CN115021867B - MIMO-LDPC efficient detection decoding method based on factor graph - Google Patents
MIMO-LDPC efficient detection decoding method based on factor graph Download PDFInfo
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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
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Abstract
The invention provides a factor graph-based MIMO-LDPC efficient detection decoding method, which comprises the following steps: initializing parameters; during the t-th iteration, respectively calculating the mean value and the variance of the probability estimation values transmitted to the unreliable variable nodes by the observation nodes and the symbol probability information transmitted to the unreliable bit nodes by the check nodes; calculating joint probability information of all unreliable variable nodes; obtaining a current detection decoding result according to the joint probability information; if the iteration times reach the maximum, outputting a current detection decoding result, otherwise, if the current detection decoding result is a correct code word, outputting the current result, otherwise, judging a reliable variable node and a reliable bit node, calculating the mean value and the variance transmitted to the observation node by the reliable variable node, calculating the mean value and the variance transmitted to the observation node by the unreliable variable node, and transmitting the information transmitted to the check node by the unreliable bit node to enter the next iteration. The invention can reduce the overall operation complexity while ensuring the detection decoding performance.
Description
Technical Field
The invention relates to a factor graph-based MIMO-LDPC efficient detection decoding method, and belongs to the technical field of wireless communication.
Background
Multiple-Input Multiple-Output (MIMO) technology has been widely used in 5G, and the technology sets Multiple antennas on a transmitter and a receiver respectively to simultaneously transmit and receive radio signals, so as to improve channel capacity, transmission reliability and spectrum efficiency. Compared with a common single-input single-output system, the MIMO technology can effectively inhibit channel fading caused by multipath effect, and improves the effectiveness and reliability of a communication system. The Low-Density Parity-Check (LDPC) code is used as a long code block channel coding scheme with the error correction capability approaching to the Shannon limit, has the characteristics of good error correction capability, strong burst error resistance capability and the like, and can be well applied to a multi-antenna and multi-carrier system. The combined system of the MIMO technology and the LDPC code effectively improves the reliability, throughput and spectrum efficiency of the wireless communication system, and the research of the system and the receiving end detection decoding algorithm thereof has great significance for the development of 5G and next generation communication technologies.
In recent years, research on detection decoding algorithms in a joint system of MIMO technology and LDPC codes has also been continuously introduced. For a combined system of an MIMO technology and an LDPC code, T.L.Nar et al propose a MIMO-LDPC combined detection and decoding method, namely combining an MIMO detection factor graph and an LDPC decoding factor graph, and performing iterative updating of detection and decoding information in one iteration. Although the joint detection decoding method has excellent performance, the operation complexity is high because the MIMO detection and the LDPC decoding need to be performed simultaneously in one iteration. The QR decomposition is carried out on the channel, so that the times of iterative information updating among nodes in a factor graph are reduced, and the operation complexity of the method is reduced. However, the MIMO-LDPC joint detection decoding method based on the factor graph still has higher operation complexity, and how to reduce the operation complexity while ensuring the detection decoding performance is still an unsolved problem.
Disclosure of Invention
The invention provides a factor graph-based MIMO-LDPC efficient detection decoding method, which can reduce the overall operation complexity while ensuring the detection decoding performance and has the characteristics of low complexity and high throughput.
The invention is realized by the following technical scheme:
a MIMO-LDPC high-efficiency detection decoding method based on a factor graph, wherein the factor graph is provided with observation nodes, reliable variable nodes, unreliable variable nodes, reliable bit nodes, unreliable bit nodes and check nodes, and the method comprises the following steps:
s1, initializing and detecting decoding parameters, wherein the parameters comprise reliable variable node sets
Unreliable variable node set U = { x = 1 ,x 2 ,x 3 ,...,x n Get, reliable bit node set->
Unreliable bit node set a = { c 1 ,c 2 ,c 3 ,...,c k The reliability threshold T res Detecting the maximum iteration number I of the decoding MAX Iteration counter t =1;
s2, respectively calculating an observation node y in the factor graph during the t iteration j Passing to unreliable variable node x in set U l Mean value of the probability estimates of (1)
And variance->
And by check node e v To the unreliable bit node c in set A i Log likelihood ratio of->
And combines the log-likelihood ratio>
Conversion to unreliable variable node x l Symbol probability information of>
Wherein, theta r Set s = { theta ] for all possible values after signal modulation 1 ,θ 2 ,...,θ q The value in (c) };
s3, according to the mean value
Variance +>
And symbol probability information->
Calculating all unreliable in the set U at the t-th iterationVariable node x l Is combined probability information->
Step S4, according to the joint probability information in the step S3
Carrying out bit judgment to obtain a current detection decoding result;
s5, judging whether the iteration times reach the maximum iteration times I MAX If yes, outputting the current detection decoding result of the step S4, otherwise, entering the step S6;
s6, judging whether the current detection decoding result is a correct code word or not by using the check matrix of the LDPC code, if so, outputting the current detection decoding result of the S4, otherwise, entering the S7;
s7, making T = T +1, and according to the reliability threshold T res And judging reliable variable nodes in the set U and reliable bit nodes in the set A, calculating the mean value and the variance transmitted to the observation nodes by the reliable variable nodes, moving the reliable variable nodes from the set U to the set V, moving the reliable bit nodes from the set A to the set B, respectively calculating the mean value and the variance transmitted to the observation nodes by the unreliable variable nodes in the updated set U and the information transmitted to the check nodes by the unreliable bit nodes in the updated set A, and entering the step S2.
Further, in the step S2, the mean value is calculated according to the following formula
And variance->
Wherein j = 1.. Multidot.m,
indicating the j-th symbol, N, received by the receiver x (j) Representing and observing node y j Set of connected variable nodes, N x (j) L represents N x (j) In addition to x l Set of variable nodes outside, h jl' For fading coefficients of a multipath channel>
Is a set N x (j) Unreliable variable node x in/l l′ To the observation node y j The average value of (a),
is a set N x (j) Unreliable variable node x in/l l′ To observation node y j Variance information of +>
Is the receiver noise variance;
by the v-th check node e v To the ith unreliable bit node c in set A i The log likelihood ratio of (d) is:
c i ∈N c (v) Wherein v =1 c (v) Representing and checking node e v Set of connected bit nodes, N c (v) I represents N c (v) In addition to c i A set of other bit nodes, based on the number of bit nodes in the set>
Set of representations N c (v) Unreliable bit node c in/i i′ To check node e v A log-likelihood ratio of (d);
according to the formula
r =1,2, \ 8230;, q will the log-likelihood ratio->
Conversion to unreliable variable node x l Is compared with the symbol probability information->
Wherein N is c (l) Representing unreliable variable node x in set U l A set of connected bit nodes.
Further, the step S3 specifically includes the following steps:
step S31, calculating variable node x in set U l Information of probability estimation from observation node
Is based on the mean value->
And variance->
The specific calculation method is as follows: />
Wherein N is y (l) Representing unreliable variable node x in set U l A set of connected observation nodes;
represents the complex conjugate of the channel fading coefficient;
step S32, according to the probability information
Is based on the mean value->
And variance>
Calculating specific probability information
Step S33, calculating the unreliable variable node x in the set U during the t iteration l Joint probability information of
Wherein Z is a normalization factor of the set s.
Further, the step S4 specifically includes the following steps:
step S41, all unreliable variable nodes x are utilized l Joint probability information of
Calculating its corresponding bit log-likelihood ratio>
Wherein the content of the first and second substances,
respectively represent and variable node x l Connected, so that bit node c i Takes a value of 1 and 0 respectively>
A probability set;
step S42, utilizing bit log likelihood ratio
A decision will be made:
Further, in step S6, the check matrix of the LDPC code is H check If, if
If not, the current detection decoding result is incorrect code word, and the step S7 is entered.
Further, in step S7, the process of determining the reliable variable node and the reliable bit node includes:
step S71, calculating the unreliable variable node x in the set U according to the following formula l Mean value of
And variance>
Step S72,Calculating the unreliable variable node x according to the following formula l Reliability of (2)
r＝1,2,...,q；
Step S73, for all theta in the set S r Calculated by it
Are all greater than the reliability threshold T res If the test result is not reliable, judging that the test result is unreliable; if a calculated value is greater than or equal to>
Less than a reliability threshold T res Then the unreliable variable node x is determined l Is a reliable variable node, denoted as x l″ Unreliable bit node c connected to the reliable variable node i Is a reliable bit node, denoted as c i″ 。
Further, in the step S7, the reliable variable node x is calculated according to the following formula l″ To the observation node y j Mean value of
And variance>
y j ∈N y (l)，/>
y j ∈N y (l)。
Further, in step S7, the unreliable variable node x in the updated set U at the t-th iteration is calculated according to the following formula l To observation node y j Mean value of
And variance->
y j ∈N y (l)，/>
y j ∈N y (l)。
Further, in step S7, the updated unreliable bit node c in the set a during the t-th iteration is calculated according to the following formula i To check node e v Information of
e v ∈N e (i)。
The invention has the following beneficial effects:
1. the invention calculates the joint probability information of the unreliable variable nodes according to the mean value and the variance of the probability estimated value of the unreliable variable nodes and the log-likelihood ratio transmitted to the unreliable bit nodes by the check nodes, carries out bit judgment according to the joint probability information to obtain the current decoding result, judges the reliability of the unreliable variable nodes and the unreliable bit variables before the next iteration if the current decoding result is not a correct code word, enables the reliable variable nodes to transmit convergent feedback information to the observation nodes, moves the reliable variable nodes and the reliable bit nodes to other sets, does not update the information of the reliable variable nodes and the reliable bit nodes in the next iteration, reduces the iteration times of detection and decoding, thereby reducing the overall operation complexity while ensuring the detection and decoding performance, accelerating the convergence of the detection and decoding and obtaining higher communication throughput.
Drawings
The present invention will be described in further detail with reference to the accompanying drawings.
FIG. 1 is a flow chart of the present invention.
FIG. 2 is a diagram of a factor graph model according to the present invention.
FIG. 3 is a block diagram of the system components of the present invention.
FIG. 4 is a comparison graph of the performance simulation of the present invention.
FIG. 5 is a complexity comparison graph of the present invention.
Detailed Description
FIG. 2 is a diagram of a factor graph model adopted in the present embodiment, in which the factor graph has an observation node y j Reliable variable node x l″ Unreliable variable node x l Reliable bit node c i″ Unreliable bit node c i And check node e v The specific structure of the factor graph is the prior art. Fig. 3 shows a communication system adopted in this embodiment, which is a multi-antenna receiving end, including serial numbers 1,2 R N of (A) R A receiving antenna, a detection decoder and a signal sink, wherein the symbols received by the receiving end are marked as
The output symbol is recorded as ^ after detection and decoding>
This embodiment considers a LDPC coded single cell uplink multi-user MIMO system, where the cell has L =3 users, and each user has N t If =2 transmitting antennas, the transmitting end has N in total T =6 transmit antennas; the number of receiving antennas at the base station end is N R And (6). Considering the channel as a combined fading channel, i.e. the channel coefficient matrix +>
Each term G obeys a Rayleigh distribution, and xi is a diagonal element->
Diagonal matrix of (4), whose diagonal element->
Wherein it is present>
Obeying the lognormal distribution with the mean value of 0 and the variance of 6, and the distances between the three users and the base station are respectively D 1 ＝1，D 2 ＝1.5，D 3 =2 (km), path fading factor v =4. The LDPC codeword length is 960, the code rate is 1/3, and the modulation scheme is QPSK, i.e., q =4.
As shown in fig. 1, the factor graph-based MIMO-LDPC efficient detection decoding method includes the following steps:
s1, initializing detection decoding parameters, wherein the parameters comprise the probability of transmitting variable nodes to observation nodes
Mean value information &>
Variance information ≥>
Bit node passing to check node &>
Reliability threshold T res (ii) a Reliable variable node set->
Unreliable variable node set U = { x = 1 ,x 2 ,x 3 ,...,x n }; reliable set of bit nodes->
Unreliable bit node set a = { c = 1 ,c 2 ,c 3 ,...,c k }; detecting maximum iteration number I of decoding MAX =10, iteration counter t =1;
wherein x is l Representing the l variable node in the factor graph, wherein the value range of l is 1,2,3, n, and n is the total number of symbols sent by a sending end; y is j Representing the jth observation node in the factor graph, wherein the value range of j is 1,2, 3.., m, and m is the total number of symbols received by a receiving end; c. C i Representing the ith bit node in the factor graph, wherein the value range of i is 1,2,3, and k is the bit number generated by the information source; e.g. of the type v Representing the v-th check node in the factor graph, wherein the value range of v is 1,2, 3., w; q is the set of all possible values s = { theta after signal modulation 1 ,θ 2 ,...,θ q The number of elements in the Chinese character, s, is the value set of the variable node; in particular, it is possible to use, for example,
wherein N is T The number of the antennas at the transmitting end is, and in addition, the reliable variable node set V and the unreliable variable node set U are not intersected with each other, that is: />
Similarly, reliable bit node set B and non-reliable bit node set A satisfy >>
S2, during the t-th iteration, calculating the observed node y in the factor graph respectively j Passing to unreliable variable node x in set U l Mean value of the probability estimates of (1)
And variance->
And by check node e v To the unreliable bit node c in set A i Is greater than or equal to>
And taking the log likelihood ratio->
Conversion to unreliable variable node x l Symbol probability information of>
Wherein, theta r Set s = { theta ] for all possible values after signal modulation 1 ,θ 2 ,...,θ q The value in (c) };
specifically, the observation node y is calculated according to the following formula j To unreliable variable node x in set U l Of the mean of the probability estimates
And variance->
/>
Wherein j = 1.. Multidot.m,
indicating the j-th symbol, N, received by the receiver x (j) Representing and observing node y j Set of connected variable nodes, N x (j) L represents N x (j) In addition to x l Set of variable nodes outside, h jl' For fading coefficients of a multipath channel>
Is a set N x (j) Unreliable variable node x in/l l′ To observation node y j The average value of (a),
is a set N x (j) Unreliable variable node x in/l l′ To observation node y j Variance information of +>
Is the receiver noise variance;
by the v-th check node e v To the ith unreliable bit node c in set A i The log-likelihood ratio of (a) is:
c i ∈N c (v) Wherein v =1 c (v) Representing and checking nodes e v Set of connected bit nodes, N c (v) I represents N c (v) In addition to c i A set of other bit nodes, based on the number of bit nodes in the set>
Set of representations N c (v) Unreliable bit node c in/i i′ To check node e v A log-likelihood ratio of;
according to the formula
r =1,2, \ 8230;, q will the log-likelihood ratio->
Conversion to unreliable variable node x l Is compared with the symbol probability information->
Wherein N is c (l) Representing unreliable variable nodes x in the set U l A set of connected bit nodes.
Step S3. According to the mean value
Variance->
And symbol probability information>
Calculating all unreliable variable nodes x in the set U at the t iteration l Is combined probability information->
The method specifically comprises the following steps:
step S31, calculating unreliable variable node x in set U l Processing probability estimation information from observation nodes
In (d) is based on the mean value>
And variance->
The specific calculation method is as follows:
wherein N is y (l) Representing unreliable variable node x in set U l A set of connected observation nodes;
represents the complex conjugate of the channel fading coefficient;
step S32, according to the probability information
Is based on the mean value->
And variance->
Calculating concrete probability information
Step S33, calculating a variable node x in the set U during the t iteration l Joint probability information of
Wherein Z is a normalization factor of the set s.
Step S4, according to the joint probability information in the step S3
Carrying out bit judgment to obtain a current detection decoding result;
the method specifically comprises the following steps:
step S41, all unreliable variable nodes x are utilized l Joint probability information of
Calculate its corresponding bit log likelihood ratio->
Wherein the content of the first and second substances,
respectively represent and variable node x l Connected, so that bit node c i Takes a value of 1 and 0 respectively>
A probability set;
step S42, utilizing bit log likelihood ratio
A decision will be made:
S5, judging whether the iteration times reach the maximum iteration times I MAX =10, if yes, outputting the current detection decoding result of the step S4, otherwise, entering the step S6;
s6, judging whether the current detection decoding result is a correct code word or not by using a check matrix of the LDPC code, if so, outputting the current detection decoding result of the S4, and otherwise, entering the S7;
specifically, the check matrix of the LDPC code is H check If at all
If not, the current detection decoding result is incorrect code word, and the step S7 is entered.
S7, enabling T = T +1, and enabling the reliability threshold T to be used according to res Judging reliable variable nodes in the set U and reliable bit nodes in the set A, calculating the mean value and the variance transmitted to observation nodes by the reliable variable nodes, moving reliable node variables from the set U to the set V, moving the reliable bit nodes from the set A to the set B, respectively calculating the mean value and the variance transmitted to the observation nodes by the unreliable variable nodes in the updated set U and the log-likelihood ratio transmitted to the check nodes by the unreliable bit nodes in the updated set A, and entering the step S2;
the method specifically comprises the following steps:
step S71, calculating the unreliable variable node x in the set U according to the following formula l Mean value of
And variance
Step S72, calculating the unreliable variable node x according to the following formula l Reliability of (2)
/>
r＝1,2,...,q；
Step S73, for all theta in the set S r Calculated by it
Are all greater than the reliability threshold T res If the test result is not reliable, judging that the test result is unreliable; if a calculated value is greater than or equal to>
Less than a reliability threshold T res Then the unreliable variable node x is determined l Is a reliable variable node, denoted as x l″ An unreliable bit node c connected to the reliable variable node i Is a reliable bit node, denoted as c i″ ；
Step S74, calculating reliable variable node x according to the following formula l″ To observation node y j Mean value of
And variance->
y j ∈N y (l)，/>
y j ∈N y (l)；
Step S75, calculating the unreliable variable node x in the updated set U during the t iteration according to the following formula l To the observation node y j Mean value of
And variance->
y j ∈N y (l)，
y j ∈N y (l)；
Step S76, calculating the unreliable bit node c in the updated set A during the t iteration according to the following formula i To check node e v Information of (2)
Fig. 4 is a diagram showing simulation effect of block error rate when the received signal-to-noise ratio changes in the embodiment, where the abscissa in the diagram is the received signal-to-noise ratio ρ r The calculation formula is
Wherein, P t =1 is the symbol normalized power of the transmitting end; the ordinate represents the Block Error rate (BLER). The simulation experiment carries out comparative analysis on the two methods: 1) Using reliability threshold T in detecting decoding process res Judging the nodes, and setting reliable nodes to transmit convergence information to the observation nodes, namely the method; 2) A MIMO-LDPC detection decoding method without reliable node judgment; in addition, in the simulation experiment process, the reliability thresholds of the method are set to be T respectively res ＝0、T res ＝1×10 -7 And (6) carrying out simulation.
It can be seen from fig. 4 that when the reliable node feeds back the convergence information, the BLER performance of decoding detection is significantly improved; at T res When the node is not equal to 0, the method has 0.4dB gain compared with a detection decoding method without reliable node judgment; at T res ＝1×10 -7 Compared with a detection decoding method without reliable node judgment, the method has 1.7dB gain, and the system throughput is effectively improved; meanwhile, as the SNR of the receiving end increases, the BLER gain also gradually increases.
As shown in fig. 5, the method adopts the complexity comparison between different reliability thresholds and the unreliable node determination method, the abscissa is different complexity comparison types, and the ordinate is the percentage of the reduced operation times of the MIMO-LDPC detection decoding method compared with the unreliable node determination in each frame in this embodiment; when the reliable node transmits convergence information to the observation node, the total iteration times of detection decoding are greatly reduced, and the operation complexity of the detection decoding method is further reduced.
The above description is only a preferred embodiment of the present invention, and therefore should not be taken as limiting the scope of the invention, and the equivalent variations and modifications made in the claims and the description of the present invention should be included in the scope of the present invention.
Claims (5)
1. A MIMO-LDPC high-efficiency detection decoding method based on a factor graph is provided, wherein the factor graph comprises observation nodes, reliable variable nodes, unreliable variable nodes, reliable bit nodes, unreliable bit nodes and check nodes, and is characterized in that: the method comprises the following steps:
s1, initializing and detecting decoding parameters, wherein the parameters comprise reliable variable node sets
Unreliable variable node set U = { x = 1 ,x 2 ,x 3 ,...,x n Get, reliable bit node set->
Unreliable bit node set a = { c 1 ,c 2 ,c 3 ,...,c k }, reliability threshold T res Detecting the maximum iteration number I of decoding MAX Iteration counter t =1;
s2, respectively calculating an observation node y in the factor graph during the t iteration j Passing to unreliable variable node x in set U l Of the mean of the probability estimates
And variance->
And by check node e v To the unreliable bit node c in set A i Is greater than or equal to>
And combines the log-likelihood ratio>
Conversion to unreliable variable node x l Symbol probability information of>
Wherein, theta r Set s = { theta ] for all possible values after signal modulation 1 ,θ 2 ,...,θ q The value in (c) };
s3, according to the mean value
Variance->
And symbol probability information->
Calculating all unreliable variable nodes x in the set U at the t iteration l Is combined probability information->
Step S4, according to the joint probability information in the step S3
Carrying out bit judgment to obtain a current detection decoding result;
s5, judging whether the iteration times reach the maximum iteration times I MAX If yes, outputting the current detection decoding result of the step S4, otherwise, entering the step S6;
s6, judging whether the current detection decoding result is a correct code word or not by using a check matrix of the LDPC code, if so, outputting the current detection decoding result of the S4, otherwise, entering the S7;
s7, making T = T +1, and according to the reliability threshold T res Judging reliable variable nodes in the set U and reliable bit nodes in the set A, calculating the mean value and the variance transmitted to the observation nodes by the reliable variable nodes, moving the reliable variable nodes from the set U to the set V, moving the reliable bit nodes from the set A to the set B, and respectively calculating the mean value and the variance transmitted to the observation nodes by the unreliable variable nodes in the updated set U and the signal transmitted to the check nodes by the unreliable bit nodes in the updated set AThen, the step S2 is carried out;
the step S3 specifically includes the following steps:
step S31, calculating variable node x in set U l Information of probability estimation from observation node
In (d) is based on the mean value>
And variance>
The specific calculation method is as follows:
wherein N is y (l) Representing unreliable variable node x in set U l A set of connected observation nodes;
represents the complex conjugate of the channel fading coefficient;
step S32, according to the probability information
Is based on the mean value->
And variance->
Calculating specific probability information>
/>
Step S33, calculating unreliable variable node x in set U during the t iteration l Joint probability information of
Wherein Z is a normalization factor of the set s;
the step S4 specifically includes the following steps:
step S41, all unreliable variable nodes x are utilized l Joint probability information of
Calculate its corresponding bit log likelihood ratio->
Wherein, the first and the second end of the pipe are connected with each other,
respectively represent and variable node x l Connected, so that the bit node c i Takes a value of 1 and 0 respectively>
A probability set;
step S42, utilizing bit log likelihood ratio
A decision will be made:
In step S7, the process of determining the reliable variable node and the reliable bit node includes:
step S71, calculating the unreliable variable node x in the set U according to the following formula l Mean value of
And variance->
Step S72, calculating the unreliable variable node x according to the following formula l Reliability of (2)
Step S73, for all theta in the set S r Calculated by it
Are all greater than the reliability threshold T res If the test result is not reliable, judging that the test result is unreliable; if a certain calculated->
Less than a reliability threshold T res Then the unreliable variable node x is determined l Is a reliable variable node, denoted as x l″ Unreliable bit node c connected to the reliable variable node i Is a reliable bit node, denoted as c i″ 。
2. The factor graph-based MIMO-LDPC efficient detection and decoding method according to claim 1, wherein: in the step S2, the mean value is calculated according to the following formula
And variance->
Wherein j = 1.. Multidot.m,
indicating the j-th symbol, N, received by the receiver x (j) Representing and observing node y j Set of connected variable nodes, N x (j) L represents N x (j) In addition to x l Set of variable nodes outside, h jl' For the fading coefficient of the multipath channel, is->
Is a set N x (j) Unreliable variable node x in/l l′ To the observation node y j The average value of (a),
is a set N x (j) Unreliable variable node x in/l l′ To observation node y j Variance information of +>
As noise to the receiverVariance;
by the v-th check node e v To the ith unreliable bit node c in set A i The log likelihood ratio of (d) is:
wherein v =1 c (v) Representing and checking node e v Set of connected bit nodes, N c (v) I represents N c (v) In addition to c i A set of other bit nodes, based on the number of bit nodes in the set>
Set of representations N c (v) Unreliable bit node c in/i i′ To check node e v A log-likelihood ratio of;
according to the formula
Pick up the log likelihood ratio>
Conversion to unreliable variable node x l Is compared with the symbol probability information->
Wherein N is c (l) Representing unreliable variable nodes x in the set U l A set of connected bit nodes.
3. The factor-graph-based MIMO-LDPC efficient detection decoding method according to claim 1 or 2, wherein: in the step S6, the check matrix of the LDPC code is H check If at all
If the current detection decoding result is correct code word, the current detection decoding result is output, otherwise, the current detection decoding result is incorrect code word, and step S7 is entered.
4. The factor-graph-based MIMO-LDPC efficient detection decoding method according to claim 1 or 2, wherein: in the step S7, the reliable variable node x is calculated according to the following formula l″ To the observation node y j Mean value of
And variance>
5. The factor-graph-based MIMO-LDPC efficient detection decoding method according to claim 1 or 2, wherein: in step S7, the unreliable variable node x in the updated set U during the t-th iteration is calculated according to the following formula l To observation node y j Mean value of
And variance->
/>
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