CN111641416B - Multi-normalization-factor low-density parity check code decoding method - Google Patents
Multi-normalization-factor low-density parity check code decoding method Download PDFInfo
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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
- H03M13/1148—Structural properties of the code parity-check or generator matrix
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Abstract
The invention belongs to the technical field of mobile communication, and relates to a low-density parity check code decoding method with multiple normalization factors, which comprises the steps of calculating the minimum information and the average information absolute value of a check node; calculating a weight vector corresponding to each check node; calculating a normalization factor of the current check node by using the sum of the ratio and the weight, and updating the posterior information value of the variable node adjacent to the check node; decoding a code word according to the posterior information value, and storing a check result in a first vector; judging whether iteration is stopped, if not, updating the information value transmitted to the check node by the variable node, finishing one iteration and continuing to enter the next iteration period; otherwise, ending decoding and outputting code words; the invention breaks the check nodes into zero, each check node can obtain respective weight factor, and the updating of the normalization factor is integrated into the iteration process, so that the weight factor is closer to the optimal value, and better decoding performance is obtained.
Description
Technical Field
The invention belongs to the technical field of mobile communication, and relates to a method for calculating normalization factors by a normalization minimum-Sum (NMS) method and improving irregular QC-LDPC code decoding performance, in particular to a low-density parity check code decoding method with multiple normalization factors.
Background
A Low-density Parity-check (LDPC) code is a linear block code with excellent performance, the decoding performance of the decoding method is firstly proposed by Gallager in 1962 and can be very close to the Shannon limit. Quasi-Cyclic (QC) -LDPC code is a structured LDPC code word, and compared with the random generation of LDPC, the code mode is simpler and more convenient, and the performance is more excellent. In 2016, QC-LDPC codes become a channel coding scheme of a Physical Downlink Shared Channel (PDSCH) of a 5G NR system.
The BP algorithm is the most excellent decoding method of the LDPC code, but functions which are difficult to implement in hardware, such as tanh, are involved in the decoding process, so that relevant researchers obtain the NMS algorithm by optimizing a formula. The initial NMS method is mainly applied to regular LDPC code words, and the normalization factor obtained by using a correlation formula is poor in performance of irregular LDPC code words, but the irregular LDPC code words are superior to the regular code words in performance. The decoding method of irregular LDPC code words in the last decade mainly focuses on the improvement of NMS method, thereby reducing the decoding complexity or improving the decoding performance. The improved algorithms include AN-MS, smMS, DE-MS and the like, however, the methods use a single normalization factor to complete the decoding process, and as the number of iterations increases, the normalization factor adopted by the current iteration is not suitable for the decoding of the subsequent iteration process, thereby reducing the decoding performance to a certain extent.
Disclosure of Invention
The invention aims to solve the problem that the existing decoding method cannot update the normalization factor in an iterative manner. And providing a method for utilizing the minimum information absolute value and the average absolute value as an intermediate medium to further obtain the normalization factors of each check node under different iteration times, and successfully integrating the updating of the normalization factors into the decoding process of the LDPC. The technical scheme of the invention is as follows:
a method for decoding low density parity check code with multiple normalization factors comprises the following processes:
receiving prior information value from channel, and constructing check matrix H MN It means that there are M check nodes and N variable nodes;
in the current iteration period, traversing the check nodes, and solving the minimum information absolute value and the average information absolute value of the current check node according to all the information value amplitudes transmitted from the variable nodes to the current check node;
solving the ratio of the minimum information absolute value and the average information absolute value of the current check node, and adding a weight to the ratio to obtain a normalization factor of the current check node;
updating the information value transmitted to the adjacent variable node by the check node and the posterior information value of the adjacent variable node by using the normalization factor;
until the M check nodes are traversed, decoding a code word according to the posterior information value by using the calculated normalization factor, and storing the check result in a certain vector;
judging whether an iteration stopping condition is met, if the iteration stopping condition is not met, traversing the N variable nodes, updating the information values transmitted from the variable nodes to the check nodes, and continuing to enter the next iteration cycle after one iteration is completed; otherwise, ending decoding and outputting code words from the corresponding vectors.
The invention has the following advantages and beneficial effects:
the method simplifies the mode of solving the normalization factor by Monte Carlo simulation, and integrates the updating process of the normalization factor into the iterative decoding process by combining the thought of the adaptive normalization minimum sum method. Compared with the mode of solving the normalization factor by the existing method, the method has the advantages that the whole verification nodes are broken into zero, each verification node is independently analyzed, and the normalization factor belonging to each verification node can be obtained according to the average absolute value and the minimum absolute value of each verification node, so that the transmitted information is closer to the optimal value, and the decoding performance is improved. The decoding process of the invention relates to division operation with low bit magnitude, when the check matrix size is larger, the added resource consumption can be controlled within a reasonable range by utilizing a layered decoding structure, and the decoding speed can not be reduced.
Drawings
FIG. 1 is a diagram of a decoding scenario employed by the present invention;
FIG. 2 is a flowchart illustrating a multi-normalization factor LDPC decoding process according to the present invention;
FIG. 3 is a decoding flow employed in one embodiment of the present invention;
FIG. 4 is a diagram of relationship conversion between check nodes and variable nodes in the present invention;
FIG. 5 is a decoding flow diagram employed in a preferred embodiment of the present invention;
fig. 6 is a graph comparing the decoding performance of the present invention and the prior art at different snr.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be obtained by a person skilled in the art without making any creative effort based on the embodiments in the present invention, belong to the protection scope of the present invention.
To better illustrate the specific implementation steps of the method, the following is illustrated by way of example in conjunction with fig. 1:
the code word in this embodiment is the QC-LDPC code in the 5G NR protocol 212, as shown in fig. 1, the reference diagram is selected as the reference diagram 2, where 1 in the reference diagram only indicates that a cyclic setting matrix with the size of Z _ C × Z _ C is located at this position, and a specific conversion shift value needs to look at the protocol 212, and 0 indicates that an all-zero matrix with the size of Z _ C × Z _ C is located at this position. In the embodiment of the invention, the lifting value Z _ C is 384, the debugging mode is BPSK, and Gaussian white noise scrambling is utilized.
In this embodiment, as shown in fig. 2, the process of the low density parity check code decoding method using multiple normalization factors at least includes:
in each iteration period, calculating the minimum information absolute value and the average information absolute value of each check node;
obtaining a normalization factor of the current check node by using a ratio of the minimum information absolute value and the average information absolute value of the current check node and a weight;
updating the information value transmitted to the adjacent variable node by the check node and the posterior information value of the adjacent variable node by using the obtained normalization factor, decoding a code word according to the posterior information value, and storing the check information in a first vector;
if the maximum iteration times are reached, namely the last iteration period is reached or all the first vectors are zero vectors, ending decoding and outputting code words, otherwise, updating the information value of each variable node and continuing to enter the next iteration period.
In a more preferred embodiment, as shown in fig. 3, the process of finding the corresponding weight vector according to the codeword characteristics and updating the normalization factor in the iterative process is as follows:
receiving prior information value from channel, and constructing check matrix H MN It means that there are M check nodes and N variable nodes;
initializing parameters, including information value C transferred from check node m to variable node n mn The variable node n transmits the information value V to the check node m nm Posterior information value V of variable node n n The initial index i =1 searched by the check node m, the initial index j =1 searched by the variable node m, the initial iteration number K =1, and the maximum iteration number is K; m is more than or equal to 1 and less than or equal to M, N is more than or equal to 1 and less than or equal to N, M is the row number of the check matrix, N is the column number of the check matrix, and an inspection matrix H with rows representing check nodes and columns representing variable nodes is constructed MN 。
For a more intuitive understanding of the check matrix H MN In this embodiment, the check matrix H is assumed MN The row number M =3 and the column number N =5, as follows:
it can be seen from the matrix that when the element in the ith row and jth column is 1, it means that the ith row and jth column are connected, and for making the expression more visual, the matrix is converted into the Tanner graph form shown in fig. 4, and it can be seen that 1 is converted into a solid line, which means that the two are connected. Meanwhile, for convenience of expression, the number of lines is converted into C1, C2, which is expressed as a node form in Tanner, namely a check node; and converting the column into V1 and V2. The column is a variable node.
In this embodiment, the prior information value y from the channel is stored n For all schoolsCheck node m and variable node n, order C mn The value of the information indicating that the mth check node passes to its neighboring variable node q is equal to 0 nm The information value of the nth variable node to the mth check node is equal to y n A posteriori information V of each variable node n ＝ n . In this example M =16128, n =19968.
In the current iteration period, traversing the check nodes, and solving the minimum information absolute value and the average information absolute value of the current check node according to all the information value amplitudes transmitted from the variable nodes to the current check node;
in the process, the amplitudes of all information values transmitted to the check node i are stored, and the absolute value | V of the average information transmitted to the check node i is calculated according to the amplitudes i ' | and minimum information absolute value | V i ″|。
Obtaining | V i "" and | V i ' I ratio, setting the current iteration times as kth iteration, and selecting the weight omega which is correspondingly larger than zero k Then, the ratio and the weight are added to obtain a normalization factor oc of the check node i in the kth iteration ik 。
Furthermore, the method for solving the normalization factor through the Monte Carlo simulation is simplified, and the weight vector required by the method is calculated;
c in the defined Log-Likelihood Ratio Belief-Propagation (LLR BP) decoding algorithm mn Has a value of C 1 In MS algorithm C mn Has a value of C 2 The normalized factor |. May be expressed by E (| C) 1 |)/E(|C 2 I) is approximated by E (| C) 1 I) and E (| C) 2 |) can be obtained by means of monte carlo simulation, and the formula is as follows:
E(|C 2 |)＝E(min(|X 1 |,|X 2 |,…,|X W |))
wherein { X l :l＝1,2…W}＝{V n′m N'. Epsilon.N (m) \\ N }, where N (m) \ N denotes the set N (m) = { N: H } mn =1} subset of elements n removed, H mn And W is the value of the position of the mth row and the nth column of the check matrix H, and the degree of the corresponding check node is minus 1.
From the formula, the solution of E (| C) 1 I) requires the use of an exponential function and an ln function, which are difficult to implement in hardware. Both equations need to be simplified if the normalization factor is updated during the iteration.
Will utilize E (| C) in Monte Carlo simulation 1 |) reduced to | C m | 1 ＝f(∑ n′∈N(m)\γm f(|V n′m |))，E(|C 2 |) to | C m | 2 ＝min n∈N(m) |V nm |；
Definition | C m | 3 ＝(∑ n∈N(m) |V nm |)/ρ m Wherein γ is m And ρ m Respectively represents the column index and the degree of the absolute value of the second smallest (second smallest) information of the mth check node,
f(x)＝f -1 (x)。
the magnitude relation between the three can be obtained as | C m | 1 ≤|C m | 2 <|C m | 3 To | C m | 2 And | C m | 3 As an intermediary, a normalization factor of the mth check node can be obtained as
Δ represents a weight factor that will be treated as noise plus, | C m | 1 、|C m | 2 、|C m | 3 The value of (a) is highly random and further determination of the sign and magnitude of Δ is required. There is a feature of the NMS algorithm that is based on the number of iterations that are promoted>
Is gradually close to 1 and->
Without this feature, the proportion of Δ that is positive is greater than the proportion of Δ that is negative as the iteration progresses.
As a preferred mode, the maximum iteration times are grouped into 5 to 7 groups, and the weight factors gradually increase with the number of the groups of the maximum iteration times, that is, the number of elements in the weight factor vector formed by the weight factors is 5 to 7.
Is provided with
num represents the number of delta larger than 0 in M rows, and R is obtained through simulation h Rapidly increasing to 1 as the number of iterations increases, and R h Since Δ is approximately a constant greater than 0, since it is 0.7 or more from the beginning to the end, the magnitude of Δ needs to be further determined to improve decoding performance.
And when the code length or code rate of the QC-LDPC code word is different, the change rule of the delta along with the iteration times is slightly different. Let a difference
Different R's can be obtained by simulation diff The change rule of the proportion in the decoding iteration process is as follows: r as the number of iterations increases diff And gradually increases.
Preferably, the weight value corresponding to the first group of iteration times is 0.1-0.15, and the weight value corresponding to the last group of iteration times is 0.6-0.7.
The size of the normalization factor is determined by the weight vector and the ratio of the minimum information value to the average information value, the range of the value is difficult to determine accurately, and in a preferred embodiment, the inventor improves delta into a vector through multiple simulation experiments: [0.125,0.25,0.375,0.5,0.625], the values can be expressed in fixed points by using decimal digits of 3 bits, so that the fixed point calculation is easier and the hardware implementation is easy.
According to the setting, selecting the weight according to the iteration times, firstly dividing the maximum iteration times into 5 groups, when the iteration times belong to the 1 st group, selecting the 1 st value in the vector delta as the current weight, when the iteration times belong to the 2 nd group, selecting the 2 nd value in the vector delta as the current weight, and so on, and obtaining the normalization factor of the current check node by using the current weight
|C i | 2 Is the minimum information absolute value, | C, of the ith node i | 3 Is the average absolute value of information, Δ, of the ith node k Representing the value used by the vector delta according to the number of iterations k.
Decoding a code word according to the posterior information value after traversing the M check nodes, and storing the check result in a first vector;
after traversing the M check nodes, uniformly storing check results corresponding to the normalization factors of all the check nodes in a first vector, namely an error vector; the normalization factor is used for solving the value of the information value transmitted from the current check node to the adjacent node and is represented as follows:
wherein, C iq An information value representing an adjacent variable node q of the ith check node; is a direct change ki Representing the normalization factor of the ith check node in the kth iteration period, namely the kth iteration; s iq The sign bit of the information value of the check node i transferred to the vector variable node q under the current iteration times is represented; | V n′i L represents the average information value of the ith check node at other adjacent variable nodes except the adjacent variable node q; n (i) represents the set of neighboring variable nodes of the ith check node.
Judging whether an iteration stopping condition is met or not, if the iteration stopping condition is not met, traversing the N variable nodes, updating information values transmitted to the check nodes by the variable nodes, and continuing to enter the next iteration cycle after one iteration is completed; otherwise, ending decoding and outputting code words from the corresponding vectors.
The iteration stopping condition comprises that the maximum iteration time is reached or the first vector is an all-zero vector, namely the iteration time reaches the maximum iteration time K or the error is an all-zero vector.
Updating the information value transferred from the variable node to the check node by using the posterior information value and the information for storing the variable node transferred from the check node to the variable node, wherein the information is represented as V by taking the check node i and the variable node q as an example im ＝V q -C iq ；V qm Representing the information value transmitted to the adjacent check node i by the variable node q; v q Representing a posterior information value of a variable node q; c mq Representing the information value passed by check node i to its neighboring variable node q.
A specific embodiment of the present invention is given below, as shown in fig. 5, comprising the following steps:
s1, inputting prior information y n Then, a check matrix H is constructed MN Determining the number M of check nodes and the number N of variable nodes, and setting the maximum iteration number K;
s2, initializing parameters, including a check node index i =1, a variable node index j =1, and an iteration cycle, namely, an iteration number k =1; wherein i belongs to M, j belongs to N, and K belongs to K;
s3, judging whether i is larger than M, and if so, solving the minimum information value absolute value and the average information absolute value of the ith check node;
s4, solving a normalization factor of the ith check node by using the weight vector and the ratio;
s5, updating posterior information values of variable nodes adjacent to the ith check node, wherein i = i +1, and returning to the step S3;
s6, decoding a code word according to the posterior information value, and storing a check result of the check result in an error variable;
s7, judging whether an iteration stopping condition is met, if so, ending decoding and outputting code words from corresponding vectors; otherwise, entering step S8;
s8, updating information values transmitted to the check nodes by the variable nodes, initializing posterior information of each variable node, and enabling k = k +1, i =1, j =1; returning to step S3.
It can be seen from fig. 6 that the decoding performance of the present invention (MNF-MS is the method of the present invention) is better than that of the other methods, with an error rate of 10 -6 In order of magnitude, the decoding performance of the invention is improved by about 0.15dB compared with DE-MS and about 0.29dB compared with AN-MS.
The invention simplifies the method for solving the normalization factor by Monte Carlo simulation on the basis of a normalization minimum Min-Sum (NMS for short) and a Density Evolution minimum Sum (DE-MS for short) method to obtain a new method for solving the normalization factor. Firstly, the ratio of the average absolute value and the minimum absolute value of check node information is obtained, then a weight value which is larger than zero is added to the ratio to obtain a corresponding normalization factor, and the specific numerical value of the weight value is selected according to the iteration times. The method of the invention breaks the check nodes into zero, each check node can obtain the respective normalization factor, and the updating of the normalization factors is integrated into the iteration process, so that the normalization factors are closer to the optimal values, and the decoding performance better than that of the NMS and MS methods is obtained.
In the description of the present invention, it is to be understood that the terms "coaxial", "bottom", "one end", "top", "middle", "other end", "upper", "one side", "top", "inner", "outer", "front", "center", "both ends", and the like, indicate orientations or positional relationships based on those shown in the drawings, and are only for convenience of description and simplicity of description, and do not indicate or imply that the devices or elements referred to must have a particular orientation, be constructed and operated in a particular orientation, and thus, are not to be construed as limiting the present invention.
In the present invention, unless otherwise explicitly specified or limited, the terms "mounted," "disposed," "connected," "fixed," "rotated," and the like are to be construed broadly, e.g., as being fixedly connected, detachably connected, or integrated; can be mechanically or electrically connected; the terms may be directly connected or indirectly connected through an intermediate, and may be communication between two elements or interaction relationship between two elements, unless otherwise specifically limited, and the specific meaning of the terms in the present invention will be understood by those skilled in the art according to specific situations.
Although embodiments of the present invention have been shown and described, it will be appreciated by those skilled in the art that changes, modifications, substitutions and alterations can be made in these embodiments without departing from the principles and spirit of the invention, the scope of which is defined in the appended claims and their equivalents.
Claims (9)
1. A method for decoding a low density parity check code with multiple normalization factors, the method comprising:
receiving prior information value from channel, and constructing check matrix H MN It means that there are M check nodes and N variable nodes;
in the current iteration period, traversing the check nodes, and solving the minimum information absolute value and the average information absolute value of the current check node according to all the information value amplitudes transmitted from the variable nodes to the current check node;
solving the ratio of the minimum information absolute value and the average information absolute value of the current check node, and adding a weight to the ratio to obtain a normalization factor of the current check node;
updating the information value transmitted to the adjacent variable node by the check node by using the obtained normalization factor, and updating the posterior information value of the adjacent variable node;
until the M check nodes are traversed, decoding a code word by using the calculated posterior information value, and storing a check result in a vector;
judging whether an iteration stopping condition is met, if the iteration stopping condition is not met, traversing the N variable nodes, updating the information values transmitted from the variable nodes to the check nodes, and continuing to enter the next iteration cycle after one iteration is completed; otherwise, ending decoding and outputting code words from corresponding vectors.
2. The method of claim 1, wherein the normalization factor of the current check node is expressed as:
wherein is alpha m A normalization factor, | C, representing check node m m | 1 After the second small information value is removed, the check node m obtained by the residual information is transmitted to the information value of the corresponding adjacent node; i C m | 2 Represents the minimum information value passed to check node m; i C m | 3 Representing the average information value passed to check node m; Δ is a weight greater than 0.
3. The method for decoding the ldpc code with multiple normalization factors according to claim 2, wherein the calculation formula of the absolute value of the mean information transmitted to the check node m is expressed as:
wherein, | V nm I represents the information value transmitted from the variable node n to the check node m; rho m Representing the degree of the check node m; n (m) represents a set of neighboring variable nodes of check node m.
4. The method according to claim 1 or 2, wherein the weight selection comprises dividing the maximum iteration number into L groups, and correspondingly setting a weight factor vector consisting of L weights; and selecting corresponding weight values according to the grouping of the current iteration times.
5. The method of claim 4, wherein the maximum iterations are grouped into 5-7 groups, and the weight is gradually increased with the number of the groups of the maximum iterations.
6. The method of claim 5, wherein the first set of iterations has a weight of 0.1-0.15, and the last set of iterations has a weight of 0.6-0.7.
7. The method of claim 1, wherein updating a posteriori information values of variable nodes adjacent to the check node comprises updating a formula for routing check node m to variable node q information, wherein the formula for updating adjacent node q posteriori information is represented by V q ＝V q +C mq ；
Wherein, C mq Representing the information value transmitted by the check node m to the adjacent variable node q; is at a position of km Representing a normalization factor of the check node m in the kth iteration period, namely the kth iteration; s mq Representing the sign bit of the information value of the check node m transmitted to the vector variable node q under the current iteration times; i V n′m I represents the information value transmitted to the node m by the adjacent variable node n' of the check node m; n (m) represents a set of neighboring variable nodes of the mth check node.
8. The method of claim 1, wherein the stop iteration condition comprises reaching a maximum number of iterations or the first vector being an all-zero vector.
9. The method as claimed in claim 1, wherein updating the information value passed from the variable node to the check node comprises updating the information value of the variable node with the information value of the check node, expressed as
V qm ＝V q -C mq
Wherein, V qm Representing the information value transmitted to the adjacent check node m by the variable node q; v q An information value representing a variable node q; c mq Representing the information value passed by the mth check node to its neighboring variable node q.
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