JP2010041677A - Decoder, decoding method, and decoding program - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To provide a decoder capable of reducing computational complexity, while maintaining high correction capability. <P>SOLUTION: The decoder 10 has: a first decoding section 11 for enabling input of a received word and disappearance position information indicating a position of an erroneous symbol in the received word and for generating a first received word, where the symbol is corrected based on a decoding graph, and first disappearance position information reflecting the corrected symbol; a matrix processing section 12 for extracting a disappearance vector Z and a coefficient matrix H', and for generating a conversion matrix T for converting the coefficient matrix H' to an upper triangular matrix H" and a first syndrome from the first received word; a matrix decoding section 13 for generating a second received word, the erroneous symbol is corrected, and second disappearance position information reflecting the corrected symbol, and for performing correction to a second syndrome reflecting the corrected symbol; and a second decoding section 14 for generating a third received word corrected based on the decoding graph and third disappearance position information reflecting the corrected symbol. <P>COPYRIGHT: (C)2010,JPO&INPIT

Description

  The present invention relates to a decoding method and a decoding apparatus for linear codes such as LDPC (Low Density Parity Check) codes.

  In recent years, LDPC codes have been considered promising as codes with excellent correction capability. One of LDPC code decoding algorithms is the Sum-Product method (for example, Non-Patent Documents 1 to 3).

  When video or audio streaming transmission is performed on an IP network, a lost packet may be sent by UDP (User Datagram Protocol) in order to maintain real-time performance. In such a case, if there is a section for wireless transmission on the transmission path, it is necessary to take measures against lost packets. As a countermeasure against this, it is conceivable to interleave the packets and perform error correction coding. As an error correction code to be used, an LDPC code that easily increases the interleave length is also a promising candidate.

  For example, as shown in FIG. 7, p × k bits of data are made into blocks of p bits, k bits of data obtained from each block are encoded, and (n−k) bits of parity are added. As a result, a total of p × (n−k) bits of parity is added, and these parities form an (n−k) block. At the time of transmission, header data (such as a UDP header / IP header) is added to each block as data of one packet to form an IP packet. Interleaving may be performed by collecting a plurality of bits instead of one bit from one block and encoding them into one codeword, or collecting and encoding one bit from a plurality of blocks.

  Even if n packets are not prepared after transmission, if the lost packet data is lost and error correction processing is performed on all of the p code words to restore one bit at a time, the original block Can be restored. IP packets have a maximum packet length of 1,500 bytes in Ethernet (registered trademark), the IP header length is 20 bytes as standard, and the UDP header length is 8 bytes, so the data is a maximum of 1,472 bytes. = 11,776 bits can be used. When streaming transmission is performed, it is required to increase the amount of data included in one packet as much as possible and to reduce the transmission rate increased by the header as much as possible and efficiently transmit the data. It is considered to be about 10,000 bits. When one IP packet is converted into one symbol of the code, the addition of the symbols performs an exclusive OR of about 10,000 bits.

Hereinafter, decoding of the LDPC code will be described. The LDPC code is a kind of linear code, but the linear code is a generator matrix G of k rows and n columns and a check matrix of (n−k) rows and n columns where G · H ^T = 0. With H, the structure of the code can be defined. And H · G ^T = 0 may be described.

Data (vector) D = (d ₀ , d ₁ ,..., D _(k−1) ) is multiplied by a generator matrix G, and codeword (vector) C = (c ₀ , c ₁ ,..., C _{(n -1)} Encoding is performed by obtaining) = D · G. H · C ^T = H · G ^T · D ^T = 0 holds. A received word (vector) R = (r ₀ , r ₁ ,..., R _(n−1) ) in which an error (including erasure) has occurred is transmitted, and the error (vector) is expressed as E = (e ₀ , e ₁ ,..., E _(n-1) ), R = C + E.

Solution 1)
Syndrome _{S = (s 0, s 1} , ..., s (nk-1)) is the ^{S T = H · R T =} H · (C + E) T = H · C T + H · E T = H · E T can get. When x erasures (x <(n−k)) occur, out of n symbols of error (vector) E, (n−x) symbols other than the erasure position are 0. The above equation S = H · R ^T = H · E ^T is a first-order x-ary simultaneous equation with the values of the remaining x lost symbols as variables. Since the number of equations is (n−k), it is possible to correct an error by solving this and obtaining the size of each symbol.

Solution 2)
The LDPC code has very many elements of 0 in the parity check matrix H among linear codes. That is, the code has a feature that non-zero elements have a low density. In the BCH code, almost half of the elements of the parity check matrix H are “1”, and in the Reed-Solomon code, all the elements of the parity check matrix H are non-zero, whereas in the LDPC code, only a few percent of the elements of the parity check matrix H are present. It is non-zero. Some codes have less than 1% non-zero elements.

In selecting E such that 0 = H · C ^T = H · (R−E) ^T , since there are very few non-zero elements in each row of the check matrix H, the derived first-order x-ary simultaneous equations Each formula of
(0) Expression with no disappearance at a position corresponding to a non-zero element: meaningless as a simultaneous equation (1) Expression with only one disappearance at a position corresponding to a non-zero element: That expression Only the loss value can be calculated. (2) The values are classified into three types having two or more disappearances at positions corresponding to non-zero elements.

  If correction is performed using the group formula of (1), the formula becomes the group formula of (0), and some of the formulas of the group of (2) including the corrected erasure are part of the group of (1). It becomes the following formula. This is repeated and corrected until the number of expressions in the group of (1) becomes zero.

  A specific example is shown in FIG. 8A. A code having a code length of 12 and a number of data symbols of 6 and based on the binary check matrix shown in FIG. 8A is taken as an example.

FIG. 8B is a graph showing the relationship between each symbol of the received word and each symbol of the syndrome based on this parity check matrix. This graph is called a decoding graph. That is, the decoding graph is a graph showing the relationship between each symbol of the received word and each symbol of the syndrome. Symbol s ₀ of the leftmost syndrome, r ₀ of the symbols of the received word, r _1, is connected to the _{r 2, r 3, r 0} , r 1, r 2, r 3 is the value of the code word as if _{received, s 0 = r 0 + r} 1 + r 2 + r 3 = 0 (+ is the exclusive oR (exclusive-or) is used as a) shows that to be a.

FIG. 8C is an example in which r ₀ and r ₅ of the received word are lost. syndromes including r ₀ is s _0, s _3, the syndrome containing the r ₅ is s _1, s _5. In addition, among the symbols of the received words connected to the syndromes s ₀ , s ₁ , s ₃ , and s ₅ , only one symbol is lost. Therefore, from s ₀ or s ₃ to r _0, the r ₅ from s ₁ or s _5, it is possible to correct and restore. In the above description, there are four group expressions in (1) and two group expressions in (0). If corrected based on the group expression in (1), All are (0) group formulas.

FIG. 8D is an example in which r ₂ and r ₃ of the received word are lost. The syndrome including r ₂ is s ₀ and s ₅ , and the syndrome including r ₅ is also s ₀ and s ₅ . Also, among the received word of symbols connected to the syndrome s _0, s _5, lost symbol are both two. It is clear what value r ₂ + r ₃ will be, but no more can be determined. In the above description, there are four (0) group expressions and two (2) group expressions, and there is no (1) group expression from the beginning.

8E to 8G are examples in which r ₁ , r ₃ , r ₆ , r ₇ , and r ₉ of the received word are lost. First, as shown in FIG. 8E, among the symbols of the received word connected to the syndrome s ₀ , there are two erasures r ₁ and r ₃ . In the syndrome s ₁ , there are two disappearances r ₆ and r ₇ . In syndrome s ₂ , the disappearance is one of r ₉ . In the syndrome s ₃ , there are _three disappearances r ₁ , r ₇ and r ₉ . In syndrome s ₄ , the disappearance is one of r ₆ . In syndrome s ₅ , the disappearance is one of r ₃ .

First, as shown in FIG. 8F, when the disappearances r ₃ , r ₆ , and r ₉ are restored from the syndromes s ₂ , s ₄ , and s ₅ and this result is fed back to other syndromes, the syndrome s ₀ is obtained. Of the symbols of the received word, the erasure is _one of r ₁ . In syndrome s ₁ , the disappearance is one of r ₇ . In the syndrome s ₃ , there are two disappearances r ₁ and r ₇ .

Therefore, as shown in FIG. 8G, erasures r ₁ and r ₇ can be restored from the syndromes s ₀ and s ₁ , and all symbols can be correctly decoded in this way.

When the code length of the code is n, the number of data is k, the rate is R = k / n, and the degree (the number of “1” s in each column of the parity check matrix) is deg, and the erasure of x symbols is corrected, solution 2) The amount of calculation at is O (x × deg / (1-R)). In contrast, the calculation amount in solution 1), only the syndrome processing stage solving simultaneous equations is O (x ^2/2), further processing of the simultaneous equations data, there is a process for obtaining the syndromes. In a normally used LDPC code, since x is several hundred or more and deg / (1-R) is about several tens, solution 1) requires several times to several tens of times the amount of solution 2). It will be. To require a calculation amount means that processing time is required, or that many decoding resources for reducing the processing time are required.

However, in the case of Solution 1), a correction capability corresponding to the capability of the code can be obtained, but the correction capability of Solution 2) is inferior to that of Solution 1). A simple example is shown in FIG. In Figure 9, the received word symbols _{r a, r b, r c} , r d is disappeared, the solution 2) does not refer only to individually each row of the check matrix H, such cases are corrected Can not. However, in Solution 1), assuming that the syndrome values calculated from each row are s _w , s _x , s _y , and s _z , r _a = s _w + s _y + s _z , r _b = s _x + s _y + s _z , R _c = s _w + s _x + s _y , r _d = s _w + s _x + s _y + s _z . Thus, in Solution 1), unlike Solution 2), the relationship between rows is also referred to, so the decoding process becomes very complicated.
RG Gallager, “Low density parity check codes”, in Research Monograph series. Cambridge, MIT Press (1963) DJ MacKay, “Good error-correcting codes based on very sparse matrices”, IEEE Trans. Inform. Theory, vol.45, pp.399-431 (1999) RM Tanner, “A recursive approach to low complexity codes”, IEEE Trans. Inform. Theory, vol.27, pp.533-547 (1981)

  However, in the above two conventional solutions, the solution 1) has an excellent correction capability, but requires a large amount of calculation, and the solution 2) based on the decoding graph does not require a large amount of calculation. There is a problem that the correction ability is inferior to that of Solution 1).

  In order to solve the above-described problems, an object of the present invention is to provide a decoding device that can reduce the amount of calculation while maintaining a high correction capability.

  In order to achieve the above object, a decoding apparatus according to the present invention corrects an error of a linear code using a check matrix corresponding to the linear code, and includes a received word composed of a plurality of symbols, Erasure position information indicating the position of a symbol having an error in the received word is input, and correction is performed in the symbol having an error in the received word based on a decoding graph indicating a decoding method corresponding to the check matrix. A first decoding unit that generates a first received word in which a possible symbol is corrected, and first erasure position information in which the position of the corrected symbol is reflected in the erasure position information; If the first received word, the first erasure position information, and the check matrix are used to extract an erasure vector composed of an erroneous symbol and a coefficient matrix that is a coefficient of the erasure vector, and the rows are replaced, a triangle In the matrix A matrix processing unit that generates a conversion matrix that performs processing for converting the coefficient matrix into a permutation triangular matrix, and generates a first syndrome from the first received word based on the parity check matrix; and the generated conversion From the matrix and the first syndrome, the second received word in which the symbol having the error in the first received word is corrected, and the position of the corrected symbol is reflected in the first erasure position information. A matrix decoding unit that generates second erasure position information and corrects the first syndrome to a second syndrome reflecting the corrected symbol; and the generated second received word and second Erasure position information, a third received word in which a correctable symbol of the second received word is corrected based on the decoding graph, and a position of the corrected symbol is the second erasure position information. Reflected in And a second decoding section that generates a third erasure locator information.

  According to this, two types of correction processing, that is, error correction processing by the first decoding unit and the second decoding unit and error correction processing by the matrix processing unit and the matrix decoding unit are performed. Here, the error correction processing by the first decoding unit and the second decoding unit is a correction processing method based on a decoding graph with a small amount of calculation. Further, the error correction processing by the matrix processing unit and the matrix decoding unit can correct errors that cannot be corrected by the correction processing based on the decoding graph. For this reason, the decoding process is performed by combining these two types of correction processes, so that the amount of calculation can be reduced while maintaining a high correction capability.

  In addition, the present invention can be realized not only as such a decoding apparatus but also as a method using a processing unit constituting the apparatus as a step. Furthermore, the present invention can be realized as a program for causing a computer to execute these steps, or can be realized as a recording medium such as a computer-readable CD-ROM on which the program is recorded, or as information, data, or a signal indicating the program. It can also be realized. These programs, information, data, and signals may be distributed via a communication network such as the Internet.

  As described above, according to the decoding device of the present invention, the decoding process is performed by combining the correction process based on the decoding graph and the correction process capable of correcting an error that cannot be corrected by the decoding graph. Thus, it is possible to reduce the amount of calculation while maintaining high correction capability.

  Embodiments of the present invention will be described below with reference to the drawings.

(Embodiment 1)
FIG. 1 is a block diagram showing an example of a functional configuration of the decoding device 10 according to Embodiment 1 of the present invention. As illustrated in FIG. 1, the decoding device 10 according to Embodiment 1 includes a first decoding unit 11, a matrix processing unit 12, a matrix decoding unit 13, a second decoding unit 14, an end determination unit 15, and a selection unit 16. It has. The decoding device 10 is a computer that includes a CPU (Central Processing Unit) and the like, inputs necessary data into a memory, executes a program, and outputs the data.

  The first decoding unit 11 receives a received word composed of a plurality of symbols and erasure position information indicating the position of a symbol having an error in the received word, and indicates a decoding method corresponding to a predetermined check matrix Based on the decoding graph, a first received word in which a correctable symbol is corrected among symbols having a received word error, and a first erasure position in which the position of the corrected symbol is reflected in the erasure position information And information. Further, the first decoding unit 11 generates a first flag for determining whether or not there is an erroneous symbol in the first received word.

  The matrix processing unit 12 includes, from the first received word generated by the first decoding unit 11, the first erasure position information, and the parity check matrix, an erasure vector composed of an erroneous symbol and an erasure vector coefficient, And generating a transformation matrix that performs processing for transforming the coefficient matrix into a permutation triangular matrix that becomes a triangular matrix if the rows are replaced, and the first syndrome is derived from the first received word based on the parity check matrix. Generate. In addition, the matrix processing unit 12 generates a second flag for determining whether or not the coefficient matrix can be converted into a replacement triangular matrix.

  The matrix decoding unit 13 includes a second received word obtained by correcting a symbol having an error in the first received word from the transformation matrix generated by the matrix processing unit 12 and the first syndrome, and first erasure position information. The second erasure position information reflecting the corrected symbol position is generated, and the first syndrome is corrected to the second syndrome reflecting the corrected symbol.

  The second decoding unit 14 is configured to correct a correctable symbol of the second received word based on the decoding graph from the second received word generated by the matrix decoding unit 13 and the second erasure position information. 3 received words and third erasure position information in which the position of the corrected symbol is reflected in the second erasure position information. In addition, the second decoding unit 14 generates a third flag for determining whether or not there is a symbol with an error in the third received word, and there is a symbol with an error in the third received word. When it is determined that the second syndrome has been corrected, the second syndrome is corrected to the third syndrome by reflecting the error-corrected symbol in the second syndrome.

  The end determination unit 15 determines whether or not to end the linear code error correction.

  The selection unit 16 outputs the first received word, the first erasure position information, and the first syndrome to the matrix decoding unit 13, or the third received word, the third erasure position information, and the third syndrome. Are to be output to the matrix decoding unit 13.

  Here, the first received word, the first erasure position information, the first syndrome, the second received word, the second erasure position information, the second syndrome, the third received word, the third erasure position Information and each data such as the third syndrome are generated in each processing unit and then written in the memory, and each processing unit reads necessary data from the memory and performs each process.

  FIG. 2 is a flowchart showing a decoding process executed by the decoding apparatus 10.

  First, a received word and erasure position information are input to the first decoding unit 11 (S102).

  Next, based on the decoding graph, the first decoding unit 11 corrects all correctable symbols among the symbols with the received word error, and generates a first received word (S104). Also, the first decoding unit 11 generates first erasure position information by reflecting the corrected symbol position in the erasure position information (S104).

  Then, the first decoding unit 11 generates a first flag for determining whether or not there is an erroneous symbol in the first received word (S106).

  If it is determined by the first flag that there is an error in the first received word (YES in S106), the matrix processing unit 12 calculates an error from the first received word, the first erasure position information, and the check matrix. An erasure vector composed of a certain symbol and a coefficient matrix serving as a coefficient of the erasure vector are extracted (S108). Specifically, the matrix processing unit 12 is a coefficient matrix composed of an erasure vector that is a vector composed of symbols with errors based on the first erasure position information, and a column corresponding to the erasure vector in the check matrix. And extract.

  Then, the matrix processing unit 12 generates a second flag for determining whether or not the coefficient matrix can be converted into a replacement triangular matrix (S110).

  Specifically, the matrix processing unit 12 performs conversion processing of the coefficient matrix into the replacement triangular matrix, and determines whether the conversion processing has succeeded or failed, thereby converting the coefficient matrix into the replacement triangular matrix. A second flag for determining whether or not conversion is possible is generated.

  When it is determined that the conversion to the replacement triangular matrix is possible with the second flag (YES in S110), the matrix processing unit 12 generates a conversion matrix that performs processing for converting the coefficient matrix into the replacement triangular matrix, A first syndrome is generated from the first received word based on the parity check matrix (S114). Specifically, the matrix processing unit 12 generates a first syndrome that is calculated by multiplying the parity check matrix and the first received word. Further, the matrix processing unit 12 generates a conversion matrix that is calculated so that a value obtained by multiplying the erasure vector and the replacement triangular matrix is the same as a value obtained by multiplying the first syndrome and the conversion matrix.

  Then, the matrix decoding unit 13 generates a second received word and second erasure position information from the transformation matrix and the first syndrome, and corrects the first syndrome to the second syndrome (S116). . Specifically, the matrix decoding unit 13 selects a row having only one non-zero element from among the rows of the replacement triangular matrix, and obtains the row of the transformation matrix corresponding to the selected row and the first syndrome. By calculating the multiplied value, the value of the symbol having an error is calculated, and the second received word and the second erasure position information are generated. Further, the matrix decoding unit 13 corrects the first syndrome to the second syndrome by reflecting the error-corrected symbol in the first syndrome.

  Next, the second decoding unit 14 performs a third operation in which all correctable symbols of the second received word are corrected based on the decoding graph from the second received word and the second erasure position information. A received word and third erasure position information in which the corrected symbol position is reflected in the second erasure position information are generated (S118).

  Next, the second decoding unit 14 generates a third flag for determining whether or not there is a symbol having an error in the third received word (S120).

  When it is determined that there is an error in the third received word with the third flag (YES in S120), the second decoding unit 14 reflects the symbol in which the error is corrected in the second syndrome, The second syndrome is corrected to the third syndrome (S122).

  Then, the end determination unit 15 determines that the error correction of the linear code has not ended, and determines the third received word, the third erasure position information, and the third syndrome as the first received word, respectively. The first erasure position information and the first syndrome are output to the matrix decoding unit 13. Thereby, the matrix decoding part 13 produces | generates a 2nd received word and 2nd erasure | elimination position information, and correct | amends a 1st syndrome to a 2nd syndrome (S116).

  Further, when it is determined by the first flag that there is no error in the first received word (NO in S106), the end determination unit 15 determines that the end is due to completion of linear code error correction, The first received word is output as an error-corrected received word (S124). Further, when it is determined by the second flag that conversion to the replacement triangular matrix is impossible (NO in S110), the end determination unit 15 determines that the end is due to the error correction of the linear code, The first received word and the first erasure position information are output as the received word where the error remains and the position information of the remaining error (S126). Further, when it is determined by the third flag that there is no error in the third received word (NO in S120), the end determination unit 15 determines that the end is due to completion of error correction of the linear code, The third received word is output as an error-corrected received word (S128). In this way, the decoding process ends.

  3A to 3C are diagrams for specifically explaining an example of the decoding process of the decoding device 10. Here, the description will be made assuming that the code length of the code to be decoded is n and the number of data is k. The replacement triangular matrix is an upper triangular matrix.

  The first decoding unit 11 corrects the received word information input to the decoding device 10 and the erasure position information using the algorithm described as Solution 2 in the conventional example, and as a result of the correction, the first received word , The erasure position information of the first received word and the first flag are output. At this stage, when all the erasures can be corrected, the first received word is directly output from the decoding device 10, and when the erasure that cannot be corrected remains, the matrix processing unit 12 and the matrix decoding unit 13 are used. However, the following process is performed using the first received word and the erasure position information of the first received word. The first flag is a flag indicating whether all erasures have been corrected. Let x be the number of remaining disappearances.

Matrix processing section 12, as shown in FIG. 3A, the first received word to be input, (n-k) by multiplying the parity check matrix H of rows and n columns, the first syndrome S = (s _0, s ₁ ,..., S _(nk-1) ) are obtained and output. Here, each element of the first received word and the parity check matrix H is a binary value, and an exclusive-or process is performed in the calculation. Since the codeword is multiplied by the check matrix H to obtain 0 (vector), and the first syndrome is obtained from the magnitude of the erasure, the value of the first syndrome is lost from the check matrix H. Coefficient matrix H ′ leaving only the column corresponding to the position of and the erasure vector Z = (z ₀ , z ₁ ,..., Z _(i−1) , z _i , z _{(i + 1) ,. -1)} It agrees with the value obtained by multiplying by ₎ ).

Matrix processing unit 12, in order to obtain the value of the loss, further deforms the primary x based simultaneous equations H '· Z ^T = S ^T for the values of these lost and x number of variables. Specifically, as shown in FIG. 3B, again placing 'a · Z ^T = S ^T H' equation H and ^{· Z T = I · S T} (I is the (n-k) The following matrix ), The coefficient matrix H ′ on the left side is converted to generate an upper triangular matrix H ″. The conversion is executed by adding the rows of the coefficient matrix and exchanging the rows. The matrix I is subjected to the same transformation as the transformation on the left side to generate a transformation matrix T, which is output. This transformation matrix T satisfies H ″ · Z ^T = T · S ^T.

  The second flag is a flag indicating whether or not the triangular matrix can be formed. If the triangular matrix cannot be formed, the code word cannot be corrected. The first received word and the erasure position information of the first received word are output from the decoding device 10 as the received word and erasure position information after the correction is completed.

  Each of the selection units 16 outputs the first received word, the erasure position information of the first received word, and the first syndrome, which are the outputs of the matrix processing unit 12, after the processing of the matrix processing unit 12 ends. Thereafter, the third received word fed back from the second decoding unit 14, the erasure position information of the third received word, and the third syndrome are output.

First, the matrix decoding unit 13 selects a row having a weight of 1 (only one element is non-zero and the rest are all zero) from the rows of the upper triangular matrix H ″. 3C, as shown in Fig. 3C, the left side of the expression corresponding to this row in the above-mentioned first-order x-ary simultaneous equations is a row in which the i-th element is 0. , z _(i-1), i.e., is the value of the i-th erasure, found value of loss by calculating the values of the corresponding right-hand side, can correct the symbol. the received word R = (r _0, r ₁ , ..., r a _(n-1)), if the symbol disappears x _i-th correcting, corrected R pattern E _i = ([x _i -1 one _{0], z (i-1} ), [N−x _i 0s]) can be added and corrected.

If the disappearance is corrected, the disappearance information is excluded from the above simultaneous equations and transformed into simultaneous equations with one less variable. For the left side, z _(i-1) is eliminated from the erasure vector Z, the number of dimensions is reduced by 1, and the column corresponding to z _(i-1) is also deleted for the upper triangular matrix H ". if adding the value obtained by multiplying E _i ^T in the parity check matrix H to the syndrome S, it is corrected to the syndrome of loss has decreased state. the actual processing, information of the upper triangular matrix H "in after processing Is not used, it is not necessary to correct the information of the upper triangular matrix H ″.

  The matrix decoding unit 13 outputs the corrected result as the second received word, the erasure position information of the second received word, and the second syndrome.

  Note that the number of erasures corrected by the matrix decoding unit 13 may be one or plural. It is also possible to set the number of erasures to be corrected by the code length, the number of parity, the order, and the number of parity that has not been corrected at that time.

  The second decoding unit 14 corrects the second received word information and the second erasure information of the second received word using the algorithm described as Solution 2 in the conventional example, and the corrected result , The third received word, the erasure position information of the third received word, and the third flag are output.

Also in the second decoding unit 14, similarly to the processing of a matrix decoder 13 as x _i-th symbol of the received word is lost, the value is z _(i-1), corrected The pattern is E _i = ([x _i −1 0], z _(i−1) , [n−x _i 0]), and the value obtained by multiplying the check matrix H by E _i ^T is the syndrome S. Add and correct the syndrome.

  When the second decoding unit 14 corrects a plurality of erasures, the syndrome may be corrected every time one erasure is corrected or may be performed after correcting a plurality of erasures. good.

  Further, when all the remaining erasures are corrected by the second decoding unit 14, it is not necessary to correct the syndrome.

  When all the erasures can be corrected, the third received word is directly output from the decoding device 10, and when the erasure that could not be corrected remains, the matrix decoding unit 13 performs the third received word, The erasure position information of the third received word and the third syndrome are fed back, and the following processing is executed.

  The third flag is a flag indicating whether all erasures have been corrected.

  The control signal is a signal for instructing input / output and selection of received word information / erasure information in the decoding apparatus 10 itself and in each unit, and instructing execution of processing in each unit.

  The end determination unit 15 generates a control signal and flag information based on the input instruction of the decoding device 10, the first flag, the second flag, the third flag, and the state of each unit.

  In the decoding apparatus 10 configured as described above, two types of error correction processing by the first decoding unit 11 and the second decoding unit 14 and error correction processing by the matrix processing unit 12 and the matrix decoding unit 13 are provided. Correction processing is performed. Here, the error correction processing by the first decoding unit 11 and the second decoding unit 14 is a correction processing method based on a decoding graph with a small amount of calculation. In addition, since the matrix processing unit 12 and the matrix decoding unit 13 calculate only erasure values that cannot be obtained from the decoding graph by a determinant solution, the amount of calculation required for decoding can be reduced. In addition, the number of times the correction by the decoding graph fails is not limited to one, but if the coefficient calculation of the determinant is first performed once, the first calculated value can be used as it is after the second time. By performing the above, it becomes possible to reduce the amount of calculation required by the determinant solution. With these techniques, the amount of calculation can be reduced while maintaining high correction capability, and the speed of decoding can be increased.

  Note that since the check matrix H is a unique matrix for each code, if the function of selecting or inputting information of the check matrix H according to the used code is provided, the decoding apparatus 10 that handles a plurality of codes. It is clear that can be configured.

  Moreover, although it converted to the upper triangular matrix, the same algorithm can be applied even if it converts to the lower triangular matrix. In addition, it is clear that the same effect can be obtained whether or not there is a process of gathering in a part of the matrix such as top-bottoming or bottom-striking the triangulated part. That is, even if it is not an upper triangular matrix, it may be a matrix that becomes a triangular matrix by replacing rows.

  The operations of the present invention are all operations according to the definition of the sign. For example, if the code is on the Galois field GF (2) or its extension field, the addition is an exclusive-or operation. That is.

  When the transmitted packet arrives late and arrives after decoding is started, it can also be handled as a corrected packet.

  Code parameters such as code length, number of data, and check matrix H information may be incorporated in each unit from the beginning in the decoding apparatus 10 that always handles the same code, or a control signal in the decoding apparatus 10 that handles a plurality of codes. In this case, the decoding apparatus 10 that handles arbitrary codes can be configured to read these parameters from the outside as control signals.

(Embodiment 2)
FIG. 4 is a block diagram illustrating an example of a functional configuration of the matrix processing unit 12 according to Embodiment 2 of the present invention. As illustrated in FIG. 4, the matrix processing unit 12 according to the second embodiment includes a coefficient extraction unit 21, a triangular matrix generation unit 22, a transformation matrix generation unit 23, and a syndrome generation unit 24.

  The coefficient extraction unit 21 includes an erasure vector Z, which is a vector composed of symbols with errors based on the first erasure position information, and a coefficient matrix H ′ composed of columns corresponding to the erasure vector Z in the check matrix H. And extract.

  The triangular matrix generation unit 22 converts the coefficient matrix H ′ into an upper triangular matrix H ″.

  The syndrome generator 24 generates a first syndrome S that is calculated by multiplying the check matrix H and the first received word.

  The transformation matrix generation unit 23 generates a transformation matrix T that is calculated so that the value obtained by multiplying the erasure vector Z and the upper triangular matrix H ″ is the same as the value obtained by multiplying the first syndrome S and the transformation matrix T. To do.

  Processing performed by the matrix processing unit 12 will be described in detail below.

  First, the coefficient extraction unit 21 obtains a coefficient of a first-order x-ary simultaneous equation having the erasure value as x variables as a coefficient matrix H ′ obtained by deleting columns other than the column at the erasure position from the check matrix H. And output as coefficient information of (n−k) rows and x columns.

  The triangular matrix generation unit 22 performs processing to convert the coefficient matrix H ′ into the upper triangular matrix H ″ from the input coefficient information. The second flag indicating whether or not the triangular matrix can be formed is a triangle. Output from the matrix generator 22.

The conversion matrix generation unit 23 generates the conversion matrix T by performing the same process as the process of converting the coefficient matrix H ′ into the upper triangular matrix H ″ on the (n−k) -th unit matrix I _(nk) . In addition, the triangular matrix generation unit 22 outputs processing information related to the conversion processing to the conversion matrix generation unit 23. The processing information notifies the processing such as the replacement of the a row and the b row and the addition of the d row to the c row. It is also possible to notify the user at once after the processing is completed.

The syndrome generator 24 multiplies the input first received word by a check matrix H of (n−k) rows and n columns to obtain the first syndrome S = (s ₀ , s ₁ ,..., S _{(nk -1))} ) is obtained and output.

  In the matrix processing unit 12 configured as described above, in parallel with the triangulation process, the conversion process is held in the form of a conversion matrix, so that the value of the syndrome is left unchanged, and the subsequent process It is now possible to avoid having to recalculate the syndrome value when it becomes necessary to use the syndrome value.

(Embodiment 3)
5A and 5B are block diagrams showing an example of a functional configuration of the matrix decoding unit 13 according to Embodiment 3 of the present invention. As illustrated in FIGS. 5A and 5B, the matrix decoding unit 13 according to the third embodiment includes an erasure value calculation unit 31, a correction unit 32, and a syndrome correction unit 33.

  The erasure value calculation unit 31 selects a row having only one non-zero element among the rows of the upper triangular matrix H ″, and selects the row of the transformation matrix T corresponding to the selected row and the first syndrome S. By calculating the multiplied value, the value of a symbol having an error is calculated, and second erasure position information is generated.

  The correcting unit 32 generates a second received word based on the calculated symbol.

  The syndrome correction unit 33 corrects the first syndrome S to the second syndrome based on the calculated symbol.

  The process performed by the matrix decoding unit 13 will be described in detail below.

  The erasure value calculation unit 31 selects a row having a weight of 1 among the rows of the upper triangular matrix H ″ and multiplies the row of the transformation matrix T corresponding to the selected row by the first syndrome S. To obtain one erasure value, and correct the erasure position information of the received word being corrected input to the matrix decoding unit 13. If the erasure value is corrected, Among the columns of the upper triangular matrix H ″, all the elements of the column corresponding to the corrected erasure position can be regarded as 0, so that there is always a row having a weight of 1.

  The correction unit 32 performs correction by adding the obtained erasure value to the symbol at the obtained erasure position of the received word being corrected input to the matrix decoding unit 13. Normally, the decoding process starts with the value of the symbol at the erasure position set to 0, and in this case, it is only necessary to substitute.

The syndrome correction unit 33 cancels the influence of the correction pattern E _i = ([x _i −1 0], z _(i−1) , [n−x _i 0]) on the value of the syndrome. Then, the value obtained by multiplying the check matrix H by E _i ^T is added to the syndrome S, and the corrected syndrome is output.

  The configuration of FIG. 5A is a block diagram of means for correcting one erasure. Here, the matrix decoding unit 13 generates the generated second received word, the second erasure position information, and the second syndrome, respectively, as the first received word, the first erasure position information, and the first You may decide to input as a syndrome.

  In other words, if one erasure value is calculated by the erasure value calculation unit 31, the subsequent second erasure unit 14 cannot always correct the remaining erasures. 5B, the selection unit 34 feeds back each data / information to be input to the input side and inputs it to the erasure value calculation unit 31 and the correction unit 32, as shown in FIG. 5B. Is possible. The number of erasures to be corrected may be a fixed value or variable as the decoding device 10. In the case of making it variable, it is also possible to indicate the number to be corrected using a control signal.

  In the matrix decoding unit 13 configured as described above, by introducing a part of the decoding algorithm based on the method of solving the determinant, all the erasures that can be corrected in the first decoding unit 11 have been corrected, and It has become possible to continue erasure correction of received words in which erasures that cannot be corrected remain.

(Embodiment 4)
6A and 6B are block diagrams illustrating an example of a functional configuration of the second decoding unit 14 according to Embodiment 4 of the present invention. As illustrated in FIG. 6A, the second decoding unit 14 of the fourth embodiment includes a third decoding unit 41, a corrected erasure position storage unit 42, and a syndrome correction unit 43.

  The third decoding unit 41 corrects the second received word input to the second decoding unit 14 and the erasure position information of the second received word using the algorithm described as Solution 2 in the conventional example. As a result, the third received word, the erasure position information of the third received word, and the third flag are output. At this stage, if all erasures can be corrected, the third received word is output as it is from the decoding device 10 as it is, and if erasures that could not be corrected remain, they are fed back to the matrix decoding unit 13. The third flag is a flag indicating whether all erasures have been corrected.

  When decoding by the third decoding unit 41 is not completed, in order to continue decoding by the matrix decoding unit 13, it is necessary to correct the syndrome with respect to the symbols corrected by the third decoding unit 41 now. is there. Therefore, the third decoding unit 41 outputs the corrected erasure position information to the corrected erasure position storage unit 42, and the corrected erasure position storage unit 42 stores the information of these positions. To do. The syndrome correction unit 43 corrects the input second syndrome based on the position information stored in the storage unit 42 of the corrected disappearance position, and outputs the corrected second syndrome.

  FIG. 6A shows a configuration in which the syndrome correction unit 43 corrects syndromes related to a erasures after the third decoding unit 41 corrects a erasures. Further, if all the erasures can be corrected by the third decoding unit 41, syndrome correction is unnecessary, and if not executed, this contributes to speeding up the entire decoding process.

  Also, as shown in FIG. 6B, the second decoding unit 14 of Embodiment 4 includes a graph-based 1-erasure decoding unit 45, a syndrome correction unit 43, and selection units 46 and 47.

  The graph-based 1 erasure decoding unit 45 is also a decoding unit that corrects one erasure instead of correcting all the erasures that can be corrected, although the erasure is calculated by the algorithm described as Solution 2 in the conventional example.

  FIG. 6B shows that data / information inputted by the selectors 46 and 47 is that the graph-based one erasure decoding unit 45 corrects one erasure and the syndrome correction unit 33 corrects the syndrome related to the erasure. And output data / information to be fed back are repeated while switching.

  That is, the second decoding unit 14 generates the generated third received word, the third erasure position information, and the third syndrome, respectively, the second received word, the second erasure position information, and the first erasure position information. Enter as a syndrome of 2.

  In addition, also in the decoding part 14 shown to FIG. 6B, the process of each step (S118-122) shown by FIG. 2 is performed.

  In the second decoding unit 14 configured as described above, by correcting syndromes necessary for the decoding method by solving the determinant while performing decoding based on the decoding graph, the decoding cannot be performed here. In addition, it is possible to eliminate the need to repeat the calculation of the syndrome and the conversion of the coefficient matrix of the simultaneous equations with the value of the disappearance into the upper triangular matrix.

  The decoding device according to the present invention has been described above using the above embodiment, but the present invention is not limited to this.

  That is, the embodiment disclosed this time should be considered as illustrative in all points and not restrictive. The scope of the present invention is defined by the terms of the claims, rather than the description above, and is intended to include any modifications within the scope and meaning equivalent to the terms of the claims.

  For example, in the present embodiment, each element such as the first received word and the check matrix H is a binary number, but may be a ternary number.

  In the present embodiment, each component such as the first decoding unit 11 is configured by software, but may be configured by dedicated hardware. That is, each functional block in the block diagrams (FIG. 1, FIG. 4 to FIG. 6B, etc.) may be realized as an LSI that is typically an integrated circuit. Note that these may be individually made into one chip, or may be made into one chip so as to include a part or all of them.

  The decoding device, decoding method, and decoding program according to the present invention can increase the processing speed without impairing the correction capability, and are useful for erasure correction such as packet loss during network transmission.

It is a block diagram which shows an example of a functional structure of the decoding apparatus in Embodiment 1 of this invention. It is a flowchart which shows the process of the decoding which a decoding apparatus performs. It is a figure explaining an example of a decoding process of a decoding apparatus concretely. It is a figure explaining an example of a decoding process of a decoding apparatus concretely. It is a figure explaining an example of a decoding process of a decoding apparatus concretely. It is a block diagram which shows an example of a functional structure of the matrix process part in Embodiment 2 of this invention. It is a block diagram which shows an example of a functional structure of the matrix decoding part in Embodiment 3 of this invention. It is a block diagram which shows an example of a functional structure of the matrix decoding part in Embodiment 3 of this invention. It is a block diagram which shows an example of a functional structure of the 2nd decoding part in Embodiment 4 of this invention. It is a block diagram which shows an example of a functional structure of the 2nd decoding part in Embodiment 4 of this invention. It is explanatory drawing of transmission packet generation. It is explanatory drawing of the decoding algorithm based on a decoding graph. It is explanatory drawing of the decoding algorithm based on a decoding graph. It is explanatory drawing of the decoding algorithm based on a decoding graph. It is explanatory drawing of the decoding algorithm based on a decoding graph. It is explanatory drawing of the decoding algorithm based on a decoding graph. It is explanatory drawing of the decoding algorithm based on a decoding graph. It is explanatory drawing of the decoding algorithm based on a decoding graph. It is explanatory drawing of the difference of the correction capability of the solution 1 and the solution 2. FIG.

Explanation of symbols

DESCRIPTION OF SYMBOLS 11 1st decoding part 12 Matrix processing part 13 Matrix decoding part 14 2nd decoding part 15 End judgment part 16 Selection part 21 Coefficient extraction part 22 Triangular matrix generation part 23 Transformation matrix generation part 24 Syndrome generation part 31 Erasure value calculation part 32 Correction unit 33 Syndrome correction unit 34 Selection unit 41 Third decoding unit 42 Storage unit of corrected erasure position 43 Syndrome correction unit 45 Graph-based one erasure decoding unit 46, 47 Selection unit

Claims (8)

A decoding apparatus that corrects an error of a linear code using a check matrix corresponding to the linear code,
A reception word composed of a plurality of symbols and erasure position information indicating a position of a symbol having an error in the reception word are input, and the reception is performed based on a decoding graph indicating a decoding method corresponding to the check matrix. A first received word in which a correctable symbol is corrected among symbols having a word error, and first erasure position information in which the position of the corrected symbol is reflected in the erasure position information are generated. A first decoding unit;
From the generated first received word, first erasure position information, and the check matrix, an erasure vector composed of erroneous symbols and a coefficient matrix that is a coefficient of the erasure vector are extracted, and a row is obtained. A matrix processing unit that generates a conversion matrix that performs processing to convert the coefficient matrix into a permutation triangular matrix that becomes a triangular matrix if replaced, and generates a first syndrome from the first received word based on the parity check matrix;
From the generated transformation matrix and the first syndrome, a second received word in which a symbol having an error in the first received word is corrected, and the corrected symbol in the first erasure position information. A matrix decoding unit that generates second erasure position information reflecting a position and corrects the first syndrome to a second syndrome reflecting the corrected symbol;
A third received word in which a correctable symbol of the second received word is corrected based on the decoding graph from the generated second received word and second erasure position information, and the corrected And a second decoding unit that generates third erasure position information in which the position of the symbol is reflected in the second erasure position information. The matrix processing unit
A coefficient extraction unit that extracts the erasure vector, which is a vector composed of symbols with errors based on the first erasure position information, and a coefficient matrix composed of columns corresponding to the erasure vector in the check matrix. When,
A triangular matrix generator for converting the coefficient matrix into the replacement triangular matrix;
A syndrome generator for generating a first syndrome calculated by multiplying the parity check matrix and the first received word;
A transformation matrix generation unit that generates the transformation matrix calculated so that a value obtained by multiplying the erasure vector and the replacement triangular matrix is the same as a value obtained by multiplying the first syndrome and the transformation matrix. The decoding device according to claim 1. The matrix decoding unit
By selecting a row having only one non-zero element among the rows of the permutation triangular matrix and calculating a value obtained by multiplying the row of the transformation matrix corresponding to the selected row and the first syndrome. Calculating a value of a symbol having an error and generating the second erasure position information,
A correction unit that generates the second received word based on the calculated symbol;
The decoding apparatus according to claim 1, further comprising: a syndrome correction unit that corrects the first syndrome to the second syndrome based on the calculated symbol. The matrix decoding unit generates the generated second received word, the second erasure position information, and the second syndrome, respectively, the first received word, the first erasure position information, and the It inputs as 1st syndrome. The decoding apparatus of any one of Claims 1-3 characterized by the above-mentioned. When there is a symbol with an error in the third received word, the second decoding unit further reflects the symbol with the error corrected in the second syndrome, so that the second And the generated third received word, the third erasure position information, and the third syndrome are respectively converted into the second received word and the second syndrome. The erasure position information and the second syndrome are input. The decoding device according to any one of claims 1 to 4. further,
An end determination unit for determining whether to end error correction of the linear code;
The first decoding unit generates a first flag for determining whether or not there is an erroneous symbol in the first received word;
The matrix processing unit generates a second flag for determining whether or not the coefficient matrix can be converted into the replacement triangular matrix;
The second decoding unit generates a third flag for determining whether or not there is a symbol having an error in the third received word, and there is a symbol having an error in the third received word. The second syndrome is corrected to the third syndrome by reflecting the error-corrected symbol in the second syndrome,
The termination determination unit
If it is determined by the first flag that there is no error in the first received word, it is determined that error correction of the linear code has been completed, and the first received word is received after error correction. Output as a word,
If it is determined by the second flag that conversion to the replacement triangular matrix is impossible, it is determined that error correction of the linear code has been completed, and the first received word and the first erasure are The position information is output as the received word where the error remains and the position information of the remaining error,
If it is determined by the third flag that there is no error in the third received word, it is determined that the error correction of the linear code has ended, and the third received word is received after error correction. Output as a word,
If it is determined by the third flag that there is an error in the third received word, it is determined that error correction of the linear code has not been completed, and the third received word and the third received word are corrected. The erasure position information and the third syndrome are output to the matrix decoding unit as the first received word, the first erasure position information, and the first syndrome, respectively. The decoding device according to claim 5. A decoding method for correcting an error of a linear code using a check matrix corresponding to the linear code,
A decoding graph showing a decoding method corresponding to the parity check matrix when a computer receives a received word composed of a plurality of symbols and erasure position information indicating a position of an erroneous symbol in the received word And a first erasure in which the position of the corrected symbol is reflected in the erasure position information. A first decoding step for generating position information;
A computer extracts, from the generated first received word, first erasure position information, and the parity check matrix, an erasure vector composed of erroneous symbols and a coefficient matrix that is a coefficient of the erasure vector. Matrix processing for generating a conversion matrix for performing processing for converting the coefficient matrix into a permutation triangular matrix that becomes a triangular matrix if rows are replaced, and generating a first syndrome from the first received word based on the parity check matrix Steps,
The computer corrects the second received word in which a symbol having an error in the first received word is corrected and the first erasure position information from the generated transformation matrix and the first syndrome. Matrix decoding step of generating second erasure position information reflecting the position of the corresponding symbol and correcting the first syndrome to the second syndrome reflecting the corrected symbol;
A third received word in which a correctable symbol of the second received word is corrected based on the decoding graph from the generated second received word and second erasure position information; A decoding method, comprising: a second decoding step of generating third erasure position information in which the corrected symbol position is reflected in the second erasure position information. A program for correcting an error of a linear code using a check matrix corresponding to the linear code,
A reception word composed of a plurality of symbols and erasure position information indicating a position of a symbol having an error in the reception word are input, and the reception is performed based on a decoding graph indicating a decoding method corresponding to the check matrix. A first received word in which a correctable symbol is corrected among symbols having a word error, and first erasure position information in which the position of the corrected symbol is reflected in the erasure position information are generated. A first decoding step;
From the generated first received word, first erasure position information, and the check matrix, an erasure vector composed of erroneous symbols and a coefficient matrix that is a coefficient of the erasure vector are extracted, and a row is obtained. A matrix processing step of generating a transformation matrix for performing processing for transforming the coefficient matrix into a permutation triangular matrix that becomes a triangular matrix if replaced, and generating a first syndrome from the first received word based on the parity check matrix;
From the generated transformation matrix and the first syndrome, a second received word in which a symbol having an error in the first received word is corrected, and the corrected symbol in the first erasure position information. Matrix decoding step of generating second erasure position information reflecting a position and correcting the first syndrome to a second syndrome reflecting the corrected symbol;
A third received word in which a correctable symbol of the second received word is corrected based on the decoding graph from the generated second received word and second erasure position information, and the corrected A program that causes a computer to execute a second decoding step of generating third erasure position information in which a position of a symbol is reflected in the second erasure position information.

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