0', and the remaining columns of the k-th row are configured in the same manner as the message block, and the k-th row in the first row Up to (k-1) × 1 zero matrix, (k-1) × (k-1) unit matrix and (k-1) × (nk) size matrix in order, and ( From k-1) to n-th row, a second matrix is generated by arranging (nk) × k-sized matrix and (nk) × (nk) -sized matrix in order.

    When the message block in which the first bit of the '1' is the k-th is arranged in the t th column of the first matrix,

    The t th row of the k th column is arranged as '1', the k th row is arranged as '0', and the remaining rows of the k th column are configured in the same manner as the message block, and the first to kth columns are ( k-1) × 1 sized matrix, (k-1) × (k-1) sized matrix and (k-1) × (nk) sized matrix 1) Complementary low-density inverse code, characterized by generating a second matrix by arranging (nk) × k zero matrixes and (nk) × (nk) unit matrixes in order from column to n-th column. A coding method using sparse inverse code.
12. The method of claim 1, wherein generating a codeword using the second matrix

    If the message block is composed of n bits, the length of the codeword is n ² or 1, characterized in that the encoding method using a complementary low density inverse code (sparse inverse code).
13. The method of claim 1, wherein generating a codeword using the second matrix

    When the message block is arranged in the k-th row, a codeword having a length of n ² is generated by concatenating first to nth rows of the generated second matrix in order.

    When the message block is arranged in the k-th column, a complementary low-density inverse is generated by generating a codeword of length n ² by connecting the first to nth columns of the generated second matrix in order. A coding method using a sparse inverse code.
14. A method for decoding a message generated and transmitted as a codeword by the encoding method of any one of claims 1 to 13,

    Receiving a transmission message;

    Measuring a length of the received transmission message;

    Comparing the measured lengths of the transmission messages;

    As a result of the comparison, when the measured transmission message length is n ² , the transmission message is divided into n blocks, and each block of the n blocks is arranged in rows or columns in order to form a third matrix having an size of n × n. Generating;

    In the case where the third matrix is generated by arranging each block of the n blocks in order, a row having the highest density among the n rows of the generated third matrix is selected. Selecting a column having the highest density among the n columns of the generated third matrix when the third matrix is generated by arranging each block of the n blocks in order;

    Generating partial decoded message data based on the selected row or column; And

    And a decoding method using the generated partial decoded message data, the decoding method using a complementary low density inverse code.
15. The method of claim 14,

    As a result of the comparison, when the length of the measured transmission message is '1',

    A decoding method using a complementary low density inverse code, characterized in that to generate a partial decoded message data consisting of n '0' length of the message block.
16. 15. The method of claim 14, wherein selecting the relatively densest row or column of the n rows or n columns of the generated third matrix is

    A method of decoding using a complementary low density inverse code, characterized in that for selecting the row or column containing a relatively large number of '1' among the n rows or columns.
17. The method of claim 16,

    Complementary, characterized in that the first row or column is selected based on the first row or the first column when there is more than one row or column that contains the most '1' among the n rows or columns Decoding method using sparse inverse code.
18. The method of claim 16,

    When the third matrix is generated by arranging each block of the n blocks in a row during the generating of the third matrix, if each of the n rows includes only one '1', '1' in column k Select the row containing ",

    When the third matrix is generated by arranging each block of the n blocks into columns during the generating of the third matrix, if each of the n columns includes only one '1', '1' in the kth row. A decoding method using a complementary low density inverse code, characterized in that for selecting a column containing a '.
19. 15. The method of claim 14, wherein generating partial decrypted message data based on the selected row or column

    When the selected row or column is the d-th row or column, first, data consisting of consecutive (d-1) '0's and one' 1 'in sequence are generated as partial decoded message data. Decoding method using complementary low density inverse code.
20. 15. The method of claim 14, wherein the decoding by using the generated partial decrypted message data

    And decoding the generated partial decoded message data by successively combining the generated partial decoded message data in sequence with the previously generated decoded message data.
21. 15. The method of claim 14, wherein the decoding by using the generated partial decrypted message data

    And if the length of the decoded message is greater than or equal to the length of the original message data, decoding the message as much as the length of the original message data.
22. A message block generation unit for generating a message block including n bits of fixed length from original message data;

    A k-th row in which each bit of the message block of n bits is arranged in n columns, or a k-th column in which each bit of the message block of n bits is arranged in n rows,

    If the message block is arranged in the k-th row, the k-th row, and each row except for the column where '1' first appears in the k-th row, and the remaining one configured to have only one '1' in each column Create a first matrix of size nxn of rows,

    When the message block is arranged in the k-th column, the k-th column includes each column except for the first row of '1' in the k-th column, and the remaining columns configured to have only one '1' in each row. a first matrix generator configured to generate a first matrix having a size of nxn;

    A second matrix generator which obtains an inverse of the first matrix and generates a second matrix by applying a modulus operation of 2 to the inverse matrix;

    A codeword generator for generating a codeword using the second matrix; And

    An encoding apparatus using a complementary low density inverse code including a transmitting unit for transmitting the generated codeword to the outside.
23. The method of claim 22, wherein the message block generating unit

    In the previous message block having a fixed length of n bits, the data up to the first '1' bit is deleted, and the number of bits of the deleted data is filled from the original message data with subsequent data of the previous message block, thereby fixing the data. A coding device using a complementary low density inverse code, characterized in that for generating a subsequent message block consisting of n bits of length.
24. The method of claim 23, wherein the message block generating unit

    When the number of bits of the deleted data is not completely filled from the subsequent data of the previous message block from the original message data, the non-filled data is filled with bit '1' so that the subsequent message blocks have n fixed lengths. A coding apparatus using a complementary low density inverse code, characterized in that it is generated to have a bit.
25. The method of claim 22, wherein the message block generating unit

    In the previous message block consisting of the n bits of the fixed length, the data up to the first bit of '1' is deleted, and the number of bits of the deleted data is filled with the bit '1' to the number of bits of n bits of fixed length. A coding apparatus using a complementary low density inverse code, characterized in that for generating a subsequent message block.
26. The method according to any one of claims 22 to 25,

    When the original message data is divided into a plurality of partial original message data,

    Complementary low density inverse code (sparse inverse) characterized in that for each of the partial original message data to generate a subsequent message block of a fixed length n bits using at least one of the method of claim 2 to claim 4 coding apparatus using code).
27. The method according to any one of claims 22 to 25,

    The message block generation unit

    When the original message data is divided into a plurality of partial original message data,

    From the neighboring partial original message data, the number of bits of data deleted in the previous message block is filled with subsequent data of the previous message block to produce a subsequent message block of n bits of fixed length,

    If not all the bits of the data deleted from the previous message block are filled from neighboring partial original message data, the non-filled data is filled with bit '1' to generate a subsequent message block of n bits of fixed length. An encoding apparatus using a complementary low density inverse code, characterized in that the.
28. 26. The encoding apparatus according to claim 22 or 25, wherein a length of the original message data and a length of the message block are equal to each other.
29. The method of claim 22, wherein the codeword generation unit

    If the message blocks are all composed of only '0', the encoding device using a complementary low density inverse code, characterized in that to generate one bit consisting of '0' or '1' as the codeword .
30. The method of claim 22, wherein the first matrix generator

    In the case where the first bit of the '1' in the message block is the kth bit, the message block is arranged in a t-th row or a t-th row satisfying 1≤t≤k. Encoder using a sparse inverse code.
31. The method of claim 22, wherein the first matrix generator

    If the first bit of the '1' in the message block is the k th bit, the message block is arranged in the t th row or the t th column satisfying 1≤t≤k,

    '1' present in the remaining rows or columns except for the t th row or the t th column is in the order of the rows or the columns except for the column or the row in which the first '1' appears in the t th row or the t th column A coding apparatus using a complementary low density inverse code, characterized in that the first matrix is generated such that one '1' exists in each row and each column.
32. The method of claim 31, wherein the second matrix generator

    If the message block in which the first bit of the '1' is the k-th is arranged in the t th row of the first matrix,

    The t-th column of the k-th row is arranged as '1', the k-th column is arranged as '0', and the remaining columns of the k-th row are configured in the same manner as the message block, and the k-th row in the first row Up to (k-1) × 1 zero matrix, (k-1) × (k-1) unit matrix and (k-1) × (nk) size matrix in order, and ( From k-1) to n-th row, a second matrix is generated by arranging (nk) × k-sized matrix and (nk) × (nk) -sized matrix in order.

    When the message block in which the first bit of the '1' is the k-th is arranged in the t th column of the first matrix,

    The t th row of the k th column is arranged as '1', the k th row is arranged as '0', and the remaining rows of the k th column are configured in the same manner as the message block, and the first to kth columns are ( k-1) × 1 sized matrix, (k-1) × (k-1) sized matrix and (k-1) × (nk) sized matrix 1) Complementary low-density inverse code, characterized by generating a second matrix by arranging (nk) × k zero matrixes and (nk) × (nk) unit matrixes in order from column to n-th column. Coding apparatus using sparse inverse code.
33. The method of claim 22,

    If the message block is composed of n bits, the length of the codeword is n ² or 1, characterized in that the encoding device using a complementary low density inverse code (sparse inverse code).
34. The method of claim 22, wherein the codeword generation unit

    When the message block is arranged in the k-th row, a codeword having a length of n ² is generated by concatenating first to nth rows of the generated second matrix in order.

    When the message block is arranged in the k-th column, a complementary low-density inverse is generated by generating a codeword of length n ² by connecting the first to nth columns of the generated second matrix in order. Encoder using a sparse inverse code.
35. An apparatus for decoding a message generated and transmitted as a codeword through the encoding apparatus of any one of claims 22 to 34,

    A transmission message receiver for receiving a transmission message;

    A transmission message length measuring unit measuring a length of the received transmission message;

    A transmission message length comparison unit comparing the measured transmission message lengths;

    As a result of the comparison, when the measured transmission message length is n ² , the transmission message is divided into n blocks, and each block of the n blocks is arranged in rows or columns in order to form a third matrix having an size of n × n. A third matrix generator for generating;

    In the case where the third matrix is generated by arranging each block of the n blocks in order, a row having the highest density among the n rows of the generated third matrix is selected. A selection unit for selecting a column having the highest density among the n columns of the generated third matrix when the third matrix is generated by arranging each block of the n blocks in order; ;

    A partial decoded message data generation unit configured to generate partial decoded message data based on the selected row or column; And

    A decoding apparatus using a complementary low density inverse code including a decoder to decode the generated partial decoded message data.
36. 36. The method of claim 35 wherein

    As a result of the comparison, when the measured length of the transmitted message is '1', the partial decoded message data generation unit generates partial decoded message data consisting of n '0' lengths of message blocks. A decoding apparatus using a low density sparse inverse code.
37. The method of claim 35, wherein the selection unit

    And a row or column having a relatively large number of '1's among the n rows or columns, the decoding device using a complementary low density inverse code.
38. The method of claim 37, wherein the selection unit

    Complementary, characterized in that the first row or column is selected based on the first row or the first column when there is more than one row or column that contains the most '1' among the n rows or columns A decoding apparatus using a low density sparse inverse code.
39. The method of claim 37,

    In the case of generating the third matrix by generating the third matrix by arranging each block of the n blocks in a row

    If each of the n rows includes only one '1', the row including '1' in the kth column is selected.

    In the case of generating the third matrix by generating the third matrix by arranging each block of the n blocks in a column during the generating of the third matrix.

    And if each of the n columns includes only one '1', selecting a column including '1' in the k-th row, wherein the decoding device uses a complementary low density inverse code.
40. 36. The method of claim 35, wherein the partial decrypted message data generation unit

    When the selected row or column is the d-th row or column, first, data consisting of consecutive (d-1) '0's and one' 1 'in sequence are generated as partial decoded message data. A decoding device using complementary low density inverse code.
41. The method of claim 35, wherein the decoding unit

    And decoding the generated partial decoded message data in a manner of successively combining the generated partial decoded message data in sequence with previously generated decoded message data.
42. The method of claim 35, wherein the decoding unit

    And if the length of the decoded message is greater than or equal to the length of the original message data, decoding the message as much as the length of the original message data.

Images