CN111416627A - L DPC decoding method based on simplified BP algorithm - Google Patents
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- H03M13/03—Error detection or forward error correction by redundancy in data representation, i.e. code words containing more digits than the source words
- H03M13/05—Error detection or forward error correction by redundancy in data representation, i.e. code words containing more digits than the source words using block codes, i.e. a predetermined number of check bits joined to a predetermined number of information bits
- H03M13/11—Error detection or forward error correction by redundancy in data representation, i.e. code words containing more digits than the source words using block codes, i.e. a predetermined number of check bits joined to a predetermined number of information bits using multiple parity bits
- H03M13/1102—Codes on graphs and decoding on graphs, e.g. low-density parity check [LDPC] codes
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Abstract
The invention relates to a L DPC decoding method based on a simplified BP algorithm, which belongs to the technical field of wireless communication, realizes simplification of the BP algorithm, reduces complexity of L DPC decoding, can adapt to the standard of 5G NR, applies a piecewise linear approximation function generated by an equal error linear approximation principle to replace a nonlinear function in updating of check nodes in the BP algorithm, and the improved BP algorithm only contains multiplication and addition, thereby reducing complexity of hardware realization of the BP algorithm in a 5G terminal.
Description
Technical Field
The invention belongs to the technical field of wireless communication, and relates to an L DPC decoding method based on a simplified BP algorithm.
Background
The purpose of communication is to deliver source information to a sink via a channel with high efficiency and reliability, so that the receiving end reproduces the output of the source accurately or with a given degree of distortion. Wireless communication is an important component in modern communication, and through decades of developments, wireless communication begins from analog communication of the first generation wireless communication system (1G), and has been greatly developed through 2G, 3G and 4G digital communication, and by now, 5G has become a research focus of modern communication technology, and gradually enters into a commercial deployment stage.
In order to meet the requirement of 5G ultra-large data throughput in an eMB scene, the Third Generation Partnership Project (3 GPP) confirms that a coding method of a 5G New air interface (New radio) data channel in the eMB scene is low-density parity check code (L ow-density parity-check, L DPC), and a coding method of a control channel is Polar code (Polar code). on the basis, a Quasi-Cyclic L DPC (Quasi-Cyclic DPC L DPC, QC-L) coding mode of L DPC is introduced into a data channel of 5G NR, and meanwhile, a QC-L structure is confirmed in a related standard of 3 GPP.
L DPC decoding algorithm can be divided into hard decision algorithm and soft decision algorithm according to decision mode, the hard decision algorithm is generally Bit Flipping (BF) algorithm and its improved algorithm, the hardware implementation of the algorithm is simple, but its decoding performance is weak, the soft decision algorithm is Belief Propagation (BP) algorithm based on Message Passing (MP) algorithm, which is the most primitive soft decision decoding algorithm of L DPC and has excellent decoding performance approaching to Shannon limit.
The 3GPP standard has already defined the structure and encoding process of 5 GQC-L DPC, and therefore, the research on the decoding of the DPC is also intensive, and in order to ensure the high requirements of 5G on power consumption, cost and the like, L DPC decoding also needs to be implemented with low complexity and can meet various scene requirements of 5G.
In summary, the L DPC decoding algorithm needs to achieve low complexity and excellent decoding performance, satisfy the 5G NR correlation standard in wireless communication, and be able to adapt to other L DPC codes.
Disclosure of Invention
In view of this, the present invention aims to provide an L DPC decoding method based on a simplified BP algorithm, which reduces the decoding complexity of the BP algorithm, can maintain a better decoding performance, can meet the requirement of a 5G terminal on high throughput, and overcomes the defects of high complexity and hardware implementation difficulty of the conventional decoding algorithm.
In order to achieve the purpose, the invention provides the following technical scheme:
an L DPC decoding method based on a simplified BP algorithm, comprising the following steps:
s1, check matrix H ═ M × N, where M ═ 1,2, …, M, N ═ 1,2, …, N;
s2 initialization variable node LjInitializing to channel information, wherein j represents a jth variable node; setting iteration times;
s3: updating the variable nodes and the check nodes, and obtaining the posterior information of each layer of updated variable nodes;
s4: after each iteration is completed, posterior information of variable nodes is obtained, bit hard decision is carried out on the posterior information, and decoded code words are further obtained;
s5: and checking the decoded code word, and if the check matrix H is met or the set iteration times are reached, finishing decoding.
Optionally, in step S3, the conventional BP algorithm updates the variable nodes and the check nodes through the following equations, and obtains a posteriori information of the variable nodes updated in each iteration:
s31: processing variable nodes:
s32: and (4) check node processing:
s33: updating posterior probability:
the information obtained by the variable node is transmitted to the check node connected with the variable node through the edge of the Tanner graph, and the external information transmitted from the variable node to the check node is Lj→iThe information processed by the check node is transmitted to the variable node through the edge, and the external information transmitted to the variable node by the check node is Li→jWherein j '∈ N (i) to { j } indicates that the variable node set connected with i does not include node j, i' ∈ N (j) to { i } indicates that the check node set connected with j does not include node i;
the sum of the variable node messages is updated after one iteration is finished; after the information update is completed, the message needs to be judged.
Optionally, in step S4, the a posteriori information obtained after one iteration is completed is decoded, and if yes, the decoding decision is performed
Then
Otherwise
Thereby obtaining decoded code words
If it is not
Or stopping decoding and outputting code words when the set maximum iteration times is reached; otherwise, the next iteration is performed.
Optionally, the simplified BP algorithm is an improved BP algorithm formed by an equal-error linear approximation principle, and is used for simplifying tanh (-) and tanh when the check node is updated-1Complexity of (·).
Optionally, the equal-error linear approximation principle is implemented by the following steps:
t1: selecting a proper error, and performing piecewise fitting on a hyperbolic function of a check node of the BP algorithm;
t2: let hyperbolic tangent function y be tanhx's piecewise approximation equation as y1(x) Ax + b, tan h, and the hyperbolic arc tangent function y-1Piecewise fitting approximation equation y of x2(x)＝cx+d；
T3: determining a point on the curve, and performing piecewise fitting on the curve by using the principle of equal error approximation;
t4: obtaining a function of each piecewise line segment according to the points on the curve and the piecewise line segments, and obtaining a piecewise function of the curve, wherein the piecewise linear fit corresponding to tanh (·) is y1(x)，tanh-1(. The) the corresponding piecewise linear fit is y2(x)。
The invention has the beneficial effects that:
1) the invention reduces the complexity of the BP algorithm check node updating process and is easy to realize hardware.
2) The decoding method provided by the invention has better decoding performance than a common hard decision algorithm, can be suitable for 5GNR QC-L DPC decoding, and has the characteristics of high throughput rate and low complexity.
3) The invention has universality and can be suitable for L DPC decoding of other types and standards.
Additional advantages, objects, and features of the invention will be set forth in part in the description which follows and in part will become apparent to those having ordinary skill in the art upon examination of the following or may be learned from practice of the invention. The objectives and other advantages of the invention may be realized and attained by the means of the instrumentalities and combinations particularly pointed out hereinafter.
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For purposes of promoting a better understanding of the objects, aspects and advantages of the invention, reference will now be made to the following detailed description taken in conjunction with the accompanying drawings in which:
FIG. 1 is a flow chart of L DPC simplified BP decoding algorithm;
FIG. 2 is a schematic diagram of equal error linear approximation;
FIG. 3 is a comparison of error rates of various decoding algorithms in the case of the NR long code according to example 5G;
FIG. 4 is a comparison of error rates of various decoding algorithms in the case of the short NR code according to example 5G.
Detailed Description
The embodiments of the present invention are described below with reference to specific embodiments, and other advantages and effects of the present invention will be easily understood by those skilled in the art from the disclosure of the present specification. The invention is capable of other and different embodiments and of being practiced or of being carried out in various ways, and its several details are capable of modification in various respects, all without departing from the spirit and scope of the present invention. It should be noted that the drawings provided in the following embodiments are only for illustrating the basic idea of the present invention in a schematic way, and the features in the following embodiments and examples may be combined with each other without conflict.
Wherein the showings are for the purpose of illustrating the invention only and not for the purpose of limiting the same, and in which there is shown by way of illustration only and not in the drawings in which there is no intention to limit the invention thereto; to better illustrate the embodiments of the present invention, some parts of the drawings may be omitted, enlarged or reduced, and do not represent the size of an actual product; it will be understood by those skilled in the art that certain well-known structures in the drawings and descriptions thereof may be omitted.
The same or similar reference numerals in the drawings of the embodiments of the present invention correspond to the same or similar components; in the description of the present invention, it should be understood that if there is an orientation or positional relationship indicated by terms such as "upper", "lower", "left", "right", "front", "rear", etc., based on the orientation or positional relationship shown in the drawings, it is only for convenience of description and simplification of description, but it is not an indication or suggestion that the referred device or element must have a specific orientation, be constructed in a specific orientation, and be operated, and therefore, the terms describing the positional relationship in the drawings are only used for illustrative purposes, and are not to be construed as limiting the present invention, and the specific meaning of the terms may be understood by those skilled in the art according to specific situations.
FIG. 2 is an equal error linear approximationAccording to the schematic diagram, firstly, a piecewise linear fit of a hyperbolic function can be obtained, the error is set to be 0.02, and tanh (-) are obtained according to the steps described above-1Piecewise fitting function y of (·) nonlinear curve1(x) And y2(x)：
The example is performed under the 5G NR standard, in an actual 5G system, the check matrix of the QC-L DPC code may include structures such as code rate compatibility, parity bits, and added parity bits, which are check bits added during encoding, and the actual information bits are information blocks k in the check matrix.
In the simulation, the check matrix needs to be determined first. As shown in table 1, a base map is selected according to the encoding process and the bit of the input information, the code length is obtained according to the code rate, and the final check matrix H is obtained after adding the puncturing bit and the parity check bit for code rate compatibility.
TABLE 15 relevant parameters of GNR-based matrix
The example is BPSK modulated, the modulated codeword is defined in GF (2) domain by Additive White Gaussian Noise (AWGN) channel, 5G NR QC-L DPC, and thus, symbol cj∈ (0,1), the modulation symbol after BPSK modulation is xj＝1-2cjReceiving the value y in AWGN channelj＝xj+njWherein n isj～N(0,σ2) Is channel noise, therefore
Where x ∈ (+ -1), further, initialization information L of all variable nodes can be obtainedjLet L be based on check matrix Hj→i＝Lj。
FIG. 1 is a flow chart of L DPC simplified BP decoding algorithm, in the decoding process, the main steps are that channel information is initialized to variable nodes, iteration times are set, check nodes and variable nodes are updated, bit hard decision, decoding check, node updating process is as follows:
s31: processing variable nodes:
s32: and (4) check node processing:
s33: updating posterior probability:
wherein check node is updated by y1(x) And y2(x) The process is carried out. After one iteration is completed, the variable node obtains the posterior probability information and makes bit hard decision, if it is
Then
Otherwise
Thereby obtaining decoded code words
If it is not
Or stopping decoding and outputting code words when the set maximum iteration times is reached; otherwise, the next iteration is performed. The simulation of 5G NR is performed below, and the specific parameters are shown in Table 2.
TABLE 25 GNRBER simulation parameter selection
In the case of the long code of the base diagram 1 and the short code of the base diagram 2, 100 and 10000 information bits with the same code length are respectively simulated, iterated for 25 times, and compared with a hard decoding algorithm: the BER of the bit error rate of the bit flipping algorithm is compared with the weighted bit-flipping algorithm (WBF), as shown in fig. 3 and 4.
As shown in FIG. 3, for the comparison of BER performance in the case of long code of base chart 1, the BER of the simplified BP algorithm is 10-5And the performance gain of the method is 1.3dB higher than that of a WBF algorithm and 2.3dB higher than that of a BF algorithm.
Fig. 4 depicts BER performance comparison in the case of the short code of fig. 2, and the overall decoding performance of the simplified BP algorithm is better than that of the WBF algorithm and the BF algorithm. When the error rate is 10-4The simplified BP algorithm has a gain of 0.7dB over WBF algorithm and about 1.6dB over BF algorithm, according to FIGS. 3 and 4, a comparison of the performance of QC-L DPC long and short codes is also obtained, at a bit error rate of 10-5The QC-L DPC long code has a gain of 0.5dB over the short code, and thus has better decoding performance in a 5G terminal when the QC-L DPC code length is longer.
Finally, the above embodiments are only for illustrating the technical solutions of the present invention and not for limiting, although the present invention has been described in detail with reference to the preferred embodiments, it should be understood by those skilled in the art that modifications or equivalent substitutions may be made on the technical solutions of the present invention without departing from the spirit and scope of the technical solutions, and all that should be covered by the claims of the present invention.
Claims (5)
1. An L DPC decoding method based on a simplified BP algorithm is characterized by comprising the following steps:
s1, check matrix H ═ M × N, where M ═ 1,2, …, M, N ═ 1,2, …, N;
s2 initialization variable node LjInitializing to channel information, wherein j represents a jth variable node; setting iteration times;
s3: updating the variable nodes and the check nodes, and obtaining the posterior information of each layer of updated variable nodes;
s4: after each iteration is completed, posterior information of the variable node is obtained, bit hard decision is carried out on the posterior information, and a decoded code word is further obtained;
s5: and checking the decoded code word, and if the check matrix H is met or the set iteration times are reached, finishing decoding.
2. The L DPC decoding method based on the simplified BP algorithm according to claim 1, wherein in the step S3, the conventional BP algorithm updates the variable nodes and check nodes through the following equations, and obtains the posterior information of the variable nodes after each iteration update:
s31: processing variable nodes:
s32: and (4) check node processing:
s33: updating posterior probability:
the information obtained by the variable node is transmitted to the check node connected with the variable node through the edge of the Tanner graph, and the external information transmitted from the variable node to the check node is Lj→iChecking the processed message of the nodeThe information is transmitted to the variable node through the edge, and the external information transmitted to the variable node by the check node is Li→jWherein j '∈ N (i) to { j } indicates that the variable node set connected with i does not include node j, i' ∈ N (j) to { i } indicates that the check node set connected with j does not include node i;
the sum of the variable node messages is updated after one iteration is finished; after the information update is completed, the message needs to be judged.
3. The L DPC decoding method based on simplified BP algorithm as claimed in claim 1, wherein in said step S4, the posterior information obtained after one iteration is completed is decoded and decided, if yes, the decoding is performed
Then
Otherwise
Thereby obtaining decoded code words
If it is not
Or stopping decoding and outputting code words when the set maximum iteration times is reached; otherwise, the next iteration is performed.
4. The L DPC decoding method based on the simplified BP algorithm according to claim 1, wherein the simplified BP algorithm is an improved BP algorithm formed by equal error linear approximation principle, and is used for simplifying tanh (-) and tanh (-) at check node update time-1Complexity of (·).
5. The L DPC decoding method based on the simplified BP algorithm according to claim 4, wherein the equal-error linear approximation principle implementation steps are as follows:
t1: selecting a proper error, and performing piecewise fitting on a hyperbolic function of a check node of the BP algorithm;
t2: let hyperbolic tangent function y be tanhx's piecewise approximation equation as y1(x) Ax + b, tan h, and the hyperbolic arc tangent function y-1Piecewise fitting approximation equation y of x2(x)＝cx+d；
T3: determining a point on the curve, and performing piecewise fitting on the curve by using the principle of equal error approximation;
t4: obtaining a function of each piecewise line segment according to the points on the curve and the piecewise line segments, and obtaining a piecewise function of the curve, wherein the piecewise linear fit corresponding to tanh (·) is y1(x)，tanh-1(. The) the corresponding piecewise linear fit is y2(x)。
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| US20100318872A1 (en) * | 2006-12-29 | 2010-12-16 | Zte Corporation | Decoding Method for LDPC Code Based on BP Arithmetic |
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| US20100318872A1 (en) * | 2006-12-29 | 2010-12-16 | Zte Corporation | Decoding Method for LDPC Code Based on BP Arithmetic |
| CN101106383A (en) * | 2007-08-13 | 2008-01-16 | 清华大学 | A low density checksum decoding method |
| CN101777920A (en) * | 2009-12-24 | 2010-07-14 | 北京韦加航通科技有限责任公司 | Coding method and coding and decoding device of low-density parity check code |
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