JP2009118418A - Decoder, encoder, decoding method, and encoding method - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To provide a decoder for convolutional coding for acquiring good decoded characteristics, an encoder, a decoding method, and an encoding method. <P>SOLUTION: A decoder 300 performs sum-product decoding operation over a codeword series generated by convolutional coding at an encoding side using an expanded parity check matrix generated by using a first parity check row element defined by a first parity check polynomial of convoltional coding and a second parity check row element defined by a second parity check polynomial of convolutional coding equivalent to the first check polynomial. <P>COPYRIGHT: (C)2009,JPO&INPIT

Description

  The present invention relates to a decoding device, a coding device, a decoding method, and a coding method for convolutional codes.

  One of the error correction codes is a convolutional code. The convolutional code has a feature that an encoder can be easily implemented (the encoder can be configured only by a mod2 adder and a shift register) and that an arbitrary information sequence length can be encoded. is doing. In many of the current communication systems, since transmission information is collectively collected for each variable-length packet or frame, it is desirable that the code length of the error correction code to be used is variable, which matches the characteristics of the convolutional code. For this reason, the convolutional code is adopted in error correction coding systems of many communication systems such as IEEE 802.11 wireless LAN system, GSM mobile phone, and satellite communication. In recent years, a technique called turbo code has been actively researched to improve performance by using convolutional codes connected in parallel or in columns. Turbo codes are employed in third generation mobile communication systems.

  In the convolutional code, as the constraint length K of the encoder increases, the minimum free distance between codewords increases, so that high error correction capability can be obtained (see Non-Patent Document 1).

  As an algorithm for decoding a convolutional code, a Viterbi algorithm that performs maximum likelihood (ML (Maximum Likelihood)) sequence estimation and a BCJR (Bahl-Cocke) that performs maximum posterior probability (MAP (Maximum A Posteriori probability)) estimation -Jeinek-Raviv) algorithm is widely used. In the convolutional code, it is known that a high error correction capability can be obtained by applying soft decision decoding by ML sequence estimation or MAP estimation.

By the way, the Viterbi algorithm and the BCJR algorithm perform decoding using a trellis diagram defined by the configuration of the encoder. Decoding using these algorithms requires a calculation amount and memory proportional to the number of states in the trellis diagram. Since the number of states in the trellis diagram is 2 ^K-1 states (K: constraint length of the encoder), the computational complexity increases exponentially as the constraint length K increases in these algorithms. End up. Therefore, it is difficult to implement a soft decision decoding unit of a convolutional code having a long constraint length.

  In addition, the Viterbi algorithm and the BCJR algorithm that use a trellis diagram require sequential calculation in the time direction on the trellis diagram, and are not suitable for speeding up decoding using parallel processing on hardware.

  Methods for simplifying the BCJR algorithm and reducing the amount of calculation include SOVA (Soft-Output Viterbi Algorithm), Max-Log MAP algorithm, and the like. However, since these are also decoding using the trellis diagram, like the Viterbi algorithm and the BCJR algorithm, there is a feature that a calculation amount proportional to the number of states is required, and a feature that requires sequential calculation. (See Non-Patent Document 2).

  Therefore, it has been studied to apply decoding by the Sum-Product algorithm (SPA) (Sum-Product decoding) as a decoding algorithm for convolutional codes (see Non-Patent Documents 3 and 4). The Sum-Product algorithm is also called a BP (Belief-Propagation) algorithm.

  The Sum-Product algorithm is low-density, represented by a low-density parity check (LDPC) code (the number of 1 elements in the matrix is significantly less than the number of 0 elements). This is an algorithm for decoding an error correction code defined by a parity check matrix H. By defining a parity check matrix corresponding to the configuration of the encoder used for encoding, the Sum-Product algorithm can be used for decoding the convolutional code.

  The amount of calculation of the Sum-Product algorithm is mainly governed by the size of the parity check matrix and the number (weight) of 1 standing elements in the check matrix. In the parity check matrix of the convolutional code, the number of rows corresponds to the parity sequence length, the number of columns corresponds to the code sequence length, and the size of the parity check matrix of the convolutional code is not related to the constraint length K. Increasing the encoder constraint length K increases the number of standing elements (row weights) among the row elements constituting the parity check matrix corresponding to an increase in the number of parity check polynomial terms. However, since the increase in the calculation amount with respect to the increase in the row weight is linear, it can be said that the influence on the calculation amount of the Sum-Product algorithm with respect to the increase in the constraint length K is much smaller than that of the Viterbi or BCJR algorithm.

  In addition, in the Sum-Product algorithm, the row processing / column processing of the check matrix may be performed independently for each row / column. For this reason, it is suitable for speeding up decoding processing using parallel processing on hardware, and can easily cope with high-throughput transmission required in next-generation communication systems such as fourth-generation mobile communication systems.

Based on Sum-Product decoding, min-sum decoding, offset BP decoding, Normalized BP decoding, shuffled BP decoding, and the like have been studied as methods for reducing the amount of calculation and improving decoding characteristics by devising approximations and calculation procedures. (Non-Patent Documents 5 to 7).
JG Proakis, "Digital Communications, 4th Edition," McGraw-Hill New York, 2001 P. Robertson, E. Villebrun, P. Hoeher, “A comparison of optimal and sub-optimal MAP decoding algorithms operating in the log domain,” Communications, 1995. ICC 95 Seattle RJ McEliece, DJC MacKay, JF Cheng, “Turbo Decoding as an Instance of Pearl's“ Belief Propagation ”Algorithm,” Selected Areas in Communications, IEEE Journal on, 1998 G. Colavolpe, “Design and performance of turbo Gallager codes,” Communications, IEEE Transactions on, 2004 RD Gallager, “Low-Density Parity-Check Codes,” Cambridge, MA: MIT Press, 1963. MPC Fossorier, M. Mihaljevic, and H. Imai, “Reduced complexity iterative decoding of low density parity check codes based on belief propagation,” IEEE Trans. Commun., Vol.47., No.5, pp.673-680, May 1999. J. Chen, A. Dholakia, E. Eleftheriou, MPC Fossorier, and X.-Yu Hu, “Reduced-complexity decoding of LDPC codes,” IEEE Trans. Commun., Vol.53., No.8, pp.1288 -1299, Aug. 2005. Yuichi Ogawa, “Sum-Product decoding of turbo codes”, Master's thesis, Nagaoka University of Technology, 2007.

  However, it is empirically known that decoding by the Sum-Product algorithm causes the decoding characteristics to deteriorate with respect to the BCJR algorithm as the constraint length K increases.

  The present invention has been made in view of the above points, and provides a decoding device, a coding device, a decoding method, and a coding method for convolutional codes that obtain good decoding characteristics.

  A decoding apparatus according to the present invention is a decoding apparatus that performs BP (Belief Propagation) decoding, and is equivalent to a first row element defined by a first check polynomial of a convolutional code and the first check polynomial. A second row element defined by a second check polynomial of the convolutional code, and a storage means for storing a parity check matrix formed using the code, and a code generated by the convolutional code on the encoding side And a decoding unit that performs BP decoding on the word sequence using the parity check matrix.

  An encoding apparatus according to the present invention is an encoding apparatus that generates a codeword sequence to be decoded using BP (Belief Propagation) decoding on a decoding side, and a convolutional encoding unit that generates a codeword sequence by a convolutional code; And a puncturing means for puncturing the codeword sequence using a puncture pattern based on a parity check matrix pattern used in BP decoding on the decoding side.

  The decoding method of the present invention is a decoding method for performing BP (Belief Propagation) decoding, which is equivalent to a first row element defined by a first check polynomial of a convolutional code and the first check polynomial. A codeword sequence generated by the convolutional code on the encoding side using a parity check matrix formed using a second row element defined by a second parity check polynomial of the convolutional code that is On the other hand, BP decoding is performed.

  The coding method of the present invention is a coding method for generating a codeword sequence to be decoded using BP (Belief Propagation) decoding on the decoding side, generating a codeword sequence by a convolutional code, and performing BP decoding on the decoding side Puncturing is performed using a puncture pattern based on the parity check matrix pattern used in FIG.

  ADVANTAGE OF THE INVENTION According to this invention, the decoding apparatus, encoding apparatus, decoding method, and encoding method for convolutional codes which acquire a favorable decoding characteristic are realizable.

  Hereinafter, embodiments of the present invention will be described in detail with reference to the drawings.

(Embodiment 1)
In this embodiment, in order to improve the decoding characteristics in the convolutional code Sum-Product decoding, a decoding process is performed using a method for extending the parity check matrix used for decoding and the parity check matrix expanded by the method. The decoding unit will be described with reference to the drawings.

Prior to the description of the parity check matrix of the present invention, first, a parity check matrix of a general convolutional code and Sum-Product decoding using the parity check matrix will be described. In the following description, a (7, 5) ₈ convolutional code with constraint length K = 3, coding rate R = 1/2 (= b / c) will be described as an example. Note that (7,5) ₈ is expressed in octal.

(Encoding method)
FIG. 1 shows the configuration of an encoder for a (7,5) ₈ convolutional code with a coding rate R = 1/2. In FIG. 1, the encoder 100 includes shift registers 110-1 and 110-2 and exclusive OR (mod 2 addition) 120-1 to 120-3. As shown in FIG. 1, a (7, 5) ₈ convolutional code encoder 100 outputs x _i and p _i as a data output and a parity output for a data input x _i .

The encoder 100 of FIG. 1 can be expressed using the generator polynomial expression of Equation (1).

In Expression (1), G ₁ (D) represents a feedforward polynomial, and G ₀ (D) represents a feedback polynomial. When the polynomial expression of the information sequence (data sequence) is X (D) and the polynomial expression of the parity sequence is P (D), the parity check polynomial is expressed by Expression (2).

In the encoder 100 of FIG. 1, since G ₁ (D) = D ² +1 and G ₀ (D) = D ² + D + 1, the expressions (1) and (2) are expressed by the expressions (3) and (3), respectively. Equation (4) is obtained. Note that D ^m (m = 1, 2,..., L, L: arbitrary) is a delay operator.

Here, when the information bit at the time point i is expressed as x _i , the parity bit is expressed as p _i, and the transmission sequence w _i = (x _i , p _i ), x _i , p is obtained from the parity check polynomial of Equation (4). _i satisfies Expression (5).

Here, the transmission codeword vector w is defined as w = (x ₁ , p ₁ , x ₂ , p ₂ ,..., X _i , p _i ,..., X _I , p _I ). However, 1 ≦ i ≦ I _N (I _N : information sequence length). At this time, a standard (conventional) parity check matrix H based on the parity check polynomial of Equation (4) can be expressed as shown in FIG. 2 using the relationship of Equation (5). For this parity check matrix H, relational expression (6) is established.

  The parity check matrix H based on the parity check polynomial of Equation (4) will be described in more detail using FIG. 2 again. As can be seen from Equation (6), the number of columns of the parity check matrix H is equal to the transmission codeword sequence length. Further, the number of rows of the parity check matrix H is equal to the parity sequence length.

Assuming that the row vector (parity check row vector) of the i-th row of the parity check matrix H is c _{1, i} , c _{1, i} w ^T = 0 is equivalent to the parity check polynomial of Equation (4) with respect to the time point i. is there. Thus, the elements of the parity check matrix of FIG. 2, a single parity check row vector c _{1, i} corresponding to the time point i as row elements of the i-th row, I _N-th row the row elements from the first row It has a configuration arranged up to.

ここで、ｇ_ｘ，ｍ及びｇ_ｐ，ｍは、パリティ検査行ベクトルの要素であり、１又は０である。一般式（７）に対応するパリティ検査行列を図３に示す。 It is assumed that the parity check polynomial is expressed by the general formula (7).

Here, g _{x, m} and g _{p, m} are elements of the parity check row vector and are 1 or 0. A parity check matrix corresponding to the general formula (7) is shown in FIG.

In the parity check matrix shown in FIG. 2, among the elements of c _{1 and i} , an area 210 corresponding to (x _i−2 , p _i−2 , x _i−1 , p _i−1 , x _i , p _i ). In the range of 0, 1 or 0 stands, and all elements other than the area 210 are 0. The six elements of the area 210 correspond to x _i−2 , p _i−2 , x _i−1 , p _i−1 , x _i , and p _i sequentially from the left, of which x _i−2 , x _i and 1 stands for the elements corresponding to p _i−2 , p _i−1 , and p _i, and corresponds to each term of the equation (4).

  In the entire check matrix H, the lower left and upper right elements of the matrix are zero, and the same area of 1 and 0 as the area 210 shown in FIG. 2 is arranged in a parallelogram on the diagonal of the check matrix H. Has been.

(Decryption method)
The decoding unit performs Sum-Product decoding (BP decoding), min-sum decoding approximating Sum-Product decoding, offset BP decoding, Normalized BP decoding, shuffled BP decoding, and the like based on the parity check matrix H shown in FIG. By using it, decoding can be performed.

  Hereinafter, a Sum-Product decoding algorithm will be described as an example of a decoding algorithm on the decoding side.

なお、Ａ（ｍ）は検査行列Ｈのｍ行目において“１”である列インデックスの集合を意味し、Ｂ（ｎ）は検査行列Ｈのｎ行目において“１”である行インデックスの集合を意味する。 In the following description, a binary (M × N) matrix H = {H _mn } is a parity check matrix to be decoded. Subsets A (m) and B (n) of the set [1, N] = {1, 2,..., N} are defined as follows:

A (m) means a set of column indexes that are “1” in the m-th row of the check matrix H, and B (n) is a set of row indexes that are “1” in the n-th row of the check matrix H. Means.

・ Step A ・ 1 (Initialization):
A priori logarithmic ratio β ⁽⁰⁾ _mn = λ _n is set for all pairs (m, n) satisfying H _mn = 1. λ _n is the log likelihood for each bit. Further, the loop variable (number of iterations) l _sum = 1 is set, and the maximum number of loops is set to l _{sum, max} .

なお、ｆ（ｘ）はＧａｌｌａｇｅｒのｆ関数である。 Step A.2 (line processing):
The external value logarithm ratio α ⁽ⁱ⁾ _mn is updated using the following update formula for all pairs (m, n) satisfying H _mn = 1 in the order of m = 1, 2,... . Note that i is the number of iterations.

Note that f (x) is Gallager's f function.

Step A.3 (column processing):
The external value logarithm ratio β ⁽ⁱ⁾ _mn is updated using the following update formula for all pairs (m, n) satisfying H _mn = 1 in the order of n = 1, 2 _,. .

Step A · 4 (calculation of log likelihood ratio):
For n∈ [1, N], the log likelihood ratio L ⁽ⁱ⁾ _n is obtained as the following equation.

・ Step A ・ 5 (Counting the number of iterations):
If l _sum <l _{sum, max} , l _sum is incremented, and the process returns to step A · 2. On the other hand, in the case of l _sum = l _{sum, max} , as shown in the equation (15), the codeword w is estimated, and the Sum-Product decoding is finished.

  FIG. 4 is a diagram illustrating an example of a configuration when Sum-Product decoding is used in the decoding unit. In the decoding unit 300 of FIG. 4, the log likelihood ratio storage unit 303 receives the log likelihood ratio signal 301 and the timing signal 302 and stores the log likelihood ratio of the data section based on the timing signal 302. Then, the log likelihood ratio storage unit 303 outputs the stored log likelihood ratio as a signal 304 to the row processing calculation unit 305.

  The row processing calculation unit 305 receives the log likelihood ratio signal 304 and the column-processed signal 312 as input, and performs the above-described calculation of Step A · 2 (row processing) at a position where “1” exists in the check matrix H. Do. Since the decoding unit performs iterative decoding, the row processing calculation unit 305 performs row processing using the log likelihood ratio signal 304 at the time of the first decoding (corresponding to the processing of Step A · 1 described above). In the second decoding, row processing is performed using the signal 312 after column processing. Then, the row processing calculation unit 305 outputs the signal 306 after the row processing to the post-row processing data storage unit 307.

  The post-row processing data storage unit 307 receives the post-row processing signal 306 and stores all post-row processing values (signals). Then, the post-row processing data storage unit 307 outputs the post-row processing signal 308 to the column processing computation unit 309 and the log likelihood ratio computation unit 315.

  The column processing operation unit 309 receives the signal 308 and the control signal 314 after row processing as input, confirms from the control signal 314 that it is not the last iterative operation, and at the position where “1” exists in the check matrix H, Step A · 3 (column processing) is calculated. Then, the column processing operation unit 309 outputs the column-processed signal 310 to the column-processed data storage unit 311.

  The post-column processing data storage unit 311 receives the post-column processing signal 310 and stores all post-column processing values (signals). Then, the post-column processing data storage unit 311 outputs the post-column processing signal 312 to the row processing calculation unit 305.

  The control unit 313 receives the timing signal 302, counts the number of iterations, and outputs the number of iterations to the column processing computation unit 309 and the log likelihood ratio computation unit 315 as the control signal 314.

  The log likelihood ratio calculation unit 315 receives the row-processed signal 308 and the control signal 314 as input, and determines that the last iterative calculation is based on the control signal 314, the check matrix H has “1”. Step A · 4 (calculation of log likelihood ratio) is performed on the position to obtain a log likelihood ratio signal 316. Then, the log likelihood ratio calculation unit 315 outputs the log likelihood ratio signal 316 to the determination unit 317.

  Determination section 317 receives log likelihood ratio signal 316 as input, estimates a codeword, and outputs estimated bit 318.

  The check matrix storage unit 319 stores a parity check matrix used for Sum-Product decoding, and outputs a position where “1” exists in the check matrix H to the row processing calculation unit 305 and the column processing calculation unit 309.

  The parity check matrix of the standard (conventional) convolutional code, the Sum-Product decoding algorithm and the decoding unit using the parity check matrix have been described above. Hereinafter, a parity check matrix of the present invention and a decoding unit using the parity check matrix will be described.

(Parity check matrix)
First, a method for generating a parity check matrix, which is the gist of the present invention, will be described. The parity check matrix shown in FIG. 2 is configured based on only one parity check polynomial. On the other hand, the parity check matrix according to the present embodiment is characterized in that the row is expanded based on a plurality of parity check polynomials.

・ Step B ・ 1:
First, the parity check polynomial (4) of the base convolutional code is modified to create another parity check polynomial equivalent to equation (4). A method for creating another equivalent parity check polynomial is described in Non-Patent Document 8, for example.

・ Step B ・ 2:
A parity check polynomial used for generating a parity check matrix is selected from the base parity check polynomial (4) and another parity check polynomial equivalent to the expression (4) generated in Step B · 1, as k (k ≧ 2) Select one parity check polynomial.

  Decoding characteristics can be obtained by following the following <1>, <2>, and <3> as selection criteria.

Criteria <1>:
Of the parity check polynomials equivalent to the equation (4) generated in Step B · 1, only the equivalent parity check polynomials are used, and the lower left and upper right elements of the matrix are as shown in FIGS. When the parity check matrix in which each term of the parity check polynomial is arranged in a parallelogram on the diagonal line of the check matrix H is generated and BP decoding is performed using the parity check matrix, it is excellent. Select a parity check polynomial that provides error rate characteristics. From experience, it is possible to improve the characteristics by preventing the parity check matrix from including a loop having a length of 4 as much as possible (also referred to as “loop 4”, “4-loop”, “FC (Four Cycle)”). It is known.

Criteria <2>:
A parity check polynomial whose constraint length ν is large is selected in combination with a small parity check polynomial. When the parity check polynomial is given by equation (16), the constraint length ν of the parity check polynomial is expressed by equation (17).

Criteria <3>:
Select a set of parity check polynomials that are sparse. That is, a set of parity check polynomials is selected such that the order of terms included in each parity check polynomial is as small as possible. As a result, it is possible to prevent the generation of a loop having a length of 4, which is empirically caused to deteriorate characteristics in BP decoding, as much as possible.

・ Step B ・ 3:
Using one of the parity check polynomials selected in Step B · 2 (hereinafter referred to as “first parity check polynomial”), a parity check matrix is created as shown in FIGS. (Referred to as “first parity check matrix”). Specifically, a parity check matrix is created in which regions of 0 or 1 elements corresponding to the first parity check polynomial are arranged in a parallelogram on the diagonal of the check matrix.

・ Step B ・ 4:
A parity check row vector is created based on a parity check polynomial (referred to as a “second parity check polynomial”) different from the first parity check polynomial created in Step B · 3 (“second parity check polynomial”). Called a row vector). Note that a specific method of creating the second parity check row vector will be described later with a specific example. An extended parity check matrix is created by adding the created second parity check row vector to the first parity check matrix.

  Note that the parity check row vector created based on another parity check polynomial (third and fourth parity check polynomials) is further added to the parity check matrix to which the second parity check row is added, thereby expanding the parity check matrix. A parity check matrix may be created.

By the above Step B · 1 to Step B · 4, an extended parity check matrix used in the present embodiment can be created. Hereinafter, Step B · 1 to Step B · 4 will be supplementarily described using specific examples using (7,5) ₈ convolutional codes.

これらはいずれも式（１）の生成多項式によって定義される符号のパリティ検査多項式（４）と等価となっている。 Example of Step B · 1 By modifying the base parity check polynomial (4), another parity check polynomial equivalent to the generator polynomial (1) is created. As another parity check polynomial equivalent to equation (4), there are parity check polynomials such as equations (18) and (19).

These are all equivalent to the parity check polynomial (4) of the code defined by the generator polynomial of equation (1).

Example of Step B • 2 A set of two parity check polynomials (4) and (18) is selected as a polynomial used for generating a parity check matrix.

Example of Step B • 3 A first parity check matrix is created using the parity check polynomial (4) as the first parity check polynomial. The first parity check matrix is the same as the check matrix H shown in FIG.

Example of Step B • 4 The parity check polynomial (18) is selected as the second parity check polynomial. A second parity check row vector is created based on the parity check polynomial (18) and added to the parity check matrix of FIG.

FIG. 5 shows an example of the parity check matrix created in the above procedure according to the present embodiment. FIG. 5 illustrates an extended parity check matrix obtained by adding the _second parity check row vector c2 _{, i} based on Equation (18) to the parity check matrix of FIG. The second parity check vector c _{2, i} has an element of 1 or 0 corresponding to each term of Equation (18) in the area 410 corresponding to p _i , x _i from p _i-4 , x _i-4. All other elements are 0.

Using the first parity check polynomial, a total of I _N rows of parity check matrices can be created corresponding to the range of possible time points i (1 ≦ i ≦ I _N ). Note that the second parity check row vector can be added at any time point i, and the time point i at which the second parity check row vector is added will be described later.

The parity check matrix shown in FIG. 5 is an example in which a second parity check row vector is added at time 2. Further, as another example of the parity check matrix of the present embodiment, a parity check matrix expanded by adding the third parity check row c3 _{, j} based on Equation (19) to the parity check matrix of FIG. As shown in FIG. In this manner, the parity check matrix can be extended using a parity check row based on a plurality of parity check polynomials.

  Hereinafter, Sum-Product decoding is performed based on the conventional parity check matrix H by performing Sum-Product decoding (BP decoding) based on the parity check matrix H extended according to Step B · 1 to Step B · 4. The effect of the present invention will be described using a Tanner graph with respect to the point that a decoding characteristic superior to that performed can be obtained.

  FIG. 7 is a diagram illustrating a part of the Tanner graph of the parity check matrix H illustrated in FIGS. 2 and 5. 7A shows a part of the Tanner graph of the conventional parity check matrix shown in FIG. 2, and FIG. 7B shows a part of the Tanner graph of the parity check matrix of the present invention shown in FIG. .

  In one process of Sum-Product decoding (Step A · 2 to Step A · 5), first, the log likelihood ratio of the check node is calculated using the log likelihood ratio of the variable node in Step A · 2 (row processing). Then, in step A · 3 (column processing), the log likelihood ratio of the variable node is updated using the log likelihood ratio of the check node. When this is expressed on the Tanner graph, reliability information is first propagated to the check nodes connected from each variable node by row processing, and then reliability information is propagated from each check node to the connected variable nodes. It turns out that.

Among the Tanner graph of FIG. 7A, attention to the variable node x _i. Check nodes c _{1, i} , c _{1, i + 2} are connected to the variable node x _i . Therefore, in one process of Sum-Product decoding, a set of variable nodes { _pi-2 , xi _-2 , _pi-1) connected via check nodes c1 _{, i} , c1 _{, i + 2} , P _i , x _i }, {p _i , x _i , p _{i + 1} , p _{i + 2} , x _{i + 2} } propagates to the variable node x _i .

The Tanner graph of FIG. 7B contrast, the new check node c _{2, i} is connected to the variable node x _i. The check node c _{2, i} corresponds to the parity check row vector c _{2, i} added to the parity check matrix of FIG. Check node _{c 2, i} is a variable node set _{{p i-4, x i} -4, p i-3, p i-1, p i, x i} is connected with, _{c 1, i,} It can be seen that the reliability information can be propagated to the variable node x _i from a combination of bits different from c _{1, i + 2} .

By adding this way a new check node, it is possible to increase the number of elements of the reliability information is propagated to the variable node x _i by one Sum-Product decoding. Since the reliability information of the newly added check node is reliability information propagated from a set of variable nodes different from the conventional check node, the second parity check matrix is added and expanded in this way. By performing Sum-Product decoding using the parity check matrix, decoding characteristics can be improved by the coding gain.

Further, the order of the parity check polynomial (4) corresponding to the first parity check row c _{1, i} is 2, and the order of the parity check polynomial (18) corresponding to the _second parity check row c _{2, i} is 4, by combining parity check polynomials having different orders, the time range of bits for propagating reliability can be made different between c _{1, i} and c _{2, i,} and a higher coding gain can be obtained. Obtainable.

(Selection method of time point i at which the second parity check row vector is added)
As described above, a first parity check matrix of a total of I _N rows can be created using the first parity check polynomial corresponding to the range of possible time points i (1 ≦ i ≦ I _N ). it can. Further, the second parity check row vector can be added at any time point i.

By adding the second parity check row vector in the range of the time point i (1 ≦ i ≦ I _N ), the number of elements of the reliability information propagated to the variable node x _i by one Sum-Product decoding is reduced. The coding gain can be obtained. Therefore, since the reliability information is propagated to which variable node also depends on the time when the second parity check row vector is added, the selection method of the time i at which the second parity check row vector is added is also important. It becomes an element. Therefore, hereinafter, a method of selecting the time point i at which the second parity check row vector is added will be described. This selection method is the same when adding the third, fourth and subsequent parity check rows.

  As described above, the second parity check row vector can be added at any time point i. That is, by adding a second parity check row for each time point, a second parity check row vector of I rows at the maximum can be added to the first parity check matrix.

  Increasing the number of rows of the parity check matrix increases the amount of calculation of the row processing calculation unit 305 and the column processing calculation unit 309 of the decoding unit 300, and increases the size of the memory required for the post-row processing data storage unit 307. However, the increase in the calculation amount and memory size is only proportional to the number of rows to be added, and the increase in the calculation amount of Sum-Product decoding can be performed in parallel, which hinders the speeding up of decoding. It will not be.

However, increasing the number of rows of the parity check matrix makes it easy to form a loop of length 4 that causes degradation of the decoding characteristics of Sum-Product decoding. Therefore, increasing the number of second parity check rows does not necessarily improve the decoding characteristics. If the number of second parity check rows to be added exceeds a predetermined number, the second parity check rows Even if more are added, the improvement of the decoding characteristics becomes relatively small. Therefore, adding a second parity check row for each time point and adding a second parity check row vector of I _N rows may not necessarily improve the decoding characteristics.

  Therefore, hereinafter, a supplementary explanation will be given with reference to FIG. 8 about the time point i at which the second parity check row is added.

FIG. 8 is a diagram showing a parity check matrix in the present embodiment. In FIG. 8, the same parts as those in FIG. 5 are denoted by the same reference numerals. The parity check matrix of FIG. 8 is an example in which second parity check rows are added at regular intervals T _A and every time point T _A. If T _A = 1, the second parity check row is added for all times i. The parity check matrix of FIG. 8, since _p i, two rows of _{x i} corresponding relative time i, the second parity check row shifting region 410 corresponding to the parity check polynomial (18) by 2T _A column Are arranged in a parallelogram. When adding this way a parity check row for each predetermined interval T _A, it is easy to design a parity check matrix for an arbitrary code length. In addition, since the parallelogram-like arrangement of the elements on which 1 stands is not changed in the middle of the code word, it is easy to apply the contrivances of the calculation methods shown in Non-Patent Documents 5 to 7 and the like.

Next, a method determining the interval T _A at which to add the second parity check matrix. Interval T _A is may be determined according to the following criteria.

Reference "1": When the constraint length of the second parity check polynomial and _{v 2,} so that the _{T A} ≦ _{v 2.} By doing this, Sum-Product decoding is performed at least twice, so that any one bit that is set to 1 in the first parity check row is changed to one that is set to 1 in the second parity check row. Probability can be propagated to the bits of, and a high coding gain can be obtained.

  Criterion << 2 >>: A loop having a length of 4 is prevented as much as possible by a plurality of added second parity check rows. Since the length 4 loop causes degradation of decoding characteristics in Sum-Product decoding, the smaller the number of loops of length 4 included in the parity check matrix to which the second parity check row is added, the more the decoding characteristics. Deterioration can be suppressed.

Reference "3": When applying the punctured encoded into codewords interval T _A is set to be the integral submultiple of the length of the puncture pattern. The application of punctured encoding will be described in detail in the second embodiment.

  In this way, by determining the time point i at which the second parity check polynomial is added while avoiding the deterioration factor of the decoding characteristics, by performing BP decoding using the extended parity check matrix, the decoding characteristics Will definitely improve.

  The configuration of the decoding unit according to the present embodiment is the same as that of decoding unit 300 shown in FIG. By replacing the parity check matrix stored in the check matrix storage unit 319 with the parity check matrix described in this embodiment, a decoding unit with good decoding characteristics can be configured.

  As described above, according to the present embodiment, the first parity check row element defined by the first parity check polynomial of the convolutional code and the second of the convolutional code that is equivalent to the first check polynomial. Sum-Product for a codeword sequence generated by a convolutional code on the encoding side using an extended parity check matrix formed using a second parity row element defined by a parity check polynomial Decrypt. In this way, by performing Sum-Product decoding using the extended parity check matrix, reliability propagation is performed between more different combinations of bits in one calculation process of the Sum-Product algorithm. As a result, the decoding characteristics can be improved.

  The present invention can be widely applied to various BP decoding. That is, the BP decoding of the present invention includes min-sum decoding, offset BP decoding, normalized BP decoding, and the like that approximate BP decoding as described in Non-Patent Documents 5 to 7, for example. The same applies to the embodiments described below.

(Embodiment 2)
When applying a convolutional code to a wireless communication system, it is common to use a punctured convolutional code that combines a punctured coding with a convolutional code in order to make the coding rate variable without changing the configuration of the encoder. It is. In this embodiment, a configuration of a suitable punctured encoder for using the decoding section described in Embodiment 1 for a radio reception apparatus in a radio communication system to which a punctured convolutional code is applied will be described.

  FIG. 9 shows a configuration of a transmission apparatus provided with a punctured encoder according to the present embodiment. 9 includes a convolutional coding unit 610, a puncturing unit 620, an interleaving unit 630, a modulating unit 640, a control information generating unit 660, a wireless transmitting unit 650, and a transmitting antenna 670. Note that the punctured encoder according to the present embodiment includes a convolutional encoding unit 610 and a puncturing unit 620.

  The convolutional coding unit 610 performs a convolutional coding process on the transmission information sequence, and outputs the obtained transmission codeword sequence to the puncturing unit 620.

  Puncturing section 620 performs bit puncturing (bit erasure) from the transmission codeword sequence according to a predetermined puncture pattern, and outputs the punctured transmission codeword sequence to interleaving section 630. The puncture pattern will be described later.

  Interleaving section 630 performs sequence order rearrangement processing (interleaving) on the punctured transmission codeword sequence, and outputs the interleaved transmission codeword sequence to modulation section 640.

  Modulation section 640 modulates the interleaved transmission codeword sequence with a modulation scheme such as PSK (Phase Shift Keying) or QAM (Quadrature Amplitude Modulation), and outputs the transmission modulation symbol sequence to radio transmission section 650.

  The control information generation unit 660 generates control information necessary for receiving a signal between the transmission device and the reception device, and outputs the control information to the modulation unit 640. The control information includes information indicating the puncture pattern used in the puncture unit 620. Examples of other control information include modulation scheme, transmission information sequence length, preamble signal for time / frequency synchronization, and the like.

  Radio transmission section 650 performs radio modulation processing such as D / A (Digital to Analog) conversion, frequency conversion, and RF (Radio Frequency) filter processing on the transmission modulation symbol sequence to generate a transmission RF signal.

  The transmission antenna 670 transmits a transmission RF signal.

  FIG. 10 shows the configuration of the receiving apparatus according to the present embodiment. The receiving apparatus 700 includes a receiving antenna 710, a radio receiving unit 720, a demodulating unit 730, a deinterleaving unit 740, a depuncturing unit 750, a control information detecting unit 760, and a decoding unit 770.

  The reception antenna 710 receives the transmission RF signal transmitted from the transmission device 600 and outputs it to the wireless reception unit 720.

  The radio reception unit 720 performs radio demodulation processing such as RF filter processing, frequency conversion, and A / D (Analog to Digital) conversion. Thereafter, the received baseband signals of the I channel and the Q channel are detected. Radio reception section 720 outputs the received baseband signal to demodulation section 730.

  In addition, the wireless reception unit 720 estimates channel fluctuation in the wireless propagation path between the transmission device 600 and the reception device 700 using a known signal included in the baseband signal. Radio receiving section 720 outputs the estimated channel fluctuation to control information detecting section 760.

  Demodulation section 730 obtains the log likelihood ratio of each transmitted codeword bit from the baseband signal and outputs the obtained log likelihood ratio to deinterleave section 740.

  The deinterleaving unit 740 rearranges the order of the log likelihood ratio sequence using a process reverse to the rearrangement process performed by the interleaving unit 630 in the transmission apparatus 600. Deinterleaving section 740 outputs the received log likelihood ratio sequence after deinterleaving to depuncturing section 750.

  Depuncturing section 750 sets the log likelihood ratio of the bits punctured by puncturing section 620 of transmitting apparatus 600 to 0 and adds it to the received log likelihood ratio sequence in reverse to the operation of puncturing section 620. Depuncturing section 750 outputs the depunctured received log likelihood ratio sequence to decoding section 770.

  The decoding unit 770 performs Sum-Product decoding on the depunctured received log likelihood ratio sequence using the extended parity check matrix as shown in FIG. Is output as a code result of the decoding unit 770.

(Puncture pattern design method)
Next, the puncturing method will be described in detail with reference to FIG. 11, FIG. 12, and FIG. In the present embodiment, a puncture bit (erase bit) design method based on the premise that the extended parity check matrix described in Embodiment 1 is used for decoding will be described.

FIG. 11 shows an example of puncturing processing in the puncturing unit 620. In the present embodiment, a bit arrangement pattern (puncture pattern) to be erased by puncturing is defined in units of a block having a certain length (hereinafter referred to as “puncture block”). Note that it is necessary to prepare as many puncture patterns as the number of coding rates used in communication between the transmission device 600 and the reception device 700. FIG. 11 shows a state of puncturing when the puncturing pattern Z is defined as Z = (1, 0, 1, 0, 1, 1). The block length L _p of the puncture pattern Z in FIG. 11 is L _p = 3, and the puncture unit 620 erases the bit at the position corresponding to 0 in the block of the puncture pattern Z.

  In the present embodiment, a puncture pattern is designed based on the parity check matrix used in decoding section 770. A procedure for designing a puncture pattern will be described below.

・ Step C ・ 1:
The length of the puncture pattern (also referred to as “length of the puncture block”) L _p is determined. The length L _p of the puncture pattern is an integer multiple of the constraint length v ₁ of the first parity check polynomial used for generating the parity check matrix. The shorter the length L _p of the puncture pattern, the configuration of puncturing section, depuncturing section requires only simple. Therefore, among the coding rates that need to be supported, the smallest length among the lengths of the puncture pattern that satisfies the maximum coding rate is _defined as the length L _p of the puncture block.

As an example, a case where a puncture pattern is designed based on the parity check matrix shown in FIG. 12 will be described. The parity check matrix of FIG. 12 is a matrix in which the rows of the parity check matrix of FIG. 5 are exchanged, and is a matrix equivalent to the parity check matrix of FIG. Specifically, the parity check matrix of FIG. 12 is an example in which the second parity check row vector is inserted every three rows of the first parity check row vector. Further, the second parity check row vector is an example in the case where the second parity check row vector is added at intervals of T _A = 3.

In the example shown in FIG. 12, the constraint length v ₁ of the first parity check polynomial is v ₁ = 3. Therefore, the length L _p of the puncture pattern is set to L _p = 3. When the columns of the parity check matrix of FIG. 12 are divided in units of puncture blocks and attention is paid to the divided areas, it can be seen that areas 810, 820, and 830 having the same shape are arranged in a row-shifted manner for each puncture block. In this case, the line shift number is, when the length L _p of the puncture pattern, equal to the number of inspection lines corresponding to the length L _p of the puncture pattern. In the example shown in FIG. 12, the number of row shifts is 3 of the first parity check row vectors c _{1, i-2} , c _{1, i-1} , c _{1, i} from time (i-2) to time i. There are a total of four rows, one row of the row and the second parity check row vector c2 _{, j} . Interval from time (i-2) to time i matches the puncturing pattern _{L p.}

As shown in FIG. 12, in the parity check matrix, the area of the same shape 810, 820, and 830 are arranged in a form shifted row spacing T _A at which to add the second parity check row vector, since it has become 1 (1/1) integral fraction of the length L _p of the puncture pattern. By the way, since the length L _p of the puncture pattern is an integral multiple of the constraint length v ₁ of the first parity check polynomial, the regions 810, 820, and 830 having the same shape are arranged in a row-shifted form. due to the fact that the interval T _a at which to add a parity check row vector has a integral submultiple of the constraint length v ₁ of the first parity check polynomial.

Thus, in the design of the parity check matrix, the interval T _A at which to add the second parity check row vector by a integral submultiple of the length L _p of the puncturing pattern, from the parity check matrix When a column element corresponding to a puncture block is cut out, a submatrix obtained by shifting 1 or 0 elements of the same shape in the row direction can be obtained in any of the cut out regions. Therefore, if a puncture pattern with good characteristics is designed by paying attention to only a partial matrix corresponding to one puncture block of a parity check matrix, a puncture pattern with good characteristics for a parity check matrix of an arbitrary code length Will be able to.

・ Step C ・ 2:
A partial matrix for determining a puncture pattern is cut out from the parity check matrix. Specifically, first, the parity check matrix is partitioned in puncture blocks in the column direction. Further, the parity check matrix is divided in the row direction in units corresponding to the length L _p of the puncture pattern. In this way, the parity check matrix is partitioned in a lattice pattern. Focusing on a grid including one or more elements in each column among the partitioned grids, a grid block partitioned by the grid is selected. Then, the partial matrix is cut out so that all the lattice blocks including one or more elements of 1 are included in the same row as the selected lattice block.

  In the example shown in FIG. 12, among the divided grids, the grid blocks 821 and 822 including one or more elements in each column are selected and selected, and one element is placed in the same row as the grid blocks 821 and 822. The partial matrix indicated by a frame 860 so as to include one or more lattice blocks 840 and 850 is used as a partial matrix for determining a puncture pattern. A puncture pattern is determined using this partial matrix.

・ Step C ・ 3:
Using the submatrix extracted in Step C · 2, for each possible puncture pattern, how many Sum-Product decoding processes are required before calculation can be performed using the reliability of all bits in each row. To evaluate. Then, the puncture pattern with the least number of required Sum-Product decoding processes is selected as the optimum puncture pattern. When there are a plurality of puncture patterns having the same number of required Sum-Product decoding processes, the pattern having the smallest average value of the required number of processes for each row is selected. If there are information bits whose reliability cannot be calculated no matter how many times the Sum-Product decoding process is repeated, the puncture pattern is inappropriate. If only information bits need to be decoded and there is no need to decode parity bits, there may be parity bits for which reliability cannot be calculated.

  A method for determining a puncture pattern will be specifically described with reference to FIG. FIG. 13 shows [1] Z = (1, 0, 1, 1, 1) as a puncture pattern for the coding rate 6/5 with respect to the partial matrix 860 cut out from the parity check matrix of FIG. 1, 1), [2] Z = (1, 1, 1, 0, 1, 1), [3] Z = (1, 1, 1, 1, 1, 0) three puncture patterns are applied In this case, it is shown which column element reliability information is no longer received by the receiving device. In FIG. 13, the shaded columns indicate punctured bit sequences. FIG. 13 shows an example in which the puncture pattern Z removes (punctures) one parity bit from the puncture block. FIGS. 13A, 13B, and 13C each show that the puncture pattern Z is [1]. ], [2], [3] are shown.

When attention is paid to the fourth row of [1], in this row, all the bits in which reliability information is not received by puncturing (locations where 1 is set in the puncture pattern Z) are 0. Since all the bits that are set to 1 in the 4th row are bits that are transmitted without being punctured on the transmission side (locations where 0 is set in the puncture pattern Z), the reliability information is received, and Sum A value other than 0 is obtained as the initial value β ⁽⁰⁾ _mn of the log likelihood ratio in -Product decoding. That is, in the fourth row of [1], reliability information α ⁽¹⁾ _{mn is set} to 0 for all bits that are set to 1 in the parity check row at the time when the first row processing of Sum-Product decoding is started. It can be updated with a value other than.

When attention is paid to the first row of [1], only one of the bits in which 1 is set is punctured. That is, the reliability information of the puncture bit is not obtained at the time when the first row processing of Sum-Product decoding is started, and 0 is set to the initial value β ⁽⁰⁾ _mn . Therefore, in the first row processing of the first row, the reliability information α ⁽¹⁾ _mn of the bits that are set to 1 other than the puncture bits are all 0. However, since the puncture bits reliability information is not obtained is only one in this line, the reliability information alpha ⁽¹⁾ of the puncture bits _mn is the other non-zero bits reliability information alpha ^{(1 )} Can be updated with a value other than 0 using _mn .

Therefore, the entire matrix [1] includes at least one reliability information α ⁽¹⁾ _mn that takes a value other than 0 for all the columns, so that the first column processing is performed. , All β ⁽¹⁾ _mn can be updated with a value other than zero. As a result, in the second row processing, the reliability information α ⁽¹⁾ _mn can be updated with a value other than 0 for all bits even in the first row.

In FIG. 13A, J indicates the number of elements to be removed by the puncture pattern in each row, J = 0 in the fourth row, and reliability for all the bits that are set to 1 in the parity check row. Information α ⁽¹⁾ means that _mn can be updated with a value other than 0. In the first row, J = 1, which means that there is one puncture bit in the first row for which reliability information cannot be obtained in the first row processing of the first row.

  On the other hand, as shown in FIG. 13B, when [2] is used as the puncture pattern Z, the number J of elements removed by the puncture pattern in each row is J = 1 or J = 2. The value is larger than 13A. Similarly, as shown in FIG. 13C, even when [3] is used as the puncture pattern Z, the number J of elements removed by the puncture pattern in each row is J = 1 or J = 2. The value is larger than.

Therefore, in the case of using the pattern of [2] and [3] as the puncturing pattern Z, throughout the matrix, by performing a second string processing, updating all β a ⁽²⁾ _mn at a value other than 0 Will be able to.

  In this way, for all possible puncture pattern candidates, the number (number of elements J) in which 1 on the parity check matrix is punctured is counted, and a puncture pattern with a small count number is selected. A puncture pattern with the smallest number of Sum-Product decoding processes required to obtain bit reliability information of each row can be selected. In the example described above, the puncture pattern [1] is the optimum pattern.

Incidentally, in the puncture pattern of [1], the rows where J = 0 (the fourth and eighth rows) are the second parity check row vectors (c _{2, j} and c) described in the first embodiment. _{2, j + 3} ). That is, by adding the second parity check row vector, it is possible to obtain a characteristic improvement effect that makes it possible to update the reliability information of all bits with a small number of Sum-Product decoding processes.

  That is, by adding a second parity check expression based on a check expression equivalent to the first parity check expression, it becomes possible to use reliability information of other bits, so that a transmission code is transmitted on the encoding side. Even when a word is punctured, the influence of the puncture can be dispersed, and a characteristic improvement effect can be obtained.

  By using the puncture pattern obtained as described above as the puncture pattern of puncture section 620, receiving apparatus 700 of the present embodiment can obtain high decoding characteristics with a small number of Sum-Product decoding processes.

  As described above, according to the present embodiment, convolutional coding section 610 performs error correction coding using a convolutional code to obtain a transmission codeword sequence, and puncturing section 620 performs decoding BP decoding. The transmission codeword sequence acquired by the convolutional encoding unit 610 is punctured using a puncture pattern based on the pattern of the parity check matrix used.

  Using a first row element defined by a first parity check polynomial of a convolutional code and a second row element defined by a second parity check polynomial of a convolutional code that is equivalent to the first parity check polynomial By using the puncture pattern based on the pattern of the parity check matrix to be formed, the decoding side can obtain the reliability information of the bits erased by the puncture using the reliability information of other bits. Decoding is possible with a small number of Sum-Product decoding processes. In addition, the probability can be propagated from any one bit having 1 in the first parity check row to another bit having 1 in the second parity check row. Decoding characteristics can be obtained.

  In addition, by selecting a puncture pattern from patterns that do not delete “1” on the parity check matrix as much as possible, the number of iterations for obtaining the likelihood of a codeword required at the time of BP decoding is minimized. Can do.

  In the communication system to which transmitting apparatus 600 and receiving apparatus 700 according to the present embodiment are applied, when the communication system includes a plurality of puncture patterns and the puncture patterns are switched, a plurality of types of parity check rows are displayed. In addition to the parity check matrix, no matter which puncture pattern is used, at least one type of row has one or less bits that become puncture bits among the bits that are set to 1 in the row. By using a puncture pattern as a pattern, a good decoding characteristic can be obtained regardless of which puncture pattern is used.

  That is, for all information bits, in the set of rows where 1 is set in the information bits, at least one row where 1 is set and the number of punctured bits is 1 bit at most If the puncture pattern exists, good decoding characteristics can be obtained.

  Here, if the parity check polynomial used to create the parity check matrix has only a long constraint length, when punctured coding is applied, two bits with 1 standing in one check row The possibility of being punctured becomes higher. Therefore, it is preferable to use a combination of a parity check polynomial having a long constraint length and a parity check polynomial having a short constraint length. In this way, the reliability information of all bits including puncture bits is updated with a value other than 0 using a parity check row with a short constraint length, and the reliability information of all bits becomes a value other than 0. Thereafter, a high coding gain can be obtained by a parity check row having a long constraint length, and good decoding characteristics can be obtained.

  Further, the bits erased by the puncture in the puncture block are not limited to 1 bit, and a plurality of bits may be punctured.

  The present invention is not limited to the embodiment described above, and can be implemented with various modifications. For example, in the above embodiment, the case of performing as a transmission device or a reception device has been described. However, the present invention is not limited to this, and this encoding method or decoding method can also be performed as software.

  The decoding device, the encoding device, the decoding method, and the encoding method according to the present invention are useful as a decoding device, an encoding device, a decoding method, and an encoding method in a communication system to which a convolutional code is applied. It is.

Block diagram showing the configuration of an encoder of (7,5) _8- convolutional code with coding rate R = 1/2 The figure which shows an example of a parity check matrix The figure which shows the general example of a parity check matrix The block diagram which shows an example of a structure of the decoding part which performs Sum-Product decoding The figure which shows an example of the parity check matrix in this Embodiment 1. FIG. FIG. 10 is a diagram illustrating another example of the parity check matrix in the first embodiment. The figure which shows an example of the Tanner graph in the prior art and Embodiment 1 FIG. 5 is a diagram for explaining the time point i at which the second parity check row is added. The block diagram which shows the structure of the transmitter which concerns on this Embodiment 2. FIG. FIG. 9 is a block diagram showing a configuration of a receiving apparatus according to the second embodiment. The figure which uses for description of the puncture process of the puncture part which concerns on Embodiment 2. FIG. FIG. 10 is a diagram illustrating an example of a parity check matrix in Embodiment 2. Diagram for explaining how to determine the puncture pattern

Explanation of symbols

300,770 Decoding unit 303 Log likelihood ratio storage unit 305 Row processing calculation unit 307 Row processed data storage unit 309 Column processing calculation unit 311 Column processing data storage unit 313 Control unit 315 Log likelihood ratio calculation unit 317 Determination unit 319 Check matrix storage unit 600 Transmitting device 610 Convolutional coding unit 620 Puncture unit 630 Interleaving unit 640 Modulating unit 650 Radio transmitting unit 660 Control information generating unit 670 Transmitting antenna 700 Receiving device 710 Receiving antenna 720 Radio receiving unit 730 Demodulating unit 740 Deinterleaving unit 750 Depuncture unit 760 Control information detection unit

Claims (11)

A decoding device that performs BP (Belief Propagation) decoding,
A first row element defined by a first check polynomial of a convolutional code; and a second row element defined by a second check polynomial of the convolutional code that is equivalent to the first check polynomial. Storage means for storing a parity check matrix formed by using;
Decoding means for performing BP decoding on the code word sequence generated by the convolutional code on the encoding side using the parity check matrix;
A decoding device comprising: If parity sequence length generated by the convolutional code of I _N, the parity check matrix is configured with the first row element of I _N rows, from said second row elements of a smaller number of rows than I _N rows The decoding device according to claim 1. The decoding apparatus according to claim 1, wherein a constraint length of the first check polynomial is different from a constraint length of the second check polynomial. The second row elements on the parity check matrix are spaced apart by intervals T _A from each other,
The interval T _A is the decoding apparatus according to a short claim 1 than the constraint length of the first check polynomial. The second row elements on the parity check matrix are spaced apart by intervals T _A from each other,
The interval T _A is the decoding apparatus according to claim 1 which is an integral fraction of the puncturing pattern length used on the encoding side. An encoding device that generates a codeword sequence decoded using BP (Belief Propagation) decoding on a decoding side,
Convolutional coding means for generating a codeword sequence by a convolutional code;
Puncturing means for puncturing the codeword sequence using a puncture pattern based on a parity check matrix pattern used in BP decoding on the decoding side;
An encoding device comprising: The parity check matrix is defined by a first row element defined by a first check polynomial of the convolutional code and a second check polynomial of the convolutional code equivalent to the first check polynomial. The encoding device according to claim 6, wherein the matrix is formed using two row elements. The encoding apparatus according to claim 7, wherein the second parity check polynomial includes an order included in the first parity check polynomial and an order included in the second parity check polynomial as little as possible. The encoding apparatus according to claim 6, wherein the puncture pattern is a pattern that does not delete as many bits as “1” on the parity check matrix. A decoding method for performing BP (Belief Propagation) decoding,
A first row element defined by a first check polynomial of a convolutional code; and a second row element defined by a second check polynomial of the convolutional code that is equivalent to the first check polynomial. The decoding method which performs BP decoding with respect to the codeword sequence produced | generated by the said convolutional code by the encoding side using the parity check matrix formed by using. A coding method for generating a codeword sequence decoded using BP (Belief Propagation decoding) on the decoding side,
A codeword sequence is generated by a convolutional code,
An encoding method for performing puncturing using a puncture pattern based on a parity check matrix pattern used in BP decoding on the decoding side.

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