WO2014021559A1 - Method and apparatus for encoding/decoding using sparse inverse code - Google Patents

Abstract

The present invention relates to a method and an apparatus for encoding/decoding using a sparse inverse code. The method for encoding comprises the steps of: forming a first matrix having a size of n x n, comprising a k^th column in which each bit from inputted data from the outside that comprises n number of bits is aligned in an n number of rows, each column excluding the first column in which '1' exists from the k^th column, and remaining columns configured so that only one '1' exists in each of the columns; and a step of forming a second matrix by finding a reverse matrix of the first matrix, and applying to the reverse matrix a modulus operation in which 2 is the modulus; and generating and transmitting a codeword by using the second matrix. In addition, the method for decoding comprises the steps of: receiving a transmitted message; comparing with a remaining length, which is calculated by subtracting the length of a pre-decoded message from the length of the transmitted message and the length of original message data; differentiating the transmitted message as an n block and forming a third matrix having a size of n x n, when the length of the transmitted message and the remaining length that are measured are different as a result of the comparison, and generating the transmitted message into partially decoded message data comprising all 0s, when the length of the transmitted message and the remaining length that are measured are identical as a result of the comparison; selecting the relatively densest column from an n number of columns in the third matrix which is generated; generating the partially decoded message data on the basis of the row that is selected; and decoding by using the partially decoded message data that is generated.

Description

Method and apparatus for encoding / decoding using low density inverse code

The present invention relates to a method and apparatus for encoding / decoding using a low density inverse code, wherein a matrix is generated using a message block using original message data, and an inverse matrix of the generated matrix and data density are used. A method and apparatus for encoding / decoding using a low density inverse code that can easily encode and decode a message using

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.

As a coding method exhibiting performance near the Shannon limit, for example, a method called so-called turbo coding such as parallel concatenated convolutional codes or serial concatenated convolutional codes. Is being developed.

In recent years, research has been actively conducted on low density parity check (LDPC (low-density parity-check code)) codes as one of error correction codes effective for reducing BER of transmission information in addition to these turbo coding.

The LDPC code is a coding method proposed in 1963 by R.G.Gallager and has been found to have a very good decoding performance. In particular, recent studies have shown that LDPC codes have a performance close to Shannon's limit as the code length increases in codes having low code rates.

However, according to the LDPC coding method having a very good decoding performance, there is a problem that it is not efficient in the encoding step and the calculation is complicated as compared with the decoding performance.

Accordingly, a need for a coding method capable of reducing a calculation process from an encoding stage and an improved decoding performance of data has emerged in the decoding stage.

The present invention is to solve such a problem, the present invention is to cut the original message data into a plurality of blocks by a predetermined rule, to generate a message block using the cut block, a low-density matrix using the message block Low-density inverse code that can reduce the computation used for encoding by generating a matrix and obtaining an inverse matrix of the generated matrix, and then encoding using a low-density inverse matrix by applying an operation of modulus 2 An object of the present invention is to provide a coding method using sparse inverse code.

In addition, the present invention generates a data encoded by the encoding method as a matrix, and by decoding the data based on the density of each column in the generated matrix, a complex calculation process is omitted to improve the decoding performance An object of the present invention is to provide a decoding method using a sparse inverse code that can be improved.

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

According to an encoding method using a sparse inverse code according to an embodiment of the present invention, a k-column in which n bits of input data received from the outside is arranged in n rows, Generating a first matrix having an nxn size consisting of each row except for the first '1' in k-th column and the remaining columns configured to have only one '1' in each column; 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.

On the other hand, the first matrix generated in the step of generating the first matrix is '1' present in the remaining rows except for the kth column, except that the first '1' appears in the kth column. Each row and column may have one '1' in the order of or columns.

In embodiments of the present invention, prior to generating the first matrix, receiving original message data from an external source; Chopping the received original message data on the basis of '1' to generate a plurality of truncated blocks; Generating a message block composed of at least one truncated block of the truncated blocks; The method may further include outputting message blocks including at least one '1' among the generated message blocks as input data.

In embodiments of the present invention, the step of chopping the received original message data into a plurality of blocks may be performed when a bit of '1' appears based on the first bit of the received original message data. Each time, a method of cutting between the bit in which the '1' exists and the next bit may be used.

In an embodiment of the present disclosure, the generating of the message block may include generating the message block by removing a truncated block one by one from the first message block including the truncated blocks as a whole. Second message blocks to n-th message blocks. At this time, the n-th message block may be one of all blocks consisting of '0', blocks consisting of only one '1' and blocks consisting of at least one '0' and one '1'.

Subsequently, the outputting of the message block as input data may output the first to n-th message blocks as input data in order.

In embodiments of the present invention, when the original message data consists only of '0', the original message data may be generated as the codeword.

In an embodiment of the present disclosure, generating the message block composed of at least one truncated block among the truncated blocks may generate a zero block consisting of only zeros among the truncated blocks as the codeword. can do. At this time, the step of generating a codeword based on the zero block is performed after the step of generating a codeword based on the message blocks.

In embodiments of the present invention, when the generated message blocks are a, a codeword is generated, and a message block including b at least one '1' is generated among the generated message blocks. In this case, b the input data, the first matrix, the second matrix and the codeword are generated.

In embodiments of the present invention, in order to generate a codeword using the second matrix, n ² lengths are formed by concatenating the first to nth columns of the generated second matrix in order. Generate a codeword of. At this time, when the input data is composed of n bits, the codeword generated using the second matrix has a length of n ² .

According to a decoding method using a sparse inverse code in accordance with embodiments of the present invention, a method comprising: receiving a transmission message; Comparing the length of the received transmission message with the length of the original message data minus the length of the decoded message; Generating a third matrix of size n × n by dividing the transmission message into n blocks if the length of the measured transmission message and the remaining length are different from each other as a result of the comparison; Selecting a relatively densest column among the n columns of the generated third matrix; Generating partial decoded message data based on the selected column; And decoding using the generated partial decrypted message data.

In embodiments of the present disclosure, the step of measuring the length of the received transmission message may be performed before comparing the length of the received transmission message with the remaining length.

In embodiments of the present invention, if the length of the measured transmission message and the remaining length are the same as the result of the comparison, all of the transmission message is generated as partial decoded message data composed of '0'.

In the embodiments of the present invention, in selecting the relatively densest column among the n columns of the generated third matrix, the number of '1' is relatively the highest among the n columns. Select a column In this case, when there are two or more columns including '1' relatively most among the n columns, the first column is selected based on the first column. In addition, when each of the n columns includes only one '1', a column including '1' in the kth row is selected.

In embodiments of the present invention, in the step of generating partial decoded message data based on the selected column, when the selected column is a d-th column, (d-1) '0' and one '1' The data constructed in the order is generated as partial decrypted message data.

In the embodiments of the present invention, in the decoding using the generated partial decoded message data, the generated partial decoded message data is decoded by successively combining the generated partial decoded message data in order. .

An encoding apparatus using a low density inverse code according to an embodiment of the present invention includes a k-column in which n bits are arranged in n rows of input data consisting of n bits received from the outside, and A first matrix generator configured to generate a first matrix having an nxn size consisting of each row except for the first row having '1' in k-th column and the remaining columns configured to have only one '1' in each column; 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 codeword transmitter for transmitting the generated codeword to the outside.

In an embodiment of the present invention, the original message data receiving unit for receiving the original message data from the outside; A truncation unit chopping the received original message data based on '1' to generate a plurality of truncated blocks; A block unit generating a message block composed of at least one truncated block among the truncated blocks; And an input data output unit configured to output message blocks including at least one '1' among the generated message blocks as input data.

Decoding apparatus using a 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 comparison unit for comparing the length of the received transmission message with the length of the original message data minus the length of the decoded message; A third matrix generator configured to generate a third matrix having a size of n × n by dividing the transmission message into n blocks when the measured length of the transmission message and the remaining length are different from each other; A selection unit for selecting a column having the highest density among the n columns of the generated third matrix; A partial decrypted message data generation unit generating partial decrypted message data based on the selected column; And a decoder which decodes the generated partial decoded message data.

In embodiments of the present invention, the transmission message length measuring unit for measuring the length of the received transmission message, and providing the length of the measured transmission message to the transmission message length comparison unit may be further included.

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

First, the original message data is cut into a plurality of blocks, and the input data after the initial input data consists of some blocks of the truncated blocks, thereby reducing the computational burden.

Second, by arranging the input data in a specific row and by placing an identity matrix and a zero matrix to generate an n x n matrix including the input data, further calculation process is reduced.

Third, by utilizing the rules of the inverse of the low density non-specific matrix composed of the input data, the unit matrix, and the zero matrix, the computational burden on the inverse matrix is reduced.

Fourth, the calculation process is reduced by receiving and decoding a codeword generated according to the law of the matrix in the encoding step.

Fifth, the decoding process may be efficiently performed by selecting a row related to data by using a row having data having the highest density.

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

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

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

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

A method and apparatus for encoding / decoding using a low density inverse code according to embodiments of the present invention will be described in detail with reference to the accompanying drawings. 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 low density inverse code according to embodiments of the present invention.

Referring to FIG. 1, the encoding apparatus 100 using the low density inverse code according to the embodiments of the present invention may include an original message data receiver 110, a truncation unit 120, a block unit 130, and an input data output unit 140. ), A first matrix generator 150, a second matrix generator 160, a codeword generator 170, and a transmitter 180.

The original message data receiving unit 110 receives original message data from the outside.

The cutting unit 120 chops the received original message data based on '1' to generate a plurality of cut blocks. For example, the truncation unit 120 may determine that the received original message data has a bit between the first bit and the next bit whenever a bit with a '1' appears based on the first bit (from the first bit). Can be cut. For example, when the original message data is '0001010101', the cutting unit 120 cuts the original message data into '0001', '01', '01', and '01'.

The block unit 130 generates a message block composed of at least one cut block among the blocks cut by the cut unit 120. In some embodiments of the present invention, the block unit 130 may include a first message block including all of the truncated blocks, and a second message block generated by removing the truncated blocks one by one from the first message block. A message block can be generated with n-th message blocks. For example, when the cutting unit 120 cuts the original message data of '0001010101' into '0001', '01', '01', and '01', the block unit 130 is formed of the entire cut block. '010101', '0101', and '01' may be generated from the first message block '0001010101' and the second to fourth message blocks. That is, the block unit 130 may generate a message block that is the same as the original message data cut by the cutting unit 120 or smaller in length (size) than the original message data. The block unit 130 continuously transfers the generated message blocks to the input data output unit 140.

In the embodiments of the present invention, the n-th message block generated by the block unit 130 is a block consisting entirely of '0', a block consisting of only one '1', and at least one '0' and one '1'. It can be one of the blocks consisting of '.

On the other hand, when the original message data consists only of '0', the original message data is directly generated as the codeword. For example, when the original message data is composed only of '0', the original message data may be generated as a message block through the cutting unit 120 and the block unit 130 as it is. In this case, the block unit 130 does not output the message block to the codeword generator 170 without outputting the input data output unit 140, the first matrix generator 150, and the second matrix generator 160. The codeword generator 170 may directly generate the original message data as a codeword. That is, when the original message data consists only of '0', it may be directly transmitted to the codeword generation unit 170 only through the cutting unit 120 and the block unit 130.

On the contrary, when the original message data consists only of '0', the device may be configured to directly transfer the original message data to the codeword generator 170 without passing through the cutting unit 120 and the block unit 130. will be.

Similarly, even when there is a zero block composed of only '0' among the blocks cut by the cutting unit 120, the zero block is transferred to the codeword generating unit 170 directly through the block unit 130 to be a codeword. Is generated. For example, when the original message data is '0001010100', the cutting unit 120 may be cut in order to generate a block in which '0001', '01', '01', and '00' are cut. In this case, since the last block is a zero block composed of '00', the last block is not transmitted to the input data output unit 140, the first matrix generator 150, and the second matrix generator 160, and the codeword generator ( 170 may be directly transmitted to generate a codeword.

The input data output unit 140 outputs the message blocks received from the block unit 130 as input data in order. In embodiments of the present invention, the input data output unit 140 outputs message blocks including at least one '1' among the generated message blocks as input data. Meanwhile, since the input data output unit 140 transmits a message block including at least one '1' among the message blocks generated by the block unit 130 to the first matrix generator 150, The block 130 may be configured to additionally perform the same function as that of the input data output unit 140. In this case, the block unit 130 and the input data output unit 140 are integrally formed.

The input data output unit 140 outputs the first message block, which is the original message data, as the first input data, and follows data composed of blocks other than one block among the divided blocks in the original message data. Output as input data. In the embodiments of the present invention, the input data output unit 140 converts the data consisting of the remaining blocks except the block containing the first '1' from the first bit of the previously output input data into subsequent input data. Repeat the output steps.

In addition, the input data output unit 140 may repeat outputting the input message from the original message data to the nth message block received from the block unit 130. For example, when the original message data is '0001010101', the input data output unit 140 outputs the original message data '0001010101' as first input data, which is the first input data, and the first block, '0001'. '010101', the remaining data except for the block, is output as second input data, which is subsequent input data. Subsequently, the input data output unit 140 outputs '0101', except for '01', the first block in the second input data, as the third input data, and '01', which is the first block in the third input data. Outputs '01' except for the fourth input data.

The cutting unit 120, the block unit 130, and the input data output unit 140 cut the original message data into blocks, and determine a block of the input data to be output. All methods that can reduce the computational burden through a so-called sub-routine method that cuts and blocks message data and outputs input data except for a specific block from previously output input data are within the scope of the present invention. It will be included.

The first matrix generator 150 has a kth column in which the n-bit input data received from the input data output unit 140 is arranged in n rows, and '1' is first present in the kth column. A first matrix of size nxn is formed of each row except for a row, and remaining columns configured to have only one '1' in each column.

Here, in the first matrix, '1' existing in the remaining columns except for the kth column is in each row and each column in the order of the rows or the columns except for the first '1' in the kth column. '1' is configured to exist one by one.

In embodiments of the present invention, the k-th column including the input data may be a first column, and the remaining columns may be second to nth columns.

In addition, when the first matrix generation unit 150 has k rows in which '1' exists first in the column in which the input data exists, '1' in the columns in which the input data does not exist is in the order of the rows. Accordingly, a first matrix is generated to exist in the first through (k-1) th rows and the (k + 1) through nth rows, respectively.

Here, it will be described on the premise that the input data is arranged in the first column of the first matrix.

For example, when the first matrix generator 150 receives the original message data '0001010101' as the first input data, the first matrix generator 150 arranges the first input data in the first column of the matrix and the remaining columns are represented by Equation 1 below. Generate a first matrix constructed as follows.

[Equation 1]

Subsequently, when the first matrix generator 150 receives '010101' as the second input data, the first matrix generator 150 arranges the second input data in the first column of the matrix and generates a matrix including the remaining columns as shown in Equation 2 below. do.

[Equation 2]

In addition, when the first matrix generator 150 receives '0101' as the third input data, the first matrix generator 150 arranges the third input data in the first column of the matrix and generates a matrix having the remaining columns as shown in Equation 3 below. do.

[Equation 3]

Finally, when the first matrix generator 150 receives '01' as the fourth input data, the first matrix generator 150 arranges the fourth input data in the first column of the matrix and generates a matrix having the remaining columns as shown in Equation 4 below. do.

[Equation 4]

As described above, the first matrix generator 150 configures the first matrix according to a predetermined rule based on the input data, and the number (type) of the matrix generated by the first matrix generator 150 is the original message data. It is determined by the number of blocks separated. That is, when the original message data contains a message block containing at least one '1', the number of first matrices is also a.

After obtaining the inverse of the first matrix generated by the first matrix generator 150, the second matrix generator 160 generates a second matrix by applying a modulus operation of 2 to the law. In this case, when the first matrix generator 150 generates a first matrix, the second matrix generator 160 also generates a second matrix.

For example, when the first matrix generator 150 generates the first matrices of Equations 1 to 4, the second matrix generator 160 is the first matrix of Equations 1 to 4. Generate second matrices corresponding to Equations 5 to 8;

[Equation 5]

[Equation 6]

[Equation 7]

[Equation 8]

The codeword generator 160 generates a codeword of length n ² by using a second matrix of nxn size generated by the second matrix generator 160. In embodiments of the present invention, code word generator 170 generates a code word of n ^2, the length of the first column to the n-th column of the second matrix, the generated in such a manner as to arrange them in a single line in order can do. For example, the codeword generator 170 may generate a codeword of '0100000000001000000000010000001000010101000010000000000100000000001000000000010000000000100000000001' for the second matrix of Equation 5, and generate a codeword of '010000100101001000000100000010000001' for the second matrix of Equation 6. can do.

When the codeword generator 170 generates a second matrix in the second matrix generator 160, the codeword generator 170 also generates a codeword.

The transmitter 180 transmits the codeword generated by the codeword generator 160 to the outside.

As described above, the encoding apparatus 100 using the low density inverse code cuts original message data and blocks the message message into blocks, outputs only some of the blocks as input data from the original message data, and outputs the input data. By using the original message data using the feature of generating a matrix consisting of a column consisting of a low density columns containing only one '1', the first matrix to the inverse matrix calculation method and the second inverse matrix through the arithmetic operation The computational burden can be reduced as compared to the encoding method.

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

Referring to FIG. 2, the decoding apparatus 200 using the 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, a transmission message length comparison unit 230, A third matrix generator 240, a selector 250, a partial decoded message data generator 260, and a decoder 270 are included.

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. At this time, the decoding apparatus 200 includes information on a row into which input data is inserted, information on a length of original message data, and a length of a decoded message (total length of a total decoded message up to a specific point in time). Information about at least one of the information about the information and the transmission message length may be received 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 receiver 210 may receive a transmission message of length n ² .

The transmission message length measurement unit 220 measures the length of the transmission message transmitted from the transmission message receiver 210 and provides the transmission message length comparison unit 230 with the measured length of the transmission message.

On the other hand, if the decoding apparatus 200 knows the information on the length of the transmission message without measuring the transmission message length, the received message to the transmission message length comparison unit 230 without passing through the transmission message length measurement unit 220 The transmission message may be delivered.

The transmission message length comparison unit 230 compares the length of the received transmission message with the remaining length obtained by subtracting the length of the decoded message from the length of the original message data. That is, the transmission message length comparison unit 230 compares the length of the message which has not yet been decoded with respect to the specific time point and the length of the transmission message received at the time point.

As a result of the comparison by the transmission message length comparison unit 230, when the measured length of the transmission message and the remaining length are the same, the transmission message length comparison unit 230 converts the received transmission message into the partial decoded message data generation unit 260. ), And the partial decryption message data generation unit 260 immediately generates the transmission message as partial decryption message data composed of all zeros.

Meanwhile, as a result of the comparison by the transmission message length comparison unit 230, when the measured length of the transmission message is different from the remaining length, the third matrix generator 240 uses the received transmission message to generate a third message. Create a matrix. In detail, the third matrix generator 240 divides the transmission message into n blocks to generate a third matrix of nxn size. For example, when the transmission message has n ² length, the third matrix generator 240 generates a third matrix of nxn size. For example, when the third matrix generator 240 receives a transmission message of '0100000000001000000000010000001000010101000010000000000100000000001000000000010000000000100000000001', the third matrix generator 240 generates a matrix, such as Equation 5, as a third matrix. Here, the third matrix may be a matrix having the same size as the second matrix. On the other hand, if it is not affected by the channel noise, it is generated as the same third matrix as the second matrix, but when the channel noise is affected, the corrupted transmission message is received. have. Nevertheless, the third matrix will have the same magnitude as the second matrix regardless of the channel noise.

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

In addition, the selector 250 selects the fastest column when there are two or more columns including '1' relatively most among the n columns. That is, the selector 250 selects the first column based on the first column. For example, when the density of the second row and the fifth row is the same, the selector 250 may select the second row.

In addition, when the n columns of the third matrix each include only one '1', the selector 250 selects a column including '1' in the kth row. That is, in the decoding apparatus 200 that receives the information of inserting the input data into the k-th column by the encoding apparatus 100, the selector 250 selects each of the n columns of the third matrix, each of which has only one '1'. If so, select the column containing '1' in the kth row. For example, when the third matrix is the matrix of Equation 8 (when the input device inserts the input data into the first column), the selector 250 includes the first row among the first column and the second column. Is to select the second column in which '1' is located.

The partial decoded message data generator 260 generates partial decoded message data based on the column selected by the selector 250. In the embodiments of the present invention, when the column selected by the selector 250 is the d-th column, the partial decoded message data generation unit 260 has (d-1) '0's and one' 1 'in order. The data constructed as described above is generated as partial decrypted message data.

As mentioned above, when the length of the transmission message is the same as the remaining length, the partial decryption message data generator 260 generates the transmission message as partial decryption message data composed of all zeros.

The decoder 270 decodes the partial decoded message data generated by the partial decoded message data generator 260. For example, the decoder 270 may decode the generated partial decoded message data by successively combining the generated partial decoded message data in order.

For example, when the first generated third matrix is the matrix of Equation 5, and the selector 250 selects the fourth column including the most '1', the partial decoded message data generator 260 may Obtain '0001' having the fourth bit '1' as the first partial decoded message data. Subsequently, when the generated third matrix is the matrix of Equation 6 and the selector 250 selects the second column including the most '1', the partial decoding message data generation unit 260 has a second bit. '01', which is '1', is obtained as second partial decoded message data. Subsequently, when the third matrix generated is the matrix of Equation 7 and the matrix of Equation 8, and the selector 250 selects the second column including the most '1', the partial decoding message data generation unit In step 260, '01' whose second bit is '1' is obtained as third partial decoded message data and fourth partial decoded message data, respectively.

Accordingly, when the decoder 270 continuously combines the first to fourth partial decrypted message data, the decoder 270 may decode '0001010101' data.

As described above, the decoding apparatus 200 using the low density inverse code selects the most complex and highest density column in the matrix, and restores the original message data or the partial decoded message data constituting the original message data using the order of the selected columns. can do. Therefore, unlike the conventional decoding apparatus, not only can the performance of decoding the message by simple calculations and rules, but also the noise containing the highest density of the row containing the message data Since there is no significant effect, errors can be reduced.

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

Referring to FIG. 3, according to an encoding method using a low density inverse code according to embodiments of the present invention, original message data is received (S110), the original message data is cut into a plurality of blocks (S120), A message block composed of at least one truncated block among the truncated blocks is generated (S130), and the generated message block is output as input data (S140). Generate a first matrix based on the input data (S150), generate a second matrix using the first matrix (S160), generate a codeword based on the second matrix (S170), This is transmitted to the outside (S180).

Specifically, the received original message data is chopped based on '1' to generate a plurality of truncated blocks. In embodiments of the present invention, whenever a 1 is obtained from the first bit of the original message data, the data may be chopped into a plurality of blocks. That is, whenever a bit with '1' appears in the received original message data based on the first bit, the received original message data is truncated between the bit where the '1' exists and the next bit. For example, when the original message data is '0001010101', the original message data is cut into '0001', '01', '01', and '01'.

Then, a message block composed of at least one truncated block among the truncated blocks is generated. A message block may be generated from a first message block including all of the truncated blocks, and second to n th message blocks generated by removing the truncated blocks one by one from the first message block. Here, the n-th message block may be one of blocks consisting of all '0's, blocks consisting of only one' 1 'and blocks consisting of at least one' 0 'and one' 1 '.

For example, when the original message data of '0001010101' is cut into '0001', '01', '01', and '01', the first message block, '0001010101' and the second, consisting of the truncated block as a whole '010101', '0101', and '01' may be generated as the message block to the fourth message block, respectively.

In other embodiments of the present invention, when the original message data is composed of only '0', the original message data is directly generated as a codeword through the steps of cutting and blocking the original message data. In this case, when the original message data consists only of '0', the codeword is generated from the original message data without outputting as input data, generating a first matrix, and generating a second matrix.

Similarly, if the original message data does not consist of all zeros, but there are zero blocks consisting of only zeros among the truncated blocks, the codewords are truncated and blocked. To create. For example, when the original message data is '0001010100', '0001', '01', '01', and '00' may be cut into blocks by sequentially cutting. In this case, the codeword generation step is performed on the zero block where the last block is '00'.

Subsequently, message blocks including at least one '1' among the generated message blocks are output as input data. Specifically, the first message block is output as first input data, and the second to nth message blocks are sequentially output as subsequent input data. In embodiments of the present invention, the step of outputting the data consisting of the remaining blocks except for the block containing the first '1' from the first bit of the previously output input data as subsequent input data. In addition, it may be repeated until the last block including '1' is output from the original message data.

For example, when the original message data is '0001010101', the original message data '0001010101' is output as the first input data, which is the first input data, and the remaining data, except for the '0001' block, which is the first block. 010101 'is output as second input data which is subsequent input data. Subsequently, '0101' except for '01', which is the first block in the second input data, is output as third input data, and '01', except for '01', which is the first block, in the third input data, is fourth. Output continuously as input data.

If the input data is not composed only of '0', the input data is received, and the k-th column is formed by arranging the n-bit input data into n rows in each of the n-bit input data. The first matrix is configured such that one '1' exists in the remaining columns except the column. In this case, the remaining columns are configured such that only one '1' exists in each row and each column except the row in which '1' exists first in the k-th column. When the input data received includes n bits, the first matrix may have a size of n × n.

That is, the first matrix has '1' present in the remaining columns except for the kth column, except that the first '1' appears in the kth column, in each row and each column in the order of the rows or the columns. '1' is configured to exist one by one. That is, the column in which '1' exists in the rows in which the input data does not exist is determined according to the order of the rows, and the first matrix in which the column in which '1' exists first is skipped in the row in which the input data exists. Can be configured.

In other words, when a column in which '1' exists for the first time in the column in which the input data exists is k columns, '1' in rows where the input data does not exist may correspond to the first column through k− according to the order of the rows. 1) The first matrix may be configured to exist in the column and the (k + 1) th to n th columns, respectively.

For example, the input data may be arranged in the first column, and the remaining columns may be configured as the second to nth columns. In this case, the second column is '1' in the first row except for the first '1' in the first column, and the nth column is the first column in the first column. The row where '1' exists in the last row except for and '1' exists in the third to (n-1) th columns may be formed in the order of the columns.

For example, when the input data is '0001010101', when the input data is arranged in the first column and the remaining columns are arranged in accordance with the embodiments of the present invention, a matrix such as Equation 1 may be generated as the first matrix. Can be.

If the input data is '010101', when the input data is arranged in the first column and the remaining columns are arranged according to the embodiments of the present invention, a matrix such as Equation 2 may be generated as the first matrix. .

Similarly, when the input data is '0101', when the input data is arranged in the first column and the remaining columns are arranged in accordance with the embodiments of the present invention, a matrix such as Equation 3 may be generated as the first matrix.

Finally, when the input data is '01', when the input data is arranged in the first column and the remaining columns are arranged according to the embodiments of the present invention, a matrix such as Equation 4 may be generated as the first matrix. .

Subsequently, after obtaining an inverse of the generated first matrix, a second matrix is generated by applying a modulus operation of 2 as a law. For example, if the first matrix is the matrix of Equation 1, the second matrix will be the matrix of Equation 5.

Subsequently, a codeword is generated using the second matrix and transmitted. If the second matrix has nxn size, n ² length codewords may be generated by arranging n columns in one line in order. For example, when the second matrix is the matrix of Equation 6, the generated codeword is '010000100101001000000100000010000001'.

In embodiments of the present invention, when the original message data includes a message block including at least one '1', the number of input data, first matrix, second matrix, and codeword is also a. For example, when the original message data is '0001010101', it is divided into four blocks, '0001', '01', '01', and '01', and the first matrix, the second matrix, and the codeword are also Four kinds can be achieved.

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

Referring to FIG. 4, according to a decoding method using a low density inverse code according to embodiments of the present invention, a transmission message is received (S210), a length of the transmission message is measured (S220), and a length and an original of the transmission message are provided. The remaining length is obtained by subtracting the length of the decoded message from the length of the message data (S230). As a result of the comparison, when the length of the transmission message is different from the remaining length, a third matrix is generated based on the transmission message (S240), a column having the highest density in the third matrix (S250), and the selected column After generating the partial decoded message data according to a predetermined rule based on (S260), the generated partial decoded message data are combined and decoded (S270).

In the above steps, when the blocks are classified such that only one '1' is included in the original message data, the original message data may be finally restored by repeating the steps by the number of the divided blocks.

In detail, when the length of the original message data is n bits and a transmission message of length n ² is received, since the remaining length and the transmission message length will be different, a third matrix of size nxn can be generated. For example, when the received transmission message is '010000100101001000000100000010000001', a third matrix like Equation 6 may be generated.

If the measured length of the transmission message and the remaining length are the same, a third matrix is not directly generated using the received transmission message, and the transmission message is directly generated as partial decoded message data composed of all zeros. This may occur when the codeword generated in the encoding step consists only of '0'.

Subsequently, a relatively dense row is selected from the n columns of the generated third matrix in the generated third matrix. In detail, when the third matrix is composed of n columns, a column including relatively most '1' among the n columns is selected. For example, in the third matrix as shown in Equation 6, the second column is selected as the column containing '1' the most.

If there are several columns with the same highest density, the highest density column appears first. In particular, the first column may be selected based on the first column. For example, when the density of the second column and the fifth column is equally high, the second column may be selected.

If the n columns of the third matrix each include only one '1', the column including '1' in the kth row is selected. That is, when the encoding step receives the information of inserting the input data into the k-th column, and when the n columns of the third matrix each include only one '1', the k-th row includes '1'. Select a column For example, when the third matrix is the matrix of Equation 8 (when input data is inserted into the first column by the encoding apparatus 100), '1' is positioned in the first row among the first and second columns. To select the second column.

Subsequently, a message is generated as partially decoded message data based on the column selected in the third matrix. For example, when the selected column is a d-th column, data consisting of (d-1) '0' and one '1' in order is generated as partial decoded message data.

Subsequently, decoding is performed using the generated partial decoded message data. For example, the pre-generated partial decoded message data may be decoded by successively combining the previously generated partial decoded message data in order.

For example, assuming that the original message data is '0001010101', the first generated third matrix is the matrix of Equation 5, and the fourth column including '1' most will be selected. Accordingly, '0001' having the fourth bit '1' is obtained as the first partial decoded message data. Subsequently, when the generated third matrix is the matrix of Equation 6 and the second column including the most '1' is selected, '01' having the second bit '1' is used as the second partial decoded message data. Obtained. Subsequently, when the third matrix generated is the matrix of Equation 7 and the matrix of Equation 8, and each of the second columns is selected, '01' whose second bit is '1' is the third partial decoded message data and the first matrix. Each of the four partial decrypted message data may be obtained.

Accordingly, when the first to fourth partial decryption message data are continuously combined, '0001010101' data may be finally obtained as the final decrypted data.

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.

Claims (40)

1. A k-column in which each bit is arranged into n rows of input data composed of n bits received from the outside, and one in each row and each column except a row in which the '1' first appears in the k-th column. Generating a first matrix of size nxn of remaining columns configured to have only '1' of;

   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

   And generating and transmitting a codeword using the second matrix, wherein the encoding method uses a low density inverse code.
2. The method of claim 1, wherein generating the first matrix comprises:

   The first matrix is '1' in the remaining rows except for the kth column, except that the first '1' appears in the kth column, '1' in each row and each column in the order of the rows or columns. The coding method using a sparse inverse code, characterized in that 'is configured to exist one by one.
3. The method of claim 1, prior to generating the first matrix.

   Receiving original message data from the outside;

   Chopping the received original message data on the basis of '1' to generate a plurality of truncated blocks;

   Generating a message block composed of at least one truncated block of the truncated blocks;

   And outputting, as input data, message blocks including at least one '1' from among the generated message blocks.
4. The method of claim 3, wherein chopping the received original message data into a plurality of blocks comprises:

   A sparse inverse code, characterized in that for each bit of the received original message data, a bit between which the '1' appears and a next bit are truncated. Encoding method using.
5. 4. The method of claim 3, wherein generating the message block

   The message block may include a first message block including the truncated blocks as a whole, and second message blocks to n-th message blocks generated by removing the truncated blocks one by one from the first message block. A coding method using a sparse inverse code.
6. The method of claim 5,

   The n-th message block is one of a block composed of all '0's, one block composed of only one' 1 ', and at least one block composed of' 0 'and one' 1 '. A coding method using sparse inverse code.
7. The method of claim 5, wherein the outputting of the message block as input data comprises:

   And encoding the first message block and the n-th message block as input data in order.
8. The method of claim 3,

   And encoding the original message data as the codeword when the original message data consists only of '0'.
9. The method of claim 3, further comprising: generating a message block composed of at least one truncated block among the truncated blocks.

   A coding method using a sparse inverse code, characterized by generating a zero block consisting of only zeros among the truncated blocks as the codeword.
10. The method of claim 9,

    The generating of the codeword based on the zero block is performed after generating the codeword based on the message blocks. The encoding method using a sparse inverse code.
11. The method of claim 3,

    If the generated message blocks are a, a codeword is generated,

    If there are b message blocks including at least one '1' among the generated message blocks,

    And b codewords are generated for the input data, the first matrix, the second matrix, and the codeword.
12. The method of claim 1, wherein generating a codeword using the second matrix

    And the codeword has a length of n ² when the input data consists of n bits.
13. The method of claim 1, wherein generating a codeword using the second matrix

    And a code word having an length of n ² is generated by connecting the first to n th columns of the generated second matrix in order.
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;

    Comparing the length of the received transmission message with the length of the original message data minus the length of the decoded message;

    Generating a third matrix of size n × n by dividing the transmission message into n blocks if the length of the measured transmission message and the remaining length are different from each other as a result of the comparison;

    Selecting a relatively densest column among the n columns of the generated third matrix;

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

    A decoding method using a low density inverse code, comprising: decoding using the generated partial decoded message data.
15. 15. The method of claim 14, wherein before comparing the remaining length of the received transmission message with the remaining length:

    And a method of measuring the length of the received transmission message.
16. The method of claim 14,

    If the result of the comparison, the length of the measured transmission message and the remaining length is the same,

    And decoding all of the transmission messages into partial decoded message data composed of '0's.
17. 15. The method of claim 14, wherein selecting a relatively densest column among the n columns of the generated third matrix is

    The decoding method using a sparse inverse code, characterized in that for selecting the column containing the most relatively '1' among the n columns.
18. The method of claim 17,

     Decoding method using a sparse inverse code, characterized in that the first column is selected based on the first column when there are two or more columns containing '1' relatively most among the n columns. .
19. The method of claim 17,

    If each of the n columns includes only one '1', the decoding method using a low density inverse code (sparse inverse code), characterized in that for selecting the column containing '1' in the k-th row.
20. 15. The method of claim 14, wherein generating partial decrypted message data based on the selected column

    When the selected column is a d-th column, a sparse inverse code may be generated as partial decoded message data including (d-1) pieces of '0' and one '1' in order. Decryption method used.
21. The method of claim 14, wherein the decoding using the generated partial decrypted message data is performed.

    And decoding the generated partial decoded message data by successively combining the generated partial decoded message data in order in succession.
22. A k-column in which each bit is arranged into n rows of input data composed of n bits received from the outside, and one in each row and each column except a row in which the '1' first appears in the k-th column. A first matrix generator configured to generate a first matrix having an nxn size consisting of remaining columns configured to have only '1' of;

    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 coding device using a low density inverse code including a codeword transmitter for transmitting the generated codeword to the outside.
23. The method of claim 22,

    In the first matrix, '1' existing in the remaining columns except for the kth column is '1' in each row and each column in the order of the rows or the columns except for the first '1' in the kth column. Coding apparatus using a sparse inverse code, characterized in that 'is configured to exist one by one.
24. The method of claim 22,

    An original message data receiving unit for receiving original message data from the outside;

    A truncation unit chopping the received original message data based on '1' to generate a plurality of truncated blocks;

    A block unit generating a message block composed of at least one truncated block among the truncated blocks; And

    And an input data output unit configured to output message blocks including at least one '1' from among the generated message blocks as input data.
25. The method of claim 24, wherein the cut portion

    A sparse inverse code, characterized in that for each bit of the received original message data, a bit between which the '1' appears and a next bit are truncated. Coding apparatus using the.
26. The method of claim 24,

    The message block generated by the block unit includes a first message block including all of the truncated blocks, and second message blocks to n-th message blocks generated by removing the truncated blocks one by one from the first message block. A coding apparatus using a low density sparse inverse code, characterized in that formed.
27. The method of claim 26,

    The n-th message block is one of a block composed of all '0's, one block composed of only one' 1 ', and at least one block composed of only' 0 'and one' 1 '. Coding apparatus using sparse inverse code.
28. 27. The apparatus of claim 26, wherein the input data output unit

    And encoding the first message block and the n-th message block as input data in order.
29. The method of claim 24,

    And encoding the original message data as the codeword when the original message data consists only of '0'.
30. The method of claim 24,

    The zero block consisting of only zeros among the blocks cut by the truncation unit is generated as the codeword, wherein the encoding device using a low density inverse code (sparse inverse code).
31. The method of claim 22,

    And a codeword generated by the codeword generator has a length of n ² when the input data is composed of n bits.
32. The method of claim 22,

    The codeword generator generates a codeword having a length of n ^{2 in} a manner of connecting the first to nth columns of the generated second matrix in order, thereby encoding using a low density inverse code. Device.
33. An apparatus for decoding a message generated and transmitted as a codeword through the encoding apparatus of any one of claims 22 to 32,

    A transmission message receiver for receiving a transmission message;

    A transmission message length comparison unit for comparing the length of the received transmission message with the length of the original message data minus the length of the decoded message;

    A third matrix generator configured to generate a third matrix having a size of n × n by dividing the transmission message into n blocks when the measured length of the transmission message and the remaining length are different from each other;

    A selection unit for selecting a relatively densest column among the n rows of the generated third matrix;

    A partial decrypted message data generation unit generating partial decrypted message data based on the selected column; And

    A decoding device using a low density inverse code including a decoding unit for decoding using the generated partial decoded message data.
34. The method of claim 33, wherein

    Measuring the length of the received transmission message, and using the low density inverse code (sparse inverse code) characterized in that it further comprises a transmission message length measuring unit for providing the measured length of the transmission message to the transmission message length comparison unit Decryption device.
35. The method of claim 33, wherein

    When a result of the comparison in the transmission message length comparison unit is equal to the measured length of the transmission message and the remaining length,

    And the partial decryption message data generation unit generates the partial decryption message data including all of the transmission messages as '0'.
36. The method of claim 33, wherein the selection unit

    Decoding apparatus using a sparse inverse code, characterized in that for selecting the column containing the most relatively '1' among the n columns.
37. The method of claim 36,

     If there is more than one column that contains '1' the most among the n columns,

    And the selector selects the first column based on the first column.
38. The method of claim 36,

    When each of the n columns includes only one '1',

    And the selector selects a column including '1' in the k-th row.
39. 34. The method of claim 33, wherein the partial decoded message data generation unit

    When the row selected by the selector is the d-th column, a low density inverse code (sparse inverse) characterized by generating (d-1) data consisting of '0' and one '1' in order as partial decoded message data. decoding apparatus using code).
40. The method of claim 33, wherein the decoding unit

    And decoding the generated partial decoded message data by successively combining the generated partial decoded message data in sequence in order.

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