CN108599775B - Construction method of hybrid check LDPC code - Google Patents

Construction method of hybrid check LDPC code Download PDF

Info

Publication number
CN108599775B
CN108599775B CN201810440838.0A CN201810440838A CN108599775B CN 108599775 B CN108599775 B CN 108599775B CN 201810440838 A CN201810440838 A CN 201810440838A CN 108599775 B CN108599775 B CN 108599775B
Authority
CN
China
Prior art keywords
check
ldpc code
code
nodes
node
Prior art date
Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
Active
Application number
CN201810440838.0A
Other languages
Chinese (zh)
Other versions
CN108599775A (en
Inventor
殷柳国
王平
陆建华
Current Assignee (The listed assignees may be inaccurate. Google has not performed a legal analysis and makes no representation or warranty as to the accuracy of the list.)
Tsinghua University
Original Assignee
Tsinghua University
Priority date (The priority date is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the date listed.)
Filing date
Publication date
Application filed by Tsinghua University filed Critical Tsinghua University
Priority to CN201810440838.0A priority Critical patent/CN108599775B/en
Publication of CN108599775A publication Critical patent/CN108599775A/en
Application granted granted Critical
Publication of CN108599775B publication Critical patent/CN108599775B/en
Active legal-status Critical Current
Anticipated expiration legal-status Critical

Links

Images

Classifications

    • H—ELECTRICITY
    • H03—ELECTRONIC CIRCUITRY
    • H03M—CODING; DECODING; CODE CONVERSION IN GENERAL
    • H03M13/00—Coding, decoding or code conversion, for error detection or error correction; Coding theory basic assumptions; Coding bounds; Error probability evaluation methods; Channel models; Simulation or testing of codes
    • 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
    • H03M13/116—Quasi-cyclic LDPC [QC-LDPC] codes, i.e. the parity-check matrix being composed of permutation or circulant sub-matrices
    • H—ELECTRICITY
    • H03—ELECTRONIC CIRCUITRY
    • H03M—CODING; DECODING; CODE CONVERSION IN GENERAL
    • H03M13/00—Coding, decoding or code conversion, for error detection or error correction; Coding theory basic assumptions; Coding bounds; Error probability evaluation methods; Channel models; Simulation or testing of codes
    • H03M13/29—Coding, decoding or code conversion, for error detection or error correction; Coding theory basic assumptions; Coding bounds; Error probability evaluation methods; Channel models; Simulation or testing of codes combining two or more codes or code structures, e.g. product codes, generalised product codes, concatenated codes, inner and outer codes

Abstract

The invention provides a construction method of a hybrid check LDPC code, belonging to the technical field of communication channel coding. The method comprises the steps of firstly constructing a quasi-cyclic LDPC code as a basic LDPC code; and then determining the check nodes to be replaced in the basic LDPC code. Selecting only one layer of check nodes for replacement according to the layered structure of the basic LDPC code check matrix; selecting an optimal subcode according to an EXIT function; and finally, replacing a layer of check nodes to be replaced selected in the basic LDPC code with check nodes constrained by the optimal subcode, and finishing the construction of the hybrid check LDPC code. The invention constructs the hybrid check LDPC code which is suitable for the complex interference channel and has strong practicability, can effectively reduce the error rate of data transmission on the complex interference channel and improve the communication reliability.

Description

Construction method of hybrid check LDPC code
Technical Field
The invention belongs to the technical field of communication channel coding, and particularly relates to a construction method of a hybrid check LDPC code.
Background
With the increase of transmission data, the increase of transmission terminals and the extension of transmission distance, limited spectrum resources are increasingly crowded, and a future wireless communication system needs to realize reliable information transmission under a complex interference channel. The complex application environment and the emerging endless interference means constitute the main interference sources of the complex interference channel: due to multipath interference caused by complex terrains such as mountain areas and forest trees, dense buildings and the like, the transmission signals are greatly attenuated; due to the increasing number of communication equipment, a great amount of different system interference and co-channel interference of other equipment exist; the variety of communication systems is increasingly diversified, interference is introduced into part of the communication systems due to self characteristics, and signals are periodically attenuated due to rotor shielding in a helicopter satellite communication system; in special communications, malicious interference of the other party is more likely to directly interrupt the own-party communications.
In a complex interfering channel, channel coding techniques must be used to recover the original information. A Low Density Parity Check (LDPC) code is a channel code having excellent performance which has received much attention in recent years. An LDPC code may be defined by a sparse check matrix in which the number of "1" s is much less than the number of "0" s. An LDPC code may also be formed fromThe Tanner graph shows that all nodes on the Tanner graph are divided into check nodes and variable nodes. The nodes of different types are connected by the edges in the graph according to the following rule: when the value of the ith row and the jth column in the LDPC code check matrix is 1, the check node ciAnd variable node vjAre connected. In an LDPC code, each check node may be considered a single parity check code constraint and each variable node may be considered a repetition code constraint.
The quasi-cyclic LDPC code is a class of LDPC code constructed by utilizing an algebraic structure and is an important branch of a practical LDPC code. The check matrix of the quasi-cyclic LDPC code consists of a series of small square matrixes, and each small square matrix is a zero matrix or a cyclic shift matrix of a unit matrix. The quasi-cyclic LDPC code has the advantages of high-efficiency coding and decoding due to the quasi-cyclic characteristic, so that the quasi-cyclic LDPC code is widely applied to practical communication systems. The new generation of digital satellite broadcasting standard DVB-S2, the international space data system counseling committee standard CCSDS, and the wireless local area network standard 802.11ac, etc., all incorporate quasi-cyclic LDPC codes into channel coding schemes. However, most of the quasi-cyclic LDPC codes are optimally designed for a conventional additive white gaussian noise channel, cannot cope with a large number of errors in the complex interference channel, and direct application to the complex interference channel may cause performance degradation.
Disclosure of Invention
The invention aims to overcome the defects of the prior art and provides a construction method of a hybrid check LDPC code. The invention replaces partial single parity check code constrained check nodes in the basic LDPC code with the sub-code constrained check nodes of Simplex codes and the like with stronger error correction capability, designs an algorithm for removing a short loop of the quasi-cyclic LDPC code and a sub-code optimization selection algorithm based on the EXIT function, constructs a hybrid check LDPC code which is suitable for a complex interference channel and has strong practicability, can effectively reduce the error rate of data transmission on the complex interference channel, and improves the communication reliability.
The invention provides a construction method of a mixed check LDPC code, which is characterized by comprising the following steps:
1) constructing a quasi-cyclic LDPC code as a basic LDPC code; the method comprises the following specific steps:
1-1) constructing a quasi-cyclic LDPC code with the column weight of a and the row weight of b on a GF (p) field, wherein p is a prime number, and b > a > 0;
1-2) removing the short loop of the quasi-cyclic LDPC code constructed in the step 1-1), which comprises the following specific steps:
1-2-1) setting the target girth as g and setting the optimized check matrix of the basic LDPC code as
Figure GDA0001712063890000021
Order under initialization condition
Figure GDA0001712063890000022
1-2-2) examination
Figure GDA0001712063890000023
Whether or not a loop of length 2l is present: if yes, switching to the step 1-2-3); if not, switching to the step 1-2-8);
1-2-3) calculating the value of each cyclic shift array participating in a ring with the length of 2l, and updating the calculation result into a counting matrix n; wherein n ═ { n ═ n0,0,n0,1,...n0,b-1；n1,0,n1,1,...n1,b-1；...；na-1,0,na-1,1,...na-1,b-1}，ns,tRepresenting the values of the loops with the length of 2l participated by the s-th row and the t-th column cyclic shift array, wherein s is more than or equal to 0 and less than or equal to a-1, and t is more than or equal to 0 and less than or equal to b-1;
1-2-4) counting the number of numerical values in the counting matrix n, designing M different numerical values in the number matrix n, and arranging the M numerical values from large to small into n0,n1,...,nM-1(ii) a Let n bekThe subscript index value k of (a) is 0;
1-2-5) finding a numerical value of n in the count matrix equal to nkAll corresponding cyclic shift arrays, and taking a set formed by the cyclic shift arrays as a set psi to be selected;
1-2-6) checking if there is a cyclic shift array in Ψ that satisfies a degree constraint condition, wherein the degree constraint condition is that the selected cyclic shift array is replaced with a zero matrix
Figure GDA0001712063890000024
The degrees of all constraint nodes in the node are not lower than 2: if yes, randomly selecting a cyclic shift array meeting degree constraint conditions from psi, and turning to the step 1-2-7); if not, let nkThe subscript indicated value k is k +1, and the step 1-2-5) is returned again;
1-2-7) replacing the cyclic shift array selected in the step 1-2-6) with a zero matrix;
1-2-8) judging whether l ═ g/2-1 holds: if yes, removing the short loop of the quasi-cyclic LDPC code to obtain an optimized basic LDPC code check matrix
Figure GDA0001712063890000025
And the constructed basic LDPC code enters the step 2); if not, making l equal to l +1, and returning to the step 1-2-2);
2) determining check nodes to be replaced in the basic LDPC code constructed in the step 1);
the degree of the check node selected by the plan is set as dC，2≤dCB is less than or equal to b, from
Figure GDA0001712063890000026
The degree of the selected check node is dCThe first layer of check nodes is used as the check nodes to be replaced; if it is
Figure GDA0001712063890000027
In which there are multiple layers of check nodes with degree dCPreferentially selecting the check node at the middle layer as the check node to be replaced;
3) selecting an optimal subcode according to an EXIT function; the method comprises the following specific steps:
3-1) determining a set omega of the sub-codes to be selected;
the information sequence is long as d from RM codes, BCH codes and Simplex codes meeting the single parity check constraint conditionC-1 legal subcodes are taken as candidate subcodes and are brought into a candidate subcode set omega;
3-2) fixing the basic LDPC codes constructed in the step 1), and calculating a decoding threshold value of each sub-code to be selected in omega and the combination of the basic LDPC codes according to an EXIT function;
the EXIT function expression of the variable node is as follows:
Figure GDA0001712063890000031
in the formula IE,VNDExtrinsic information representing the output of a variable node, IA,VRepresenting the average a priori mutual information, λ, of the nodes of the input variablesiIs expressed in degree dviThe ratio of edges connected to the variable nodes of (1)E,REPRepresenting the EXIT function of a variable node under a complex interference channel, Eb/N0Representing the signal-to-noise ratio;
the EXIT function of the check node consists of a check node EXIT function constrained by the single parity check code and a check node EXIT function constrained by the subcode, and the expression is as follows:
Figure GDA0001712063890000032
in the formula IE,CNDExtrinsic information representing the output of check nodes, IA,CMean prior information, p, representing the input check nodesiIs expressed and degree is dciThe ratio of edges connected to check nodes constrained by the single parity check code, IE,SPCCheck node EXIT function, rho, representing single parity check code constraint under complex interference channelCIndicating the proportion of edges connected to subcode-constrained check nodes, IE,CmptA check node EXIT function representing subcode constraint under a complex interference channel;
3-3) determining the sub-code to be selected with the lowest decoding threshold value in omega as the optimal sub-code according to the result of the step 3-2);
4) and replacing the check node to be replaced determined according to the step 2) in the basic LDPC code with the check node constrained by the optimal subcode selected according to the step 3), and finishing the construction of the hybrid check LDPC code.
The invention has the characteristics and beneficial effects that:
the invention firstly removes a short loop in the quasi-cyclic LDPC code by designing a computer search algorithm, increases the girth of the quasi-cyclic LDPC code, improves the decoding performance of the basic LDPC code, secondly optimizes the selection of the subcode, and introduces subcode redundancy while reducing the code rate loss by replacing a check node constrained by a layer of single parity check code in the basic LDPC code with a check node constrained by the subcode with stronger error correction capability, thereby effectively coping with a large number of error codes in a complex interference channel, improving the communication reliability and having strong practical value.
Drawings
FIG. 1 is a flow chart of the algorithm for removing short loops of quasi-cyclic LDPC codes in the present invention.
Fig. 2 is a bidirectional Tanner graph of a hybrid check LDPC code in the present invention.
FIG. 3 is a diagram of a periodic occlusion channel model according to an embodiment of the invention.
FIG. 4 is a diagram illustrating performance simulation comparison between a hybrid check LDPC code and two quasi-cyclic LDPC codes according to an embodiment of the present invention.
Detailed Description
The present invention provides a method for constructing a hybrid check LDPC code, which is described in detail below with reference to the accompanying drawings and specific embodiments.
The invention provides a construction method of a mixed check LDPC code, which comprises the following steps:
1) constructing a quasi-cyclic LDPC code as a basic LDPC code; the method comprises the following specific steps:
1-1) constructing a quasi-cyclic LDPC code with the column weight of a and the row weight of b on a GF (p) field, wherein p is a prime number, and b > a > 0. Check matrix H of quasi-cyclic LDPC codebCan be expressed as:
Figure GDA0001712063890000041
wherein, I (p)i,j) (i 0, 1.. said., a-1., j 0, 1.. said., b-1) indicates that p is circularly moved to the right by each row of the p-order identity matrixi,jA cyclic shift array of bit generation. Shift factor pi,j＝mod(αiβjP), wherein α andβ are two different elements in the GF (p) domain, and the order satisfying α equals a, and the order of β equals b.
1-2) removing the short loop of the quasi-cyclic LDPC code constructed in the step 1-1), wherein the flow is shown in FIG. 1, and the specific steps are as follows:
1-2-1) setting the target girth as g and setting the optimized check matrix of the basic LDPC code as
Figure GDA0001712063890000042
Order under initialization condition
Figure GDA0001712063890000043
l＝2。
1-2-2) examination
Figure GDA0001712063890000044
Whether or not a loop of length 2l is present: if yes, switching to the step 1-2-3); if not, the step 1-2-8) is carried out.
1-2-3) calculating the value of each cyclic shift matrix participating in a ring with the length of 2l and updating the calculation result into a counting matrix n. Wherein n ═ { n ═ n0,0,n0,1,...n0,b-1；n1,0,n1,1,...n1,b-1；...；na-1,0,na-1,1,...na-1,b-1}，ns,tAnd the values of the loops with the length of 2l, which are participated by the s-th row and the t-th column cyclic shift array, are shown, s is more than or equal to 0 and less than or equal to a-1, and t is more than or equal to 0 and less than or equal to b-1.
1-2-4) counting the number of numerical values in the counting matrix n, designing M different numerical values in the number matrix n, and arranging the M numerical values from large to small into n0,n1,...,nM-1. Let n bekThe subscript of (a) indicates that k is 0.
1-2-5) finding a numerical value of n in the count matrix equal to nkAnd correspondingly, all the cyclic shift arrays, and taking a set formed by the cyclic shift arrays as a to-be-selected set psi.
1-2-6) checking if there is a cyclic shift array in Ψ that satisfies a degree constraint condition, wherein the degree constraint condition is that the selected cyclic shift array is replaced with a zero matrix
Figure GDA0001712063890000051
The degrees of all constraint nodes in the node are not lower than 2: if yes, randomly selecting a cyclic shift array meeting degree constraint conditions from psi, and turning to the step 1-2-7); if not, let nkThe index indicating value k is k +1, and the procedure returns to steps 1-2-5).
1-2-7) replacing the cyclic shift array selected in the step 1-2-6) with a zero matrix.
1-2-8) judging whether l ═ g/2-1 holds: if yes, removing the short loop of the quasi-cyclic LDPC code to obtain an optimized basic LDPC code check matrix
Figure GDA0001712063890000052
And the constructed basic LDPC code enters the step 2); if not, making l equal to l +1, and returning to the step 1-2-2).
2) Determining check nodes to be replaced in the basic LDPC code constructed in the step 1);
the basic LDPC code check matrix optimized by the step 1)
Figure GDA0001712063890000053
Having a layered structure, i.e.
Figure GDA0001712063890000054
Can be divided into a layers. In the same layer, the degrees of the variable nodes are the same, and the degrees of the check nodes are also the same; due to the short-loop removing operation in the step 1), the degrees of the check nodes located in different layers are not completely the same. According to
Figure GDA0001712063890000055
The hierarchical structure of (1) selects only one layer of check nodes to finish node replacement in the step (4), thereby ensuring that the loss of code rate is reduced while introducing subcodes. The degree of the check node selected by the plan is set as dC(2≤dCB) or less, if there are multiple layers of check nodes, the degree is dCPreferably, the middle layer is selected to maximize the number of rings in the basic code Tanner graph participated by the subcode, thereby correcting the ring errors to the maximum extent。
3) Selecting an optimal subcode according to an EXIT function; the method comprises the following specific steps:
3-1) determining a candidate sub-code set omega.
All legal subcodes form a set of subcodes to be selected. The legal subcodes first need to satisfy the single parity check constraint condition, i.e. one column of values in the generator matrix in the systematic form is all '1'. In addition to the known first order RM and BCH codes, all Simplex codes also satisfy the above constraints. On GF (2), (2)rSimplex code of-1, r) is (2)r-1,2r-r-1) a dual code of a hamming code. According to the characteristics of the dual codes, the generation matrix of the Simplex code is the check matrix of the corresponding dual Hamming code. (2r-1,2r-r-1) System Hamming code's check matrix HHamConsisting of all rvele vectors that are not all 0, then HHamWhich necessarily contains 1 column and all 1 columns. Therefore, according to the dual characteristic, the generator matrix of all Simplex codes contains all 1 column, that is, all Simplex codes conform to the single parity check constraint. The legal subcode must satisfy the requirement that the information sequence length is dC-1. And taking the legal subcodes meeting the conditions as the subcodes to be selected and bringing the subcodes into a subcode set omega to be selected.
3-2) fixing the basic LDPC codes constructed in the step 1), and calculating the decoding threshold of each sub-code to be selected in omega and the combination of the basic LDPC codes according to the EXIT function.
The EXIT function of a variable node may be expressed as:
Figure GDA0001712063890000056
in the formula IE,VNDExtrinsic information representing the output of a variable node, IA,VRepresenting the average a priori mutual information, λ, of the nodes of the input variablesiIs expressed in degree dviThe ratio of edges connected to the variable nodes of (1)E,REPRepresenting the EXIT function of a variable node under a complex interference channel, Eb/N0Representing the signal-to-noise ratio.
The EXIT function of the check node is composed of a check node EXIT function constrained by a single parity check code and a check node EXIT function constrained by a subcode, and can be represented as follows:
Figure GDA0001712063890000061
in the formula IE,CNDExtrinsic information representing the output of check nodes, IA,CMean prior information, p, representing the input check nodesiIs expressed and degree is dciThe ratio of edges connected to check nodes constrained by the single parity check code, IE,SPCCheck node EXIT function, rho, representing single parity check code constraint under complex interference channelCIndicating the proportion of edges connected to subcode-constrained check nodes, IE,CmptAnd (3) representing the checking node EXIT function of the subcode constraint under the complex interference channel.
3-3) determining the sub-code to be selected with the lowest decoding threshold value in omega as the optimal sub-code according to the result of the step 3-2), and setting the code length of the optimal sub-code as nCA bit.
4) And replacing a layer of check nodes selected according to the step 2) in the basic LDPC code with check nodes constrained according to the optimal subcode selected in the step 3), and finishing the construction of the hybrid check LDPC code.
The specific replacement process can be represented by a bidirectional Tanner graph structure of the hybrid check LDPC code. The bidirectional Tanner graph of the hybrid check LDPC code is shown in fig. 2, and there are two types of nodes, namely variable nodes and check nodes:
the variable nodes of the mixed check LDPC code are the same as those of the basic LDPC code, the number of the variable nodes is (b-a) · p, and all the variable nodes correspond to the coding sequence of the basic LDPC code one by one.
The check nodes of the mixed check LDPC code are different from the basic LDPC code and comprise p check nodes constrained by the sub-codes besides (a-1). p check nodes constrained by the single parity check code. The check nodes constrained by p subcodes have the code length n selected according to the step 3)CBit and information sequence length dC-1 bit optimal subcode pair base LDPC code with a layer degree d selected according to step 2)CThe check node of (2) is replaced. After replacement, the check node satisfies the subcode constraintWhile implying the single parity check code constraints already present in the basic LDPC code. Subcode constraints are that the base LDPC code sequence corresponding to the variable nodes connected to the check node of each subcode constraint has dCBit, before selection dC-1 bit as subcode information sequence to subcode code to generate length nC-dCA +1 bit check sequence. The single parity check code constraint means that the check bits corresponding to all 1 column positions in the sub-code generating matrix and dCThe information sequence of-1 bit satisfies the existing single parity check equation of the basic LDPC code, so that the check bit is not transmitted in the communication channel. If there is pCBit puncturing, then checking the remaining n of the sequence after subcode encodingC-dC-pCThe bits being transmitted in a communication channel, forming nC-dC-pCAnd the subcode variable nodes with the degree number of 1. All check nodes constrained by single parity check codes in the mixed check LDPC code only participate in parity check, and have no directly corresponding coding sequence; check node constrained by each subcode and length nC-dC-pCThe subcode code sequences of bits correspond.
Thus, the hybrid check LDPC code construction is completed. From (a, b, p) base LDPC code and (n)C,dC-1) the information sequence of the hybrid check LDPC code obtained by the sub-code construction is (b-a) p bits long, and each sub-code check sequence is provided with pCBit puncturing, the code length is (b + n)C-dC-pC) P bits. Then, the code rate of the hybrid check LDPC code can be expressed as:
Figure GDA0001712063890000062
examples
As an example of a complex interference channel, the embodiment of the present invention considers the transmission application under the periodic shielding channel, and the channel model thereof is shown in fig. 3. In this model, the communication signal is attenuated with a rectangular window: in an occlusion period, a signal is only interfered by additive white Gaussian noise during an occlusion-free period, and the relative amplitude is 0; the signal is greatly attenuated during the period with the occlusion, and the attenuation amplitude and the occlusion proportion depend on the specific application scene. The model can be used for channel modeling of practical communication scenes such as helicopter satellite communication and multi-rotor unmanned aerial vehicle communication.
And constructing a quasi-cyclic LDPC code, wherein the parameter p is 61, a is 3, b is 5, alpha is 13, and beta is 9, so that the quasi-cyclic LDPC information sequence is 122 bits long and the code length is 305 bits. Assuming that the target girth g is 14, after removing short loops (loops with a loop length of 12 or less) from the cyclic LDPC code, the obtained basic LDPC code check matrix is as follows:
Figure GDA0001712063890000071
and selecting the middle layer of the basic LDPC code check matrix for expansion, wherein the degree of the selected single parity check node is 5. The sub-codes are optimally selected from first-order RM codes, BCH codes and Simplex codes. According to the optimization result of the EXIT graph, if a first-order RM code or BCH code is adopted for expansion, the decoding convergence threshold is 2.101dB, and if a Simplex code is adopted for expansion, the decoding convergence threshold is 1.995 dB. Thus, for the (122, 305) base LDPC code, the Simplex code is the optimal sub-code. Each subcode-constrained check node transmits 2 check bits on a communication channel, and a hybrid check LDPC code with an information sequence length of 122 bits, a code length of 427 bits and a code rate of 2/7 can be constructed.
Fig. 4 shows the decoding performance of the designed (122, 427) mixed check LDPC code in the periodic occlusion channel, compared with the decoding performance of the (142, 497) and (200, 900) quasi-cyclic LDPC codes. Fig. 4 shows that the frame error rate is 10% in the case of 10% and 25% channel occlusion ratio-4And in time, the decoding performance of the hybrid check LDPC code is 1.2dB better than that of the quasi-cyclic LDPC code with the same code rate. Fig. 4 also shows that the decoding performance of the hybrid check LDPC code with the code rate of 2/7 is better than that of the (200, 900) quasi-cyclic LDPC code with the code rate of 2/9, and from the perspective of engineering application, the bandwidth efficiency of the hybrid check LDPC code adopted on the periodic shielding channel is improved by 28.6% compared with that of the quasi-cyclic LDPC code.

Claims (1)

1. A construction method of a hybrid check LDPC code is characterized by comprising the following steps:
1) constructing a quasi-cyclic LDPC code as a basic LDPC code; the method comprises the following specific steps:
1-1) constructing a quasi-cyclic LDPC code with the column weight of a and the row weight of b on a GF (p) field, wherein p is a prime number, and b > a > 0;
1-2) removing the short loop of the quasi-cyclic LDPC code constructed in the step 1-1), which comprises the following specific steps:
1-2-1) setting the target girth as g and setting the optimized check matrix of the basic LDPC code as
Figure FDA0001655843360000011
Order under initialization condition
Figure FDA0001655843360000012
l＝2；
1-2-2) examination
Figure FDA0001655843360000013
Whether or not a loop of length 2l is present: if yes, switching to the step 1-2-3); if not, switching to the step 1-2-8);
1-2-3) calculating the value of each cyclic shift array participating in a ring with the length of 2l, and updating the calculation result into a counting matrix n; wherein n ═ { n ═ n0,0,n0,1,...n0,b-1；n1,0,n1,1,...n1,b-1；...；na-1,0,na-1,1,...na-1,b-1}，ns,tRepresenting the values of the loops with the length of 2l participated by the s-th row and the t-th column cyclic shift array, wherein s is more than or equal to 0 and less than or equal to a-1, and t is more than or equal to 0 and less than or equal to b-1;
1-2-4) counting the number of numerical values in the counting matrix n, designing M different numerical values in the number matrix n, and arranging the M numerical values from large to small into n0,n1,...,nM-1(ii) a Let n bekThe subscript index value k of (a) is 0;
1-2-5) finding a numerical value of n in the count matrix equal to nkAll corresponding cyclic shift arrays, and taking a set formed by the cyclic shift arrays as a set psi to be selected;
1-2-6) checking if there is any in ΨThe cyclic shift array satisfying degree constraint condition, wherein the degree constraint condition refers to that the selected cyclic shift array is replaced by zero matrix
Figure FDA0001655843360000014
The degrees of all constraint nodes in the node are not lower than 2: if yes, randomly selecting a cyclic shift array meeting degree constraint conditions from psi, and turning to the step 1-2-7); if not, let nkThe subscript indicated value k is k +1, and the step 1-2-5) is returned again;
1-2-7) replacing the cyclic shift array selected in the step 1-2-6) with a zero matrix;
1-2-8) judging whether l ═ g/2-1 holds: if yes, removing the short loop of the quasi-cyclic LDPC code to obtain an optimized basic LDPC code check matrix
Figure FDA0001655843360000015
And the constructed basic LDPC code enters the step 2); if not, making l equal to l +1, and returning to the step 1-2-2);
2) determining check nodes to be replaced in the basic LDPC code constructed in the step 1);
the degree of the check node selected by the plan is set as dC，2≤dCB is less than or equal to b, from
Figure FDA0001655843360000016
The degree of the selected check node is dCThe first layer of check nodes is used as the check nodes to be replaced; if it is
Figure FDA0001655843360000017
In which there are multiple layers of check nodes with degree dCPreferentially selecting the check node at the middle layer as the check node to be replaced;
3) selecting an optimal subcode according to an EXIT function; the method comprises the following specific steps:
3-1) determining a set omega of the sub-codes to be selected;
the information sequence is long as d from RM codes, BCH codes and Simplex codes meeting the single parity check constraint conditionC-1 legal subcodes are taken as candidate subcodes and are brought into a candidate subcode set omega;
3-2) fixing the basic LDPC codes constructed in the step 1), and calculating a decoding threshold value of each sub-code to be selected in omega and the combination of the basic LDPC codes according to an EXIT function;
the EXIT function expression of the variable node is as follows:
Figure FDA0001655843360000021
in the formula IE,VNDExtrinsic information representing the output of a variable node, IA,VRepresenting the average a priori mutual information, λ, of the nodes of the input variablesiIs expressed in degree dviThe ratio of edges connected to the variable nodes of (1)E,REPRepresenting the EXIT function of a variable node under a complex interference channel, Eb/N0Representing the signal-to-noise ratio;
the EXIT function of the check node consists of a check node EXIT function constrained by the single parity check code and a check node EXIT function constrained by the subcode, and the expression is as follows:
Figure FDA0001655843360000022
in the formula IE,CNDExtrinsic information representing the output of check nodes, IA,CMean prior information, p, representing the input check nodesiIs expressed and degree is dciThe ratio of edges connected to check nodes constrained by the single parity check code, IE,SPCCheck node EXIT function, rho, representing single parity check code constraint under complex interference channelCIndicating the proportion of edges connected to subcode-constrained check nodes, IE,CmptA check node EXIT function representing subcode constraint under a complex interference channel;
3-3) determining the sub-code to be selected with the lowest decoding threshold value in omega as the optimal sub-code according to the result of the step 3-2);
4) and replacing the check node to be replaced determined according to the step 2) in the basic LDPC code with the check node constrained by the optimal subcode selected according to the step 3), and finishing the construction of the hybrid check LDPC code.
CN201810440838.0A 2018-05-10 2018-05-10 Construction method of hybrid check LDPC code Active CN108599775B (en)

Priority Applications (1)

Application Number Priority Date Filing Date Title
CN201810440838.0A CN108599775B (en) 2018-05-10 2018-05-10 Construction method of hybrid check LDPC code

Applications Claiming Priority (1)

Application Number Priority Date Filing Date Title
CN201810440838.0A CN108599775B (en) 2018-05-10 2018-05-10 Construction method of hybrid check LDPC code

Publications (2)

Publication Number Publication Date
CN108599775A CN108599775A (en) 2018-09-28
CN108599775B true CN108599775B (en) 2020-09-01

Family

ID=63636292

Family Applications (1)

Application Number Title Priority Date Filing Date
CN201810440838.0A Active CN108599775B (en) 2018-05-10 2018-05-10 Construction method of hybrid check LDPC code

Country Status (1)

Country Link
CN (1) CN108599775B (en)

Families Citing this family (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN112448724B (en) * 2019-08-29 2023-07-07 华为技术有限公司 Data coding method and device

Citations (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN1691522A (en) * 2004-04-05 2005-11-02 美国博通公司 Method and device of ldpc (low density parity check) code signal and checkout decode using parallel and simultaneous
CN107251439A (en) * 2015-02-11 2017-10-13 三菱电机株式会社 Method and AMC controllers for adaptive modulation and coding AMC

Family Cites Families (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
TWI415396B (en) * 2009-11-23 2013-11-11 Nat Univ Tsing Hua Decoder and decoding method for low-density parity check codes constructed based on reed-solomon codes

Patent Citations (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN1691522A (en) * 2004-04-05 2005-11-02 美国博通公司 Method and device of ldpc (low density parity check) code signal and checkout decode using parallel and simultaneous
CN107251439A (en) * 2015-02-11 2017-10-13 三菱电机株式会社 Method and AMC controllers for adaptive modulation and coding AMC

Non-Patent Citations (2)

* Cited by examiner, † Cited by third party
Title
Design of Check-Hybrid LDPC Codes for Data Communications over Helicopter-Satellite Channels;Ping Wang等;《2017 IEEE 86th Vehicular Technology Conference (VTC-Fall)》;20170927;1-5 *
可快速编码的大围长 QC - LDPC 码构造方法;彭海英等;《计算机工程》;20180131;第44卷(第1期);128-133 *

Also Published As

Publication number Publication date
CN108599775A (en) 2018-09-28

Similar Documents

Publication Publication Date Title
RU2354045C2 (en) Device and method for encoding and decoding block codes with low density of parity control with variable coding rate
US8196012B2 (en) Method and system for encoding and decoding low-density-parity-check (LDPC) codes
CN101039119B (en) Encoding and decoding methods and systems
CN108540141B (en) Polar code coding and decoding method and device
CN108964669B (en) LDPC code quadratic programming decoding method based on degree decomposition and alternative multiplier method
CN107370560A (en) Coding and speed matching method, the device and equipment of a kind of polarization code
CN100592639C (en) Low density parity check coding method, device and parity check matrix generating method
CN107528596B (en) Fibonacci-Lucas sequence-based Type-II QC-L DPC code construction method
CN108270510B (en) Communication method and communication equipment based on LDPC code
JP2022502963A (en) Methods and equipment for constructing Polar codes
KR20080074858A (en) Methods and devices for decoding and encoding data
CN113810062B (en) GEL coding method and device facing next generation Ethernet
US11184034B2 (en) Method and device for decoding staircase code, and storage medium
CN108599775B (en) Construction method of hybrid check LDPC code
CN111034055A (en) Simplified check node processing in non-binary LDPC decoders
Jamali et al. Low-complexity decoding of a class of Reed-Muller subcodes for low-capacity channels
CN113193874B (en) LDPC code encoding method, LDPC code encoding device, electronic device, and storage medium
EP4270793A1 (en) Low-density parity-check encoding method, low-density parity-check decoding method, encoding device, decoding device and medium
EP2686964B1 (en) Decoding method, decoding device and corresponding computer program product
CN114421974A (en) Polar code BPL decoding method with improved factor graph selection mode
CN114374397A (en) Method for three-dimensional Turbo product code decoding structure and optimizing iteration weight factor
EP3829088B1 (en) Decoder, decoding method, and computer storage medium
CN112534724A (en) Decoder and method for decoding polarization code and product code
Huang et al. Research of Error Control Coding and Decoding
CN109450453B (en) Method for constructing PTG-LDPC code

Legal Events

Date Code Title Description
PB01 Publication
PB01 Publication
SE01 Entry into force of request for substantive examination
SE01 Entry into force of request for substantive examination
GR01 Patent grant
GR01 Patent grant