CN111555759A - Design method of generalized LDPC code - Google Patents
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- 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
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Abstract
The invention belongs to the technical field of digital communication, and particularly discloses a design method of a generalized LDPC code, which comprises the steps of selecting code word bits with large influence on performance by utilizing trapping set information of a traditional LDPC global code, carrying out secondary coding by adopting a short code with excellent performance, and attaching check bits obtained by secondary coding to the back of the traditional LDPC code word so as to form the generalized LDPC code word; on the basis, an algorithm for selecting global code check nodes is also provided to select check nodes with accurate received information as far as possible, and the check nodes and variable nodes corresponding to check bits in the component code are sequentially connected through new edges in a factor graph of the generalized LDPC code, so that the purpose of further improving the performance of the code words is achieved. The invention obviously improves the performance of the traditional LDPC code at the cost of little complexity increase and extremely small code rate loss, and can further expand the application of the LDPC code in the practical communication system.
Description
Technical Field
The invention belongs to the technical field of digital communication, and particularly relates to a design method of a generalized LDPC code.
Technical Field
5G is a new generation mobile communication system, and the service objects are not limited to mobile phone communication services. The method faces more complex application scenes, such as emerging fields of Internet of vehicles, artificial intelligence, VR/AR, big data, smart cities, industrial Internet of things and the like. In order to correct errors during signal transmission due to noise present in the channel, channel coding techniques must be employed. Among various current channel coding schemes, Low Density Parity Check (LDPC) codes have excellent decoding performance as one of the most promising channel coding schemes. The third generation Partnership Project (3 GPP) organization has determined that 5G will use LDPC codes as the medium and long code coding scheme for Mobile Broadband enhancement (eMBB) scene traffic.
To meet the requirement of low-delay transmission, the LDPC code cannot adopt a code word with a very long code length. When the LDPC code employs a medium-short frame length (typically 500-3000 bits), the error correction performance is affected due to the presence of more short loops, i.e., trapping sets. Especially, the error floor is easy to occur at the time of high signal-to-noise ratio, thereby preventing the application of the method in services requiring high reliability, such as mobile high-definition video transmission and the like.
In order to reduce the error floor, researchers have proposed various solutions, wherein the solution idea is mainly divided into two categories, one category is to construct a better code word structure or check matrix to avoid short loops and trapping sets, and the other category is to improve the decoding algorithm to remedy the existing trapping set problem.
The construction method of the LDPC code check matrix can be roughly classified into a random construction method and a structural construction method. The former is to search through a computer according to the degree distribution of set variable nodes and check nodes, and the check matrix of the LDPC code generated in the way has no definite mathematical structure, so the coding complexity is higher. For example, the construction method proposed in the document gooder-correcting codes based on vertical sparse matrix [ J ]. IEEE Transactions on information Theory,1999,45(2): 399-. The Progressive Edge-Growth (PEG) algorithm proposed in Hu Xiaoyu et al, Progressive Edge-Growth Tanner graphs [ C ]// Global electronic Conference,2001.GLOBECOM '01.San Antonio: IEEEPress,2002:995 1001, is also a random construction method, by which the Edge is gradually added between variable nodes and check nodes, and the factor graph's girth (girth) is maximized as much as possible each time a new Edge is added, thereby constructing a large-girth LDPC codeword. In the structured construction method, the constructed matrix generally has a cyclic or quasi-cyclic structure, and the coding hardware is simple to implement. For example, a quasi-cyclic Construction algorithm for LDPC Codes is proposed by Lin Shu, M.Forssorer and Kou Yu et al based on the Finite Geometry theory (European Geometry and projection Geometry) in the documents Low intensity Parity check Codes based on fine geometries: a reverse [ C ]//2000.proceedings. IEEE International Symposium on Information theory. Sorrent: 2001, IEEE Press: 2711-.
However, relying on a well-constructed check matrix to reduce false floors often results in a loss of waterfall performance. Researchers also consider how to optimize the decoding algorithm to mitigate the error floor effect. The decoding algorithm optimization is also mainly divided into two categories, and the distinction is based on whether the size and the category of the trapping set of the code pattern to be processed need to be known exactly in the decoding process. Such as: zhengya Zhang et al, in the document of lower LDPC error flow bypass processing [ C ]//2008IEEE Global Telecommunications conference.new trees: IEEE Press,2008:1-6, propose a post-processing technique to weaken the information strength from the falsely satisfied check node on the one hand, and strengthen the information strength from the unsatisfied check node on the other hand, thereby correcting the error variable point in the trap set and reducing the error floor. Kang Jingyu et al have proposed backward tracking techniques in the document iterative decoding of algorithm with back tracking to lower the error-ratios of LDPC codes [ J ]. IEEE Transactions on communications,2011,59(1):64-73. it is possible to reduce the error floor for multiple code types without knowing the prior knowledge of the trapping set for the decoded code type. The technique is effective in the case of fewer unsatisfied check nodes, however, for those LDPC code patterns with many unsatisfied check nodes in the trapping set, the backward tracking technique requires a large number of inversion operations and decoding iterations. Yang et al, in the document A new two-stage decoding scheme with unreliable path search to lower the error-layer-flow for low-emphasis-decoding [ J ] IET Communications,2017,11(14): 2173-; the scheme is divided into two stages, firstly, conventional belief propagation iterative decoding is carried out, and if the decoding fails, after Log-likelihood Ratio (LLR) of partial variable nodes is modified according to trap set information, iterative decoding is carried out again. Simulation results show that compared with the traditional BP algorithm, the scheme of Yang et al can be well improved in performance.
In 2014, Zhang Xiaojie et al proposed the concept of separation degree in document a general method for defining low error rates of LDPC codes, based on reasonable assumptions, in order to reduce the error floor effect and destroy the trapping set. They found that assuming all variable nodes outside a trapping set receive reliable information from the channel, if all incorrect variable nodes in the trapping set are k-disjoint and k is large enough, then all errors in the trapping set can be corrected using a belief propagation decoder. By utilizing the separation degree characteristic of variable nodes in the trapping sets, the variable nodes provide an effective method for destroying the trapping sets. However, for many LDPC codes, the variable nodes in the trapping set often do not satisfy this property. For example, the variable nodes in the (12, 4) trapping set of the Margulis code have only 2 separation or 3 separation, while the (8, 8) trapping set of the RS-LDPC code with the code length of 2048 and the information length of 1723 has only 1 separation. So the above approach may only work for certain LDPC codes.
In summary, it is not a good idea to reduce or even eliminate the error floor effect from the viewpoint of codeword construction or decoding algorithm; the former generally results in a loss of waterfall zone performance, while the latter generally does not significantly improve waterfall zone performance and increases complexity significantly.
Disclosure of Invention
The invention aims to provide a design method of a generalized LDPC code aiming at the problem of the error floor of the traditional LDPC code.
The method comprises the following steps: determining an LDPC code as an original LDPC code, selecting a small number of bits from the code words of the original LDPC code as information bits of a short block code to carry out secondary coding according to trap set information of the original LDPC code, and adding check bits of newly coded code words behind the code words of the original LDPC code to form the code words of the generalized LDPC code.
Further, the selection of the information bits of the short block code adopts the following algorithm:
1) generating a trapping set table T of the original LDPC code and calculating the minimum of each kind of trapping set
And average
Representing Euclidean distance of a variable node to an error boundary, where minimum
Is recorded as minimal
Average
Is marked as average
2) Selecting the trapping set class which does not meet the requirement of the check node and has the most number from the T, recording the trapping set class as an A group of trapping sets, and recording the other types of trapping sets as a B group of trapping sets;
3) selecting at least three types of trapping sets from the B groups of trapping sets to form a group of new trapping sets by adopting the same principle as that in the step 2), and recording the new trapping sets as E;
4) making Q an empty set, if some trapping sets in A have common variable nodes, inserting the variable nodes into the tail of Q, and deleting the trapping sets containing the variable nodes from A;
5) definition J ═ Ei，EiRepresenting the ith type trapping set in the E, carrying out self-statistics on the occurrence frequency of each variable node in the J and arranging the variable nodes according to a descending order; inserting the first variable node in the ordered sequence into the tail part of Q, and including the variable node in JDeleting all trapping sets of points; repeating the process until the occurrence frequency of each variable node in J is equal to 1, and then inserting a first variable node which does not belong to Q into the tail part of Q for each trapping set in J;
6) traversing all trapping sets in the A, and if one trapping set and the Q have no common variable node, inserting the first variable node in the trapping set into the head of the Q;
7) if the potential of Q is larger than or equal to the information bit length k of the component code, selecting the first k variable nodes as the information bits of the component code and terminating the algorithm; otherwise, returning to the step 5) by letting i be i + 1; and outputting Q as the selected variable node set until all the trap sets of the types in the J are used.
Further, in step 3), if there are multiple trapping sets with the same minimum number of unsatisfied check nodes, the minimum is selected
The type of trapping set of (1).
Furthermore, during the secondary encoding, each variable node corresponding to the check bit of the short block code in the generalized LDPC code is connected to a check node of the original LDPC code through an edge.
Further, the selection algorithm of the check nodes of the original LDPC code specifically includes the following steps:
inputting the information bits of the selected short block code, and recording as a variable node set V ═ V1，v2，…，vk}；
① marking the check node connected with each variable node in V, and the collection is marked as check node collection Cflag；
② all out of C for LDPC global title codeflagThe check nodes in the short block code count the occurrence frequencies of all types of trap sets in the group A and part or all types of trap sets in the group E related to the selection algorithm of the information bits of the short block code, and arrange the check nodes according to the ascending order of the occurrence frequencies;
and thirdly, expressing the code length of the component code by n, selecting the first n-k check nodes from the above arrangement, then pairing the check nodes with the n-k variable nodes of the component code in sequence, and adding a new edge between each pair of nodes.
The invention has the following advantages and beneficial effects:
the invention provides a design framework of a generalized LDPC code, which comprises the following steps: selecting a few code word bits from the LDPC global code words as information bits, adopting short codes with excellent performance as component codes to carry out secondary coding, and then adding generated check bits behind the LDPC code words, thereby obtaining the generalized LDPC code words. Therefore, the invention provides a component code information bit selection algorithm. The invention also optimizes the design framework of the generalized LDPC code, namely, a new edge is added between the check node of the LDPC global title code and the variable node corresponding to the check bit of the component code codeword, thereby further improving the performance. Therefore, the invention provides a selection algorithm of the check node corresponding to the LDPC code. The generalized LDPC code design framework and the optimization method thereof can obtain obvious coding gain under the conditions of small code rate loss and small complexity increase.
Drawings
FIG. 1 is a block diagram of a generalized LDPC code in an embodiment of the present invention
Fig. 2 is a schematic factor graph of a generalized LDPC code in an embodiment of the present invention.
Fig. 3 is a factor graph obtained by optimizing the generalized LDPC code in the embodiment of the present invention.
FIG. 4 is a graph comparing the performance of the generalized LDPC code and its optimization scheme proposed by the present invention with the conventional LDPC code.
Detailed Description
The invention is further described below with reference to the accompanying drawings:
firstly, according to trapping set information of the LDPC code, a small number of bits are selected from a code word of the original LDPC code to be used as information bits of a short block code with excellent performance for secondary coding, and check bits of a newly coded code word are attached to the back of the code word of the original LDPC code, so that a generalized LDPC code is formed. Hereinafter, the original LDPC code is also called global title code, and the short block code is also called component code. In this embodiment, a Mackay (408,204) LDPC code is used as a global title code, and a (17, 9) square residual (QR) code is used as a component code to perform a generalized LDPC code design, in some other embodiments of the present invention, short codes such as a hamming code and a BCH code may also be used, and a schematic structural block diagram of the corresponding generalized LDPC code is shown in fig. 1.
Because the global title code is much longer than the component code, only a few codeword bits can be selected for secondary encoding. In this embodiment, a variable node selection algorithm based on trapping set information is used to select variable nodes having a large influence on performance as information bits of component codes, and the specific steps are as follows:
minor in step three of the present embodiment
And average
The related calculation method provided in Ageneralmedethodfor finding error rates of LDPC codes (Cole C, Wilson S, Hall E, et al.) is adopted, and the details are not repeated herein.
In other embodiments, if longer code words are selected for the component codes, four or more trapping set types may be selected as needed in step three.
The variable nodes selected according to the above algorithm are secondarily encoded ((17, 9) QR code), and the check bits of the obtained component code are appended to the code word of the original LDPC code, thereby obtaining the generalized LDPC code word in the present embodiment. The generalized LDPC code can be decoded using the conventional BP algorithm and APP algorithm (hereinafter referred to as a "one-stage decoding algorithm"). In each iteration, the component code is decoded by adopting an APP algorithm to obtain the external information of the variable node corresponding to the component code information bit, and then the iterative decoding of the LDPC code part is carried out.
In the present embodiment, the trapping set information of the global title (Mackay (408,204) LDPC code) is shown in table 1.
TABLE 1(408, 204) LDPC code trapping set information
In this embodiment, according to algorithm 1, the trapping set type having the value 1 and not satisfying the trapping set type b with the least number of check nodes in table 1 includes two types of (3, 1) and (5, 1), where the minimum of the (3, 1) type trapping set
Smaller and further all (3, 1) type trapping sets are group a trapping sets; further according to the algorithm 1, trapping sets of types (5, 1), (6, 2) and (4, 2) are selected to form the E group of trapping sets. Finally, the variable node index set selected according to algorithm 1 is {121, 35, 13, 161, 349, 95, 119, 8, 26 }. And taking the 9 variable nodes as information bits of the (17, 9) QR code, and obtaining 8 check bits for being attached to the back of a code word of the global title code so as to construct the generalized LDPC code. The code length of the newly constructed generalized LDPC code is 416, the information bit length is 204, the code rate is reduced from the original 0.5 to the current 0.4904, and the selected variable node set is recorded as V ═ V { (V)1，v2，...，vk}。
Fig. 2 shows a schematic factor graph of a generalized LDPC code proposed in the present embodiment, and it can be seen from fig. 2 that: for variable nodes (v in the figure) at check bits of component code6，v7，v8) They can only accept information from the component code check nodes. If the error number of the whole component code part exceeds the error correction capability, the component code check node can not transmit correct information, and the variable node corresponding to the component code check bit is likely to be decoded by errors. It is believed that this can be solved by connecting these variable nodes to check nodes of the original LDPC code, and specifically, the variable nodes corresponding to the check bits of the component code are respectively connected to some check nodes of the original LDPC code (in the figure, the variable nodes are connected to some check nodes of the original LDPC code)c1-c5And other several unlabeled blocks are shown schematically) are connected by an edge, i.e., the variable node is included in the check equation for the check node. Such a design has two major benefits, 1) if the component code part is successfully decoded by the APP algorithm, the added edges can propagate the correct information more widely; 2) the newly added edges may also pass the correct information from the original LDPC code portion to the variable nodes of the component code check portion if the component code portion cannot be successfully decoded by the APP algorithm. An exemplary factor of the generalized LDPC code after adding the edge is shown in fig. 3, where a chain line indicates a newly added edge.
In the foregoing, we propose a trapping set information-based variable node selection algorithm, which has the guiding idea of selecting variable nodes covering as many trapping sets as possible, in other words, selecting variable nodes most likely to make errors. Now, selecting check nodes, which aims to increase the reliability of variable nodes corresponding to check bits of the component codes; in order that the check nodes can receive relatively correct information as much as possible, the information can be transmitted to the variable nodes of the component codes. In this embodiment, a check node selection algorithm based on trapping set information is further added, specifically as follows:
the generalized LDPC code described above is then optimized according to the optimization method described above. Algorithm 2 is first used to obtain 8 additional check nodes with indices set 53, 55, 57, 84, 123, 126, 128, 129. And sequentially connecting the check nodes with 8 variable nodes corresponding to the check bits of the generalized LDPC code component code to obtain a new (416,204) generalized LDPC code, wherein the code rate is 0.4904.
The generalized LDPC code and the optimized generalized LDPC code are modulated in a BPSK mode, a test channel is an additive white Gaussian noise channel, a one-stage decoding algorithm is adopted for coding-transmission-decoding simulation, and Frame Error Rate (FER) simulation is performed under different signal-to-noise ratios (Eb/N0)The true result is shown in FIG. 4, in which the number of iterations (itr: iteration time) of the one-stage decoding algorithm is 100. The figure shows that; compared with (408,204) the generalized LDPC code (416,204) (lines marked with triangles on the right in the figure) designed based on the method of the present invention is (408,204)-5Gain of 1.4dB can be obtained; the optimized generalized LDPC code (lines marked with triangles towards the left in the figure) reduces the false floor although the performance improvement is not obtained in the waterfall region.
In practical application, because channel coding generally needs to be defined in a specific communication protocol in advance, a check matrix of the generalized LDPC code can be set in advance to obtain a generator matrix according to a design method of the generalized LDPC code in the present invention during actual coding, so that information bits are directly coded to obtain a generalized LDPC codeword, and a corresponding decoding algorithm is also determined along with generation synchronization of the check matrix, and can be directly invoked during decoding.
The above examples are to be construed as merely illustrative and not limitative of the remainder of the disclosure. After reading the description of the invention, the skilled person can make various changes or modifications to the invention, and these equivalent changes and modifications also fall into the scope of the invention defined by the claims.
Claims (5)
1. A design method of a generalized LDPC code is characterized by comprising the steps of determining an LDPC code as an original LDPC code, selecting a small number of bits from code words of the original LDPC code of a group as information bits of a short block code to carry out secondary coding according to trap set information of the original LDPC code, and attaching check bits of newly coded code words to the back of the code words of the original LDPC code of the group to form code words of the generalized LDPC code.
2. The method of claim 1, wherein the selection of the information bits of the short block code uses the following algorithm:
1) generating a trapping set table T of the original LDPC code and calculating the minimum of each kind of trapping set
And average
Representing Euclidean distance of a variable node to an error boundary, where minimum
Is marked as
Average
Is marked as
2) Selecting the trapping set class which does not meet the requirement of the check node and has the most number from the T, recording the trapping set class as an A group of trapping sets, and recording the other types of trapping sets as a B group of trapping sets;
3) selecting at least three types of trapping sets from the B groups of trapping sets to form a group of new trapping sets by adopting the same principle as that in the step 2), and recording the new trapping sets as E;
4) making Q an empty set, if some trapping sets in A have common variable nodes, inserting the variable nodes into the tail of Q, and deleting the trapping sets containing the variable nodes from A;
5) definition J ═ Ei，EiRepresenting the ith type trapping set in the E, carrying out self-statistics on the occurrence frequency of each variable node in the J and arranging the variable nodes according to a descending order; inserting a first variable node in the ordered sequence into the tail part of Q, and deleting all trapping sets of J including the variable node; this process is repeated until the frequency of occurrence of each variable node in J is equal to 1, and then for each trapping set in J, the first variable node not belonging to Q is inserted into QThe tail of (a);
6) traversing all trapping sets in the A, and if one trapping set and the Q have no common variable node, inserting the first variable node in the trapping set into the head of the Q;
7) if the potential of Q is larger than or equal to the information bit length k of the component code, selecting the first k variable nodes as the information bits of the component code and terminating the algorithm; otherwise, let i ═ i +1, go back to step 5) until all types of trapping sets in J have been used.
3. The method of claim 2, wherein in step 3), if there are multiple trapping sets with the same minimum number of unsatisfied check nodes, the minimum number of check nodes is selected
The type of trapping set of (1).
4. The method of claim 2 or 3, further comprising connecting each variable node corresponding to the check bit of the short block code in the generalized LDPC code with a check node of the original LDPC code through an edge during the secondary encoding.
5. The method of claim 4, wherein the selection algorithm of the check nodes of the original LDPC code specifically comprises the following steps:
inputting the information bits of the selected short block code, and recording as a variable node set V ═ V1，v2，…，vk}；
① marking the check node connected with each variable node in V, and the collection is marked as check node collection Cflag；
② all out of C for LDPC global title codeflagThe check node in the short block code counts all types of trapping sets in the group A and partial or all types in the group E related to the selection algorithm of the information bits of the short block codeThe occurrence frequency of the trapping sets is collected, and the check nodes are arranged according to the ascending order of the occurrence frequency;
and thirdly, expressing the code length of the component code by n, selecting the first n-k check nodes from the above arrangement, then pairing the check nodes with the n-k variable nodes of the component code in sequence, and adding a new edge between each pair of nodes.
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Application publication date: 20200818 |