KR101718543B1 - Apparatus and method for decoding using improved bit-flipping algorithm for low density parity check code and recording medium for the same - Google Patents

Abstract

A decoding method for an LDPC code (Low Density Parity Check Code) code is disclosed. The decoding method for an LDPC code code includes an initializing step of initializing a number of decoding iterations, a weight calculating step of calculating a weight of each check node from a received signal, an inverse function value calculating step of calculating an inverse function value using the weight, A reliability updating step of comparing the inverse function value with a threshold value to invert the hard decision value and updating the reliability of the variable node by adjusting a value of the received signal; A codeword step of outputting a hard decision vector based on the hard decision value as a codeword if the syndrome vector is 0; and a codeword step of, if the syndrome vector is not 0, . The decoding method according to the present invention can provide high error correction performance by updating reliability of a variable node based on a bit inversion algorithm.

Description

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a decoding method, apparatus, and recording medium for a low-density parity check code based on an improved bit inversion algorithm,

The present invention relates to a high-performance decoding method, apparatus, and recording medium for a low-density parity check code, and more particularly to a decoding method, apparatus, and recording medium having a high error correction performance by updating reliability of a variable node based on a bit- Media.

Low Density Parity Check (LDPC) codes have been recently studied because of their excellent decoding performance. A decoding method of an LDPC code can be broadly divided into a sum-product algorithm (hereinafter referred to as SPA) and a bit-flipping (hereinafter referred to as BF) algorithm. SPA can have a decoding performance close to the channel capacity limit of a new year (Shannon) by using a message passing algorithm such as a belief propagation (BP) algorithm as an error correction code. However, the decoder using the SPA has a problem that the complexity required for decoding is very high. On the other hand, the BF algorithm is the simplest algorithm for constructing the LDPC code, and it can be implemented as a modular -2 addition by repeatedly performing the parity check operation. Therefore, the complexity required for decoding is lower than other algorithms, Ability is lower than BP.

Therefore, research is continuously carried out to improve error correction capability without increasing the complexity.

The present invention provides a decoding method and apparatus for a low density parity check code having a high error correction performance and a small number of iterative decoding times.

It is another object of the present invention to provide a method and apparatus for decoding an LDPC code using a BF decoding method using reliability update of a variable node.

According to another aspect of the present invention, there is provided a decoding method for a low-density parity-check code, the decoding method comprising: initializing a decoding repetition number; calculating a weight of each check node from a received signal; A reliability updating step of comparing the inverse function value with a threshold value to invert the hard decision value and to update the reliability of the variable node by adjusting the value of the received signal, A parity check step of calculating a syndrome vector using reliability, a codeword step of outputting a hard decision vector based on the hard decision value as a codeword if the syndrome vector is 0, and a codeword step of, if the syndrome vector is not 0, And a feedback step of feeding back to the weight calculation step.

The reliability updating step for achieving the above object includes a comparison step for comparing whether the inverse function value has a value larger than the threshold value, an inversion step for inverting the hard decision value if the inverse function value is larger than a threshold value, And a vector updating step of updating the hard decision vector using the value of the adjusted received signal.

The adjusting step may include adding an adjustment value to the value of the reception signal to generate the adjusted reception signal.

The initializing step for achieving the above object is characterized by including a reset step of resetting the number of decoding iterations to an initial value, and a setting step of setting the maximum number of decoding iterations.

The feedback step for achieving the above object is characterized by including a declaring step of declaring that decoding of the LDPC code code is unsuccessful if the number of times of decoding is equal to the maximum number of iterations of decoding and a step of deciding that the decoding iteration number is less than the maximum number of iterations And incrementing the number of repetition times by one to feed back to the weight calculation step.

According to another aspect of the present invention, there is provided a decoding apparatus for an LDPC code, comprising: a receiver for receiving an LDPC signal applied in various forms from an external source and converting the received LDPC signal into a digital code; receiving the LDPC signal from the receiver; A decoding unit for decoding the LDPC signal by inverting the hard decision value according to the calculated inverse function value, and a decoding unit for decoding the LDPC signal received from the decoding unit, And a codeword output unit for outputting a code suitable for a predetermined interface.

The decoding unit for achieving the other object includes a weight calculator for initializing a repetition number, setting a maximum repetition number, and calculating the weight from the LDPC signal when the LDPC signal is applied, Calculating a function value, determining whether the calculated inverse function value is greater than a specified threshold value, inverting the hard decision value if the calculated inverse function is greater than a specified threshold value, and performing an inverse function calculation A reliability updating unit for updating the hard decision vector in accordance with the adjusted LDPC signal when the hard decision value is inverted; and a reliability updating unit for calculating a syndrome vector using the updated hard decision vector, , And outputs the updated hard decision vector as a codeword.

The decoding method for a low density parity check code according to the present invention can provide a decoder having a low bit error rate with a small number of iterative decoding times because it has high error correction performance by updating the reliability of a variable node based on a bit inversion algorithm.

1 is a diagram illustrating an example of a parity check matrix of an LDPC code according to the present invention.
FIG. 2 is a diagram showing a parity check matrix of the LDPC code of FIG. 1 as an argument graph.
3 is a diagram illustrating an example of parity check node update in FIG.
4 is a diagram showing an example of the variable node update in Fig.
5 is a flowchart illustrating a decoding process according to an embodiment of the present invention.
6 is a simulation graph showing bit error rate performance of a decoder according to the present invention.
FIG. 7 is a simulation graph showing the average number of iterative decoding times of the decoder according to the present invention.
8 is a diagram illustrating a decoding apparatus for an LDPC code according to an embodiment of the present invention.

For a better understanding of the present invention and operational advantages of the present invention and the objects attained by the practice of the present invention, reference should be made to the accompanying drawings, which illustrate embodiments of the present invention, and to those described in the accompanying drawings.

Hereinafter, the present invention will be described in detail with reference to embodiments of the present invention with reference to the accompanying drawings. However, the present invention can be implemented in various different forms, and is not limited to the embodiments described. In order to clearly describe the present invention, parts that are not related to the description are omitted, and the same reference numerals in the drawings denote the same members.

Throughout the specification, when an element is referred to as " including " an element, it does not exclude other elements unless specifically stated to the contrary. The terms "part", "unit", "module", "block", and the like described in the specification mean units for processing at least one function or operation, And a combination of software.

FIG. 1 is a diagram illustrating an example of a parity check matrix of an LDPC code according to the present invention, and shows a parity check matrix 100 (H) of an M X N size.

In FIG. 1, N in the parity check matrix 100 (H) denotes the number of columns, the length of a codeword, and M the number of rows, which indicates the number of parity check equations. The check matrix of the LDPC code is characterized in that the number of 1's is less than the number of 0's.

FIG. 2 is a diagram showing a parity check matrix of the LDPC code of FIG. 1 by using an argument graph (Tanner Graph).

Referring to FIG. 2, variable nodes 201 to 208 represent columns in the parity check matrix 100 (H). The check nodes 211 to 214 represent a row in the parity check matrix 100 (H). In the argument graph 200, each node is connected via an edge. Here, the edge is determined by the position of an element other than '0' in the parity check matrix 100. If the check node c _i and the variable node v _j are connected through an edge, the element h _ij in the parity check matrix 100 has a value other than '0'. For example, when the check node (c ₀ ) 211 and the variable node (v ₃ ) 204 are connected through an edge, the element h ₀₃ of the parity check matrix 100 has a value other than '0' .

The number of edges connected to a particular node is called the degree of that node. When the order of the variable nodes 201 to 208 is constant at d _v and the order of the check nodes 211 to 214 is constant at d _c , the LDPC code at this time is called a Regular LDPC code. That is, if the number of elements having a value of 1 in each row of the parity check matrix 100 is the same and the number of elements having a value of 1 in each column is the same, the LDPC code is a regular LDPC code. On the other hand, the LDPC code in the case where the variable node degree (d _v ) and the check node degree (d _c ) are not constant is called an irregular LDPC code. The parity check matrix 100 shown in FIG. 1 is a regular LDPC code because the order d _v of the variable nodes is second order and the order of the check nodes d _c is fourth order constant.

The BP decoder proposed by Galgarder is one of the iterative message passing algorithms and it is decoded by exchanging messages through the edge connecting the variable node and the parity check node. At this time, the decoding process occurring in each node is called a node update. In all decoding iterations, each node exchanges messages with neighbors connected to the node through the edge using the message received in the previous iteration.

3 is a diagram showing an example of check node update in FIG. In FIG. 3, the check node (c ₀ ) 211 among the check nodes 211 to 214 is shown as an example. The check nodes (c _0), (211) as shown in Figure 3 is received is the message (q _10, q _30, q ₄₀₎ from the variable nodes (202, 204, 205), a message of a check node (r ₀₇₎ And outputs it to the variable node 208.

Referring to FIG. 2 and FIG. 3, the message of each check node c _i is updated as shown in Equation (1).

In Equation (1), q _i'j is a message of the variable nodes connected through the edge of the check node c _i . Also i'∈R _j\i indicates an index of all the elements with 1 in the j row of the parity check matrix (100).

Fig. 4 is a diagram showing an example of the variable node update of Fig. 2, in which the variable node (v ₁ ) 202 of the variable nodes 201 to 208 is shown as an example. 4, the variable node v ₁ 202 receives the message r ₀₀ from the check node 211, updates the message q ₁₁ of the variable node, and outputs it to the check node 212 do. 2 and 4, the message of each variable node v _j is updated as shown in equation (2).

In Equation (2), r _j'i is a message of the check nodes connected through the variable node v _j and the edge, and _{j '} C _ij' in Equation (2) is a message having i in the i column of the parity check matrix 100 Indicates the index of all elements. Where p _i represents the posterior probability estimate for each element.

As described above, the decoding method of the LDPC code can be largely divided into a sum-product algorithm (hereinafter referred to as SPA) and a BF algorithm.

In the BF algorithm, a hard decision vector (z _i ) can be obtained from a signal y _i received from a channel according to Equation (3).

)가 결정되고, 수학식 4에 따라 신드롬 벡터(syndrome vector)(

)를 구할 수 있다.The BF algorithm calculates a hard-decision value (z _i ) of 0 or 1 since it attempts to decode a signal strictly determined to be 0 or 1 when decoding the LDPC code. When the hard decision value z _i is calculated by Equation (3), the hard decision vector

) Is determined, and a syndrome vector (

) Can be obtained.

On the other hand, SPA attempts to decode a signal having a multilevel value in a real number range, and thus calculates a soft-decision value.

)를 이용하여 가변 노드에 연결된 검사 노드 들 중 패리티 검사 식을 만족하지 않는 검사 노드가 지정되 개수 이상일 경우에 가변 노드를 반전시킨다. 즉 BF 알고리즘은 경판정 벡터(

)를 이용하여 복호 동작을 수행한다.The BF algorithm is a neural network vector obtained at the check node (

), The variable node is inverted when the number of check nodes that do not satisfy the parity check equation among the check nodes connected to the variable node is more than the designated number. That is, the BF algorithm uses a hard decision vector (

) To perform a decoding operation.

A weighted bit-flipping (WBF) algorithm has been proposed as an attempt to improve the performance of the BF algorithm. Although the BF algorithm proposed by Galgardi gives equal weight to all the parity check equations, the WBF algorithm that improves the parity check equation gives the parity check equation with the smallest signal among the bits involved in each check as a weight of the parity check equation, The reliability of the system is differentiated.

The weight w _ji for the i-th variable node of the jth check node in the WBF algorithm can be expressed by Equation (5).

The IMWBF (Improved Modified Weighted Bit-Flipping) algorithm that improves the WBF algorithm differs from WBF in that it performs weighting by weighting the check equation, but decides the weight value. That is, the WBF algorithm uses all the information of the bits connected to each check, while the IMWBF algorithm receives the message after removing the information provided from itself. Therefore, it improves the performance by using the signal received from the channel more actively than the WBF algorithm.

However, since the reliability of the WBF algorithm and the IMWBF algorithm are kept the same throughout the decoding process, the information that the nodes obtain from the decoding process is very limited. That is, when the error bit is inverted at the check node having the error bit, the reliability of the check node should be improved. However, since the WBF algorithm and the IMWBF algorithm use the same weight for the entire decoding, There is a problem. Also, since only bits having the largest inverse function value are inverted in one iteration decoding, most of the newly obtained information is wasted.

5 is a flowchart illustrating a decoding process according to an embodiment of the present invention.

A decoding method for a bit reversal algorithm based high-performance low-density parity check code according to the present invention includes a decoder for decoding an LDPC code in a receiving apparatus by using a BF decoding method for updating the reliability of a variable node.

The decoder initializes the number of iterations k to zero and sets the maximum number of iterations k _{max at the} time of initialization (S11). Then, all the weights w _ji are calculated from the received signals according to Equation (5) (S13). When the weight is calculated, the inverse function value E _j is calculated according to Equation (6) (S15).

It is determined whether or not the inverse function value E _j calculated according to Equation (6) is larger than the specified threshold value? (S17). Where a is a positive real number with an optimal value according to the signal-to-noise ratio (SNR). If the calculated inversion function E _j is larger than the specified threshold value?, The hard decision value z _i is inverted and the value of the received signal is adjusted as shown in Equation (7).

)를 수학식 3에 의해 갱신한다(S19). 여기서 조절값(β)은 양의 정수이다.Then, according to the value y _i of the adjusted received signal,

(S19). &Quot; (3) " Here, the adjustment value? Is a positive integer.

If the calculated inversion function E _j is not larger than the specified threshold value?, The hard decision value z _i is not inverted.

)를 수학식 4에 적용하여, 신드롬 벡터(

)를 계산한다(S21). 계산된 신드롬 벡터(

)가 0 벡터이면, 경판정 벡터(

)를 부호어로서 출력하고 복호를 성공적으로 종료한다(S23). 그러나 계산된 신드롬 벡터(

)가 0 벡터가 아니면, 반복 횟수(k)가 최대 반복 횟수(k_max)에 도달하였는지 확인한다(S25).An updated hard decision vector (< RTI ID = 0.0 >

) Is applied to Equation (4), the syndrome vector (

Is calculated (S21). The calculated syndrome vector (

) Is a 0 vector, a hard decision vector (

) As a codeword and successfully ends the decoding (S23). However, the calculated syndrome vector (

) Is not a 0 vector, it is checked whether the number of repetitions k has reached the maximum number of repetitions (k _max ) (S25).

If the number of repetitions k has reached the maximum number of repetitions k _max , the decoder declares decryption failure and ends the decoding (S27). (S13) of adding 1 to the repetition count (k) and calculating all the weights w _ji from the received signal according to Equation (5) if the repetition number of times (k) is smaller than the maximum repetition number (k _max ) (S29).

6 is a simulation graph showing bit error rate performance of a decoder according to the present invention.

Referring to FIG. 6, the code used is R = 0.83, the length N of the codeword is 1944, and the maximum number of iterative decoding k _max is 200 times. The modulation scheme used here is BPSK (Binary Phase Shift Keying) and shows performance in an additive white Gaussian noise (AWGN) channel environment.

FIG. 7 is a simulation graph showing the average number of iterative decoding times of the decoder according to the present invention.

Referring to FIG. 7, the code used is R = 0.83, the code length N = 1944, and the maximum number of iterative decoding k _max is 200, as in FIG. The modulation scheme used here is BPSK (Binary Phase Shift Keying), which shows performance in an additive white Gaussian noise channel environment.

As shown in FIG. 6 and FIG. 7, the decoding method of the high performance LDPC code based on the bit inversion algorithm according to the present invention shows a lower bit error rate than the conventional decoder and can provide a small number of iterative decoding times.

8 is a diagram illustrating a decoding apparatus for an LDPC code according to an embodiment of the present invention.

8, the decoding apparatus includes a receiving unit 100, a decoding unit 200, and a codeword output unit 300. The decoding unit 10 shown in FIG. The receiving unit 100 receives an LDPC signal (LDPC) applied in various forms from the outside, converts the LDPC signal into a digital code, and outputs the digital code to the decoding unit 200.

The decoding unit 200 receives the LDPC signal y _LDPC converted into the digital code from the receiving unit 100 and performs a decoding operation according to the decoding method shown in Fig. The decoding unit 200 includes a weight calculation unit 210, an inverse function calculation unit 220, a reliability update unit 230, and a parity check unit 240. First, when the LDPC signal y _LDPC is applied from the receiver 100, the weight calculator 210 initializes the repetition number k to 0 and sets the maximum repetition number k _max . Then, all the weights w _ji are calculated from the received LDPC signal y _LDPC according to Equation (5).

The inverse function calculating unit 220 calculates the inverse function value E _j according to Equation (6) using the weight calculated by the weight calculating unit 210. The inverse function calculating unit 220 further determines whether the calculated inverse function value E _j is larger than the specified threshold value 隆 and if the calculated inverse function E _j is larger than the specified threshold value 隆, The value (z _i ) is inverted and the value of the received signal is adjusted as shown in Equation (7).

)를 수학식 3에 따라 갱신한다.The reliability updating unit 230 updates the reliability of the hard decision vector z _i according to the value y _i of the received signal adjusted when the hard decision value z _i is inverted.

) Is updated according to Equation (3).

)를 수학식 4에 적용하여, 신드롬 벡터(

)를 계산하고, 계산된 신드롬 벡터(

)가 0 벡터이면, 경판정 벡터(

)를 부호어 출력부(300)로 출력한다.The parity check unit 240 receives the hard decision vector (

) Is applied to Equation (4), the syndrome vector (

), And calculates the calculated syndrome vector (

) Is a 0 vector, a hard decision vector (

) To the codeword output unit (300).

The codeword output unit 300 converts a successfully decoded codeword into a code of a form suitable for an external device and outputs the code. That is, the codeword is converted into a code suitable for an interface with an external device and output.

While the present invention has been particularly shown and described with reference to exemplary embodiments thereof, it is evident that many alternatives, modifications and variations will be apparent to those skilled in the art.

Accordingly, the true scope of the present invention should be determined by the technical idea of the appended claims.

Claims (14)

A decoding method for an LDPC code (Low Density Parity Check Code) code,
An initializing step of initializing the number of times of decoding;
A weight calculation step of calculating a weight of each check node from the received signal;
An inverse function value calculation step of calculating an inverse function value using the weight value;
A reliability updating step of comparing the inverse function value with a threshold value to invert the hard decision value and to update the reliability of the variable node by adjusting the value of the received signal;
A parity check step of calculating a syndrome vector using the reliability of the updated variable node;
A codeword step of outputting as a codeword a hard decision vector based on the hard decision value if the syndrome vector is 0; And
And if the syndrome vector is not 0, feedback to the weight calculation step according to the number of decoding iterations.
2. The method of claim 1, wherein the reliability updating step
Comparing the inverse function value with a value larger than the threshold value;
An inversion step of inverting the hard decision value if the inverse function value is larger than a threshold value;
An adjusting step of adjusting a value of the received signal; And
And a vector updating step of updating the hard decision vector using the adjusted received signal value.
3. The method of claim 2,
And adding the adjusted value to the value of the received signal to generate the adjusted received signal.
4. The method of claim 3, wherein the initializing step
A reset step of resetting the number of decoding iterations to an initial value; And
And a setting step of setting a maximum number of decoding iterations.
5. The method of claim 4, wherein the feedback step
A declaring step of, when the number of decoding iterations is equal to the maximum number of iterations, declaring that decoding of the LDPC code code has failed; And
And a repetition number increasing step of incrementing the number of decoding iterations by 1 and feeding back to the weight calculating step if the number of decoding iterations is smaller than the maximum number of iterations.
2. The method of claim 1, wherein the weight calculation step
The weight (w _ji )

(Where yi 'represents the received signal and i'∈C j \ _i' represents the index of all elements having 1 in the j-th column of the parity check matrix.)
And decodes the LDPC code.
7. The method of claim 6, wherein the inverse function value calculation step
The inverse function value (E _j )

(Where i? _R j? _{I '} denotes an index of all elements having a 1 in j rows of the parity check matrix, S _j denotes a syndrome vector,? _Denotes a signal-to-noise (SNR), which represents a positive real number with a different optimal value.
And decodes the LDPC code.
8. A computer-readable recording medium on which program instructions for performing a decoding method for an LDPC code code according to any one of claims 1 to 7 are recorded.
A receiving unit for receiving an LDPC signal applied in various forms from the outside and converting the received LDPC signal into a digital code and outputting the converted digital code;
Receives the LDPC signal from the receiver, calculates a weight w _ji from the LDPC signal, calculates an inverse function using the calculated weight value, inverts the hard decision value according to the calculated inverse function value, A decoder for decoding the signal; And
And a codeword output unit for receiving and outputting the LDPC signal decoded by the decoding unit,
_Wherein the weight w _ji is a weight for an i th variable node of a j th check node in the WBF algorithm.
10. The apparatus of claim 9, wherein the decoding unit
A weight calculation unit for initializing a repetition number, setting a maximum repetition number, and calculating the weight from the LDPC signal when the LDPC signal is applied;
Determining whether the calculated inverse function value is greater than a specified threshold value, inverting the hard decision value if the inverse function is greater than a specified threshold value, An inverse function calculator for adjusting the LDPC signal;
A reliability updating unit for updating the hard decision vector according to the adjusted LDPC signal when the hard decision value is inverted; And
And a parity check unit for calculating a syndrome vector using the updated hard decision vector and outputting the updated hard decision vector as a codeword if the calculated syndrome vector is a 0 vector. .
11. The apparatus according to claim 10,
The weight (w _ji )

(Where yi 'represents the received signal and i'∈C j \ _i' represents the index of all elements having 1 in the j-th column of the parity check matrix.)
And decodes the LDPC code.
11. The apparatus of claim 10, wherein the inverse function calculation unit
The inverse function value (E _j )

(Where i? _R j \ _{i '} represents the index of all elements having a 1 in the j-th row of the parity check matrix)
And decodes the LDPC code.
The apparatus of claim 10, wherein the parity checker
And if the syndrome vector is not a 0 vector, it is determined whether the repetition number is greater than or equal to the maximum repetition number. If the repetition number is less than the maximum repetition number, the adjusted LDPC signal is applied to the weight calculation unit. And outputs a decoding failure signal if the number of times is greater than or equal to the maximum number of repetitions.
A computer-readable recording medium recording a program for causing a computer to function as a decoding apparatus for an LDPC code according to any one of claims 9 to 13.

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