CN117040545A - BICM-ID iterative receiving method based on LDPC code - Google Patents

BICM-ID iterative receiving method based on LDPC code Download PDF

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CN117040545A
CN117040545A CN202310994227.1A CN202310994227A CN117040545A CN 117040545 A CN117040545 A CN 117040545A CN 202310994227 A CN202310994227 A CN 202310994227A CN 117040545 A CN117040545 A CN 117040545A
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probability
information
node
bit
symbol
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丁旭辉
徐雨晨
鲜云竹
金涌家
卢琦
杨凯
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Beijing Institute of Technology BIT
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    • 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
    • H03M13/1105—Decoding
    • H03M13/1128—Judging correct decoding and iterative stopping criteria other than syndrome check and upper limit for decoding iterations
    • 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
    • H03M13/1105—Decoding
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L1/00—Arrangements for detecting or preventing errors in the information received
    • H04L1/004—Arrangements for detecting or preventing errors in the information received by using forward error control
    • H04L1/0045—Arrangements at the receiver end

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  • Probability & Statistics with Applications (AREA)
  • Theoretical Computer Science (AREA)
  • Computer Networks & Wireless Communication (AREA)
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Abstract

The BICM-ID iterative receiving method based on the LDPC code improves the frequency spectrum utilization rate under the condition of ensuring lower error rate by joint coding and modulation, introduces an outer iterative process, fully utilizes the channel symbol information and has obviously higher system gain than a BICM system; the check nodes are introduced to meet probability detection nodes on the basis of the factor graph, information is transmitted unidirectionally, normal demodulation-decoding iteration process is not influenced, iteration state can be judged in real time according to convergence, and the implementation of a receiver system is facilitated; the probability information of the check nodes meeting the probability detection nodes is used as the confidence coefficient parameter in the iteration process and used for judging the iteration stopping criterion, so that the implementation complexity of the traditional decoding stopping criterion can be reduced on the basis of ensuring the error rate performance, the iteration times and the system processing time delay at the time of low signal-to-noise ratio are reduced, and the system throughput is improved. The invention is suitable for the communication field, improves the decoding reliability and the system throughput, and further improves the communication quality.

Description

BICM-ID iterative receiving method based on LDPC code
Technical Field
The invention relates to a BICM-ID iterative receiving method based on LDPC codes, and belongs to the field of communication signal processing.
Background
Channel coding and digital modulation techniques are two digital signal processing techniques commonly used in wireless communication systems. The current channel coding techniques mainly include hamming codes, convolutional codes, concatenated codes, turbo codes, low-Density Parity-Check codes (LDPC) codes, and the like. Among them, the LDPC code has been widely studied and paid attention to because of its performance approaching Shannon limit and its advantage of being convenient for parallel processing. In order to sufficiently improve the coding gain of the channel and facilitate low complexity implementation, there are various decoding modes of the LDPC code, including a belief propagation (Belief Propagation, BP) algorithm, a BP (Log Likelihood Ratio BP, LLR-BP) algorithm represented by a log-likelihood ratio, a Min-Sum (MS) algorithm, a Normalized Min-Sum (NMS) algorithm, an Offset Min-Sum (Offset MS, OMS) algorithm, an Improved Normalized Min-Sum (incs) algorithm, and the like. However, the LDPC coding technique trades off spectrum utilization for signal transmission reliability, and introducing channel coding results in a reduction in spectrum utilization. For this deficiency, digital modulation techniques may be introduced after encoding. Based on the Bit interleaving coded modulation (Bit-Interleaved Coded Modulation, BICM) of LDPC coding, the frequency band utilization rate of the system can be obviously improved, especially in the case of high-order modulation, such as 8PSK,16QAM,64QAM and the like. The system can flexibly select the coding rate, the modulation mode and the iteration number according to the channel condition and the application requirement so as to realize the optimal balance between different performances and complexity. However, the existing combined LDPC-BICM algorithm cannot fully utilize channel information, fully exert the coding gain effect of the LDPC code, and has excessive iteration times in a low signal-to-noise ratio area and higher processing time delay.
Disclosure of Invention
Aiming at the problem that the traditional BICM system cannot fully exert the LDPC coding gain effect, the Hamming distance is maximized due to the sacrifice of a certain Euclidean distance, and the effect is not ideal under the additive Gaussian white noise (Additive White Gaussian Noise, AWGN) channel, the main purpose of the invention is to disclose a BICM-ID iterative receiving method based on the LDPC code, which comprises the steps of introducing a feedback loop, interleaving the posterior probability of the LDPC decoder, feeding back the interleaved posterior probability to a demapper as priori information, and updating the probability information of each bit by the demapper again, thereby completing an iterative process and improving the reliability of decoding; and the decoding state is judged in real time by an iterative decoding stopping criterion optimizing method, so that invalid iterative processes are reduced, processing time delay is reduced, and system throughput is improved, and therefore, communication quality is improved.
The invention aims at realizing the following technical scheme:
the invention discloses a BICM-ID iterative receiving method based on LDPC codes, which comprises the following steps:
and step one, respectively carrying out coding, interleaving, mapping and modulation processing on the original information sequence, and entering an AWGN channel for transmission.
The original information sequence M with the length of k bits is multiplied by the generating matrix G of LDPC coding to obtain a coding result C=M.G, and the length of the coded sequence C is n; and then, the coded information bits are subjected to interleaving operation through an interleaver to obtain a code element sequence X=pi (C), wherein the function pi represents a specific interleaving and de-interleaving mode. The interleaver only changes the order of the symbols, not the total length of the symbol sequence, so the sequence C and the sequence X have the same length. Passing the encoded information bits through a constellation mapping functionMapping, m coded and interleaved information bits x 0 ,x 1 ,…,x m-1 Mapping to constellation points in 1 space. Where Ω represents the complete constellation space of the mapped symbol, containing M constellation points in total, where m=2 m ，/> Representing a rounding down. The sequence X obtained after interleaving is modulated and mapped to obtain a symbol sequence +.>Can be extended to higher order modulation schemes by changing the specific form of the function map. And finally, transmitting the symbol sequence Y through an AWGN channel.
And step two, the demodulator receives the output symbols from the AWGN channel to carry out demapping, and the probability information of the transmission symbols and the corresponding bits is calculated by using the channel information and the prior probability information.
The channel output symbol sequence is represented by z= { Z 1 ,z 2 ,…,z t When deriving soft bit information using initial symbol information of a received channel, the source can be regarded as an equal probability distribution, so that the probability of each bit node initially being 0 or 1 is equal, i.e.:
wherein x is i Representing the value of the i-th bit in the transmission sequence. Mapping symbols in constellation mapping spaceThe probability of (2) is also the same, namely:
the probability information of each transmission symbol is:
wherein y is t Representing the t-th symbol, z in the sequence of transmitted symbols t Representing the t-th symbol in the received symbol sequence.Where "≡" represents its estimated value.
Based on the additive white gaussian noise channel, the probability density function is:
whereas for complex gaussian channels, the probability density function is:
wherein sigma 2 Representing the variance of the gaussian channel. y is I And y Q Representing the real and imaginary parts, z, respectively, of the channel transmit symbol y I And z Q Representing the real and imaginary parts of the channel received symbol z, respectively.
Substituting the initial probability information into the above mode and simplifying the initial probability information to obtain the initial probability information of each transmission symbol as follows:
wherein,and->Respectively representing the real part and the imaginary part, z, of the kth constellation mapping point in the constellation mapping space re And z im Representing the real and imaginary parts of the channel received symbol z, respectively.
Deriving probability information of each bit from the symbol probability information:
wherein the method comprises the steps ofConstellation point +.f representing bit b at ith position of constellation map χ>Is a set of (3).
The above formula is expressed in the logarithmic domain as:
step three, the bit probability information after demapping is processed through a deinterleaver pi -1 A global detail factor graph model is built for the LDPC-BICM-ID system receiver.
The de-interleaving only changes the bit order, has no effect on the probability information, and therefore has no effect onAnd->No distinction is made.
And constructing a factor graph model G= (VNs U CNs, xi) with a check constraint relation according to the check matrix of the LDPC code, wherein VNs represents a variable node set, CNs represents a check node set, and xi represents a variable node and an edge set of the check node, and the position of 1 in the check matrix H is corresponding to the position.
Channel received symbol sequence z= { Z 1 ,Z 2 ,…,Z t The bit stream sequence X= { X is obtained through the joint mapping module phi 1 ,X 2 ,…,X n And obtaining a sequence C= { C by a de-interleaving module pi 1 ,C 2 ,…,C n Corresponding to the variable node set VNs in the G= (VNs U.CNs, xi) model, the first k variable nodes correspondingly output a decoding final result sequence M= { M 1 ,M 2 ,…,M k }。
On the basis, the added check node satisfies the probability detection node G= { G 1 ,g 2 ,…,g n-k ' and schoolTest node normalization satisfaction probability statistics node G sum . Check node CNs= { h 1 ,h 2 ,…,h n-k Meeting probability check node g= { G to check node connected thereto 1 ,g 2 ,…,g n-k One-way transfer of information, where h i Represents the ith check node, g i Representing the ith detection node, which are in one-to-one correspondence.
And step four, completing iterative decoding of the belief propagation algorithm in the LDPC decoder.
By r ji (x i ) Represents the j-th check node C j The probability density function for a corresponding bit of "0" or "1" passed to the ith variable node. With q ij (x i ) Represents the ith variable node V i The probability density function of a "0" or "1" corresponding bit passed to the jth check node. The check node update process is expressed as:
the variable node update process is expressed as:
wherein, set R j\i Set C representing the set of positions except for the ith 1 in the jth row of the check matrix H i\j Representing the set of positions in row i in the check matrix H except for the j 1 st.
The node update procedure is expressed in the logarithmic domain as:
a node update procedure is considered an intra-iteration procedure. The node update process is repeated until a stopping criterion is reached. By Q i (x i ) The posterior likelihood probability of the ith variable node, i.e. the probability value to be finally calculated by the iterative decoding process, is represented.
The above formula is expressed in the logarithmic domain as:
and fifthly, feeding the decoded soft bit information back to the demodulator through the interleaver as prior information of next demodulation.
The interleaver only changes the sequence, does not affect probability information, does not distinguish between x and c, uses p a (x i ) A priori information representing the next demodulation process:
p a (x i ＝0)＝Q i (x i ＝0)
p a (x i ＝1)＝Q i (x i ＝1)
the above formula is expressed in the logarithmic domain as:
and step six, the demodulator updates each bit by using the prior soft bit information from the channel symbol information and the received prior soft bit information.
Using the symbol information from the channel calculated in step twoAnd the prior information p obtained by feedback in the step five a (x i The method comprises the steps of (a) updating information of each bit together, completing an outer iteration process, and obtaining updated probability information of each bit as follows:
the above formula is expressed in the logarithmic domain as:
wherein,the ith bit, b e {0,1}, y, representing the t-th symbol t T-th symbol representing channel transmission, < >>Constellation point +.f representing bit b at ith position of constellation map χ>Set of->Represents the j-th bit value corresponding to the k-th constellation mapping point.
And step seven, using probability information of the check nodes meeting the probability detection nodes as confidence coefficient parameters in the iteration process, and using the confidence coefficient parameters for judging the iteration stopping criteria.
Nodeg i Representing whether the ith check equation is satisfied, we can use the probability p (g i =0) represents a probability mass function of whether the i-th equation is satisfied or not among the check equations. Check node h i To the detection node g i The information of all variable nodes connected with the ith check node needs to be calculated, expressed as:
wherein,representation of other than g i Summation of functions of all variable nodes except V m′ ∈N(C i )\g i Represents V m′ Belonging to check node C i Connected, but not including node g i All variable node sets, f i (x) Immediate indication function I C (C i ) =δ (·) represents that the function value is 1 when all variable nodes connected to the check node modulo the two sums are 0.
The output of the detection node G is the check node satisfaction probability p (G i =0|h, Y), indicating that the check equation detection node outputs a check relationship g under the condition that the received channel sequence Y and the check matrix H are known i A probability of 0, expressed as:
check node normalized satisfaction probability node G sum Output p (G) sum ) To normalize the output values of all the detection nodes G:
with p (G) sum ) As confidence parameter, the variation in the inner and outer iterative process tends toIt can be seen that if the confidence coefficient parameter gradually tends to 1 from 0.5 and converges, the codeword is a correctly decodable codeword; if the confidence parameter converges to about 0.5 during the decoding process, it indicates that the confidence parameter converges to the error codeword during the decoding process, and the next outer iteration process can be performed, and channel information is introduced again to re-decode the frame. If the confidence level is continuously oscillating between 0.5-1, the codeword is in a non-converging pattern.
Based on the above description, the stopping criteria are expressed as: (one) when the check node normalizes the satisfaction probability p (G) sum ) Stopping the iteration of the current frame when the decoding success threshold is reached, and considering that the decoding is successful; (II) when the check node normalizes the satisfaction probability p (G) sum ) Stopping the current decoding iteration when the symbol convergence threshold value is threshold value, and entering an outer iteration process; and (III) stopping iteration when the inner and outer iteration reaches the maximum inner and outer iteration times.
The stopping criterion gives three threshold parameters T, γ, η for the judgment. Wherein T represents a decoding success threshold, gamma represents a converged continuous period threshold, and eta represents a variation range threshold.
The specific implementation process of the stopping criterion is as follows: first, the confidence coefficient p (G) sum ) If the value of (2) is greater than the decoding success threshold value T, when p (G sum ) The decoding process of the system is stopped immediately and the bit a posteriori probability outputs of the decoder outputs are decided, if > T the frame processed by the current decoder has found the correct codeword. Next, the current iteration period p (G sum ) If the difference is smaller than the threshold eta of the threshold of the set variation range, the counter is added with 1, otherwise, the counter is set to 0. When the counter reaches the threshold gamma of the continuous period for setting convergence, the current decoding process is judged to have converged, and then the decoding iteration is invalid, at the moment, the decoding inner iteration process is also immediately terminated, and the updating process of the outer iteration is started. In addition to the above two cases, when the iterative decoding process exceeds the preset number of iterations and the correct codeword cannot be found, the decoder stops the current iterative process and proceeds to the iterative process of the next frame.
And step eight, outputting bit judgment to obtain a codeword sequence decoded by the receiver, and completing the digital communication process.
Judging the first k bits according to the decoding output posterior probability information, if Q i (x i ＝0)＞Q i (x i =1), then m i And judging to be 0, otherwise, judging to be 1, so as to obtain a received code word sequence, and finishing the demodulation-decoding process.
The invention obtains the approximate posterior probability of the code word by utilizing the channel prior information and the check matrix information through the eight steps, completes the joint demodulation-decoding iteration process, and guides the stopping criterion of internal and external iteration according to the convergence analysis of the check node normalization meeting probability.
The beneficial effects are that:
1. the invention discloses a BICM-ID iterative receiving method based on LDPC codes, which combines coding and modulation, improves the frequency spectrum utilization rate under the condition of ensuring lower error rate, introduces an outer iterative process, fully utilizes channel symbol information and has obviously higher system gain than a BICM system.
2. According to the BICM-ID iterative receiving method based on the LDPC code, check nodes are introduced on the basis of a factor graph to meet probability detection nodes, information is transmitted unidirectionally, a normal demodulation-decoding iterative process is not influenced, the iterative state can be judged in real time according to convergence, and the implementation of a receiver system is facilitated.
3. The BICM-ID iterative receiving method based on the LDPC code, disclosed by the invention, utilizes probability information that check nodes meet probability detection nodes as confidence parameters in an iterative process, is used for judging an iterative stopping criterion, can reduce the implementation complexity of the traditional decoding stopping criterion on the basis of ensuring the error rate performance, reduces the iteration times and the system processing time delay when the signal to noise ratio is low, and improves the system throughput.
Drawings
FIG. 1 is a schematic overall flow chart of a BICM-ID iterative receiving method based on LDPC codes;
FIG. 2 is a detailed model of a global factor graph for joint 8PSK demodulation-LDPC decoding according to an embodiment of the present invention;
FIG. 3 is a schematic flow chart of a stopping criterion of a BICM-ID iterative receiving method based on LDPC codes;
fig. 4 is a bit error rate simulation curve of reference code pattern combined 8PSK modulation according to an embodiment of the present invention;
fig. 5 is a simulation plot of the average number of decoding iterations for a reference pattern joint 8PSK modulation receiver using design stop criteria decoding according to an embodiment of the present invention.
Detailed Description
The present invention will be described in detail with reference to the accompanying drawings and examples. The technical problems and the beneficial effects solved by the technical proposal of the invention are also described, and the described embodiment is only used for facilitating the understanding of the invention and does not have any limiting effect.
The embodiment discloses a BICM-ID iterative receiving method based on LDPC codes aiming at the U.S. deep space communication CCSDS131.1-0-1 standard, wherein the system parameters are shown in the following table:
parameters (parameters) Details of the
Number of bits per frame 120
Code rate 1/2
Punching mode Last 60 bits of check bit
Modulation scheme 8PSK
Channel model White gaussian noise
Maximum number of decoding iterations 30
Maximum number of demodulation-decoding iterations 3
As shown in fig. 1, the specific implementation steps of this embodiment are as follows:
and step one, respectively carrying out coding, interleaving, mapping and modulation processing on the original information sequence, and entering an AWGN channel for transmission.
The original information sequence M with the length of k bits is multiplied by the generating matrix G of LDPC coding to obtain a coding result C=M.G, and the length of the coded sequence C is n; and then, the coded information bits are subjected to interleaving operation through an interleaver to obtain a code element sequence X=pi (C), wherein the function pi represents a specific interleaving and de-interleaving mode. The interleaver only changes the order of the symbols, not the total length of the symbol sequence, so the sequence C and the sequence X have the same length. Passing the encoded information bits through a constellation mapping functionMapping, m coded and interleaved information bits x 0 ,x 1 ,…,x m-1 Mapping to constellation points in 1 space. Where Ω represents the complete constellation space of the mapped symbol, containing M constellation points in total, where m=2 m ，/> Representing a rounding down. The sequence X obtained after interleaving is subjected toModulation mapping to obtain symbol sequence->Can be extended to higher order modulation schemes by changing the specific form of the function map. And finally, transmitting the symbol sequence Y through an AWGN channel.
And step two, the demodulator receives the output symbols from the AWGN channel to carry out demapping, and the probability information of the transmission symbols and the corresponding bits is calculated by using the channel information and the prior probability information.
The channel output symbol sequence is represented by z= { Z 1 ,z 2 ,…,z t When deriving soft bit information using initial symbol information of a received channel, the source can be regarded as an equal probability distribution, so that the probability of each bit node initially being 0 or 1 is equal, i.e.:
wherein x is i Representing the value of the i-th bit in the transmission sequence. Each mapped symbol in the constellation mapping spaceThe probability of (2) is also the same, namely:
the probability information of each transmission symbol is:
wherein y is t Representing the t-th symbol, z in the sequence of transmitted symbols t Representing the t-th symbol in the received symbol sequence.Wherein "≡" represents the sameAnd (5) estimating a value.
Based on the additive white gaussian noise channel, the probability density function is:
whereas for complex gaussian channels, the probability density function is:
wherein sigma 2 Representing the variance of the gaussian channel. y is I And y Q Representing the real and imaginary parts, z, respectively, of the channel transmit symbol y I And z Q Representing the real and imaginary parts of the channel received symbol z, respectively.
Substituting the initial probability information into the above mode and simplifying the initial probability information to obtain the initial probability information of each transmission symbol as follows:
wherein,and->Respectively representing the real part and the imaginary part, z, of the kth constellation mapping point in the constellation mapping space re And z im Representing the real and imaginary parts of the channel received symbol z, respectively.
Deriving probability information of each bit from the symbol probability information:
wherein the method comprises the steps ofConstellation point +.f representing bit b at ith position of constellation map χ>Is a set of (3).
The above formula is expressed in the logarithmic domain as:
step three, the bit probability information after demapping is processed through a deinterleaver pi -1 A global detail factor graph model is built for the LDPC-BICM-ID system receiver.
The de-interleaving only changes the bit order, has no effect on the probability information, and therefore has no effect onAnd->No distinction is made.
And constructing a factor graph model G= (VNs U CNs, xi) with a check constraint relation according to the check matrix of the LDPC code, wherein VNs represents a variable node set, CNs represents a check node set, and xi represents a variable node and an edge set of the check node, and the position of 1 in the check matrix H is corresponding to the position.
The check matrix in the CCSDS standard is a quasi-cyclic matrix consisting of cyclic sub-matrices. The embodiment adopts an LDPC code with information bit k=120 and code rate R=1/2, and the check matrix is a 180×300 check matrix H which is formed by splicing sub-cyclic matrix M with the size of 60 in a 3×5 manner. In order to make the code pattern conform to the given code rate, the code word needs to be punched, that is, part of check bits of the code word are reserved at the transmitting end and not transmitted, and 0 is complemented at the corresponding code word position of the receiving end for decoding. In this embodiment, the last 60 bits of data of the check bit are selected to be punched, so that the transmission code rate of the data meets 1/2.
Channel received symbol sequence z= { Z 1 ,Z 2 ,…,Z t Through jointThe mapping module phi obtains the bit stream sequence x= { X 1 ,X 2 ,…,X n And obtaining a sequence C= { C by a de-interleaving module pi 1 ,C 2 ,…,C n Corresponding to the variable node set VNs in the G= (VNs U.CNs, xi) model, the first k variable nodes correspondingly output a decoding final result sequence M= { M 1 ,M 2 ,…,M k }。
On the basis, the added check node satisfies the probability detection node G= { G 1 ,g 2 ,…,g n-k Normalized meeting probability statistic node G of check node sum . Check node CNs= { h 1 ,h 2 ,…,h n-k Meeting probability check node g= { G to check node connected thereto 1 ,g 2 ,…,g n-k One-way transfer of information, where h i Represents the ith check node, g i Representing the ith detection node, which are in one-to-one correspondence. The detailed factor graph model is shown in fig. 2.
And step four, finishing an iterative decoding process of the belief propagation algorithm in the LDPC decoder.
By r ji (x i ) Represents the j-th check node C j The probability density function for a corresponding bit of "0" or "1" passed to the ith variable node. With q ij (x i ) Represents the ith variable node V i The probability density function of a "0" or "1" corresponding bit passed to the jth check node. The check node update process is expressed as:
the variable node update process is expressed as:
wherein, set R j\i Set C representing the set of positions except for the ith 1 in the jth row of the check matrix H i\j Representing the set of positions in row i in the check matrix H except for the j 1 st.
The node update procedure is expressed in the logarithmic domain as:
a node update procedure is considered an intra-iteration procedure. The node update process is repeated until a stopping criterion is reached. By Q i (x i ) The posterior likelihood probability of the ith variable node, i.e. the probability value to be finally calculated by the iterative decoding process, is represented.
The above formula is expressed in the logarithmic domain as:
and fifthly, feeding the decoded soft bit information back to the demodulator through the interleaver as prior information of next demodulation.
Similarly, the interleaver only changes order, and does not affect probability information, forX is not distinguished from c, p is used a (x i ) A priori information representing the next demodulation process:
p a (x i ＝0)＝Q i (x i ＝0)
p a (x i ＝1)＝Q i (x i ＝1)
the above formula is expressed in the logarithmic domain as:
and step six, the demodulator updates each bit by using the prior soft bit information from the channel symbol information and the received prior soft bit information.
Using the symbol information from the channel calculated in step twoAnd the prior information p obtained by feedback in the step five a (x i The method comprises the steps of (a) updating information of each bit together, completing an outer iteration process, and obtaining updated probability information of each bit as follows:
the above formula is expressed in the logarithmic domain as:
wherein,the ith bit, b e {0,1}, y, representing the t-th symbol t T-th symbol representing channel transmission, < >>Constellation point +.f representing bit b at ith position of constellation map χ>Set of->Represents the j-th bit value corresponding to the k-th constellation mapping point.
And step seven, using probability information of the check nodes meeting the probability detection nodes as confidence coefficient parameters in the iteration process, and using the confidence coefficient parameters for judging the iteration stopping criteria.
Node g i Representing whether the ith check equation is satisfied, we can use the probability p (g i =0) represents a probability mass function of whether the i-th equation is satisfied or not among the check equations. Check node h i To the detection node g i The information of all variable nodes connected with the ith check node needs to be calculated, expressed as:
wherein,representation of other than g i Summation of functions of all variable nodes except V m′ ∈N(C i )\g i Represents V m′ Belonging to check node C i Connected, but not including node g i All variable node sets, f i (x) Immediate indication function I C (C i ) =δ (·) represents that the function value is 1 when all variable nodes connected to the check node modulo the two sums are 0.
The output of the detection node G is the check node satisfaction probability p (G i =0|h, Y), indicating that the check equation detection node outputs a check relationship g under the condition that the received channel sequence Y and the check matrix H are known i A probability of 0, expressed as:
check node normalized satisfaction probability node G sum Output p (G) sum ) To normalize the output values of all the detection nodes G:
with p (G) sum ) As a confidence coefficient parameter, the change trend in the inner and outer iterative processes can know that if the confidence coefficient parameter gradually tends to 1 from 0.5 and converges, the codeword is a correctly decodable codeword; if the confidence parameter converges to about 0.5 during the decoding process, it indicates that the confidence parameter converges to the error codeword during the decoding process, and the next outer iteration process can be performed, and channel information is introduced again to re-decode the frame. If the confidence level is continuously oscillating between 0.5-1, the codeword is in a non-converging pattern.
Based on the above description, the stopping criteria are expressed as: (one) when the check node normalizes the satisfaction probability p (G) sum ) Stopping the iteration of the current frame when the decoding success threshold is reached, and considering that the decoding is successful; (II) when the check node normalizes the satisfaction probability p (G) sum ) Stopping the current decoding iteration when the symbol convergence threshold value is threshold value, and entering an outer iteration process; and (III) stopping iteration when the inner and outer iteration reaches the maximum inner and outer iteration times.
The stopping criterion gives three threshold parameters T, γ, η for the judgment. Wherein T represents a decoding success threshold, gamma represents a converged continuous period threshold, and eta represents a variation range threshold.
As shown in fig. 3, the specific implementation process of the stopping criterion is as follows: first, the confidence coefficient p (G) sum ) If the value of (2) is greater than the decoding success threshold value T, when p (G sum ) The decoding process of the system is stopped immediately and the bit a posteriori probability output of the decoder is decided, assuming that the frame processed by the current decoder has found the correct codeword. Next, the current iteration period p (G sum ) If the difference is small from the value of the previous cycleAnd when the threshold eta of the variation range is set, the counter is increased by 1, otherwise, the counter is set to 0. When the counter reaches the threshold gamma of the continuous period for setting convergence, the current decoding process is regarded as being converged, the subsequent decoding iteration is invalid, and at the moment, the decoding inner iteration process is also immediately terminated and the updating process of the outer iteration is started. In addition to the above two cases, when the iterative decoding process exceeds the preset number of iterations and the correct codeword cannot be found, the decoder stops the current iterative process and proceeds to the iterative process of the next frame.
And step eight, outputting bit judgment to obtain a codeword sequence decoded by the receiver, and completing the digital communication process.
Judging the first k bits according to the decoding output posterior probability information, if Q i (x i ＝0)＞Q i (x i =1), then m i And judging to be 0, otherwise, judging to be 1, so as to obtain a received code word sequence, and finishing the demodulation-decoding process.
According to the embodiment, LDPC codes and 8PSK modulation are combined, the frequency band utilization rate is improved on the basis of guaranteeing the channel coding gain, the iteration stopping criterion is judged according to the convergence analysis of the check node normalization meeting probability, the implementation complexity and the iteration times of the traditional stopping criterion are reduced, the time delay can be effectively reduced, and the system throughput is improved.
For the simulation analysis of the error rate and average internal and external iteration times of the example, three threshold parameters T, gamma and eta of the stopping criterion are respectively set as 0.83,3,0.008, and simulation results are shown in fig. 4 and 5. As shown in fig. 4, compared with the BICM system, the combined code-modulated LDPC-BICM-ID system improves the bit error rate performance of the system to a certain extent, and the stopping criterion designed by the present invention does not substantially affect the bit error rate performance. As shown in fig. 5, at a low signal-to-noise ratio, the stopping criterion based on this example greatly reduces the average decoding iteration number.
While the foregoing is directed to embodiments of the present invention, other and further embodiments of the invention may be devised without departing from the basic scope thereof, and the scope thereof is determined by the claims that follow.

Claims (9)

1. A BICM-ID iterative receiving method based on LDPC codes is characterized in that: comprises the following steps of the method,
step one, respectively carrying out coding, interleaving, mapping and modulation treatment on an original information sequence, and entering an AWGN channel for transmission;
step two, the demodulator receives the output symbol from the AWGN channel to demap, and calculates the probability information of the transmission symbol and the corresponding bit by using the channel information and the prior probability information;
step three, the bit probability information after demapping is processed through a deinterleaver pi -1 Establishing a global detailed factor graph model aiming at the LDPC-BICM-ID system receiver;
step four, finishing iterative decoding of the belief propagation algorithm in the LDPC decoder;
step five, the decoded soft bit information is fed back to a demodulator through an interleaver and used as prior information of next demodulation;
step six, the demodulator updates each bit by using the prior soft bit information from the channel symbol information and the received prior soft bit information;
step seven, using probability information of the check nodes meeting the probability detection nodes as confidence parameters in the iteration process, and using the confidence parameters for judging an iteration stopping criterion;
and step eight, outputting bit judgment to obtain a codeword sequence decoded by the receiver, and completing the digital communication process.
2. The method for iterative receiving of BICM-ID based on LDPC code as claimed in claim 1, wherein: the implementation method of the first step is that,
the original information sequence M with the length of k bits is multiplied by the generating matrix G of LDPC coding to obtain a coding result C=M.G, and the length of the coded sequence C is n; thereafter, the encoded information bits are passed through an interleaverPerforming interleaving operation to obtain a code element sequence X=pi (C), wherein a function pi represents a specific interleaving and de-interleaving mode; the interleaver only changes the order of the symbols, does not change the total length of the symbol sequence, and thus the sequence C and the sequence X have the same length; passing the encoded information bits through a constellation mapping function{0,1} n →Ω t Mapping, m coded and interleaved information bits x 0 ,x 1 ,…,x m-1 Mapping to constellation points in 1 space; where Ω represents the complete constellation space of the mapped symbol, containing M constellation points in total, where m=2 m ， Representing a downward rounding; the symbol sequence is obtained after modulation mapping of the sequence X obtained after interleavingThe method can be expanded into a higher-order modulation mode by changing the specific form of the function mapping; and finally, transmitting the symbol sequence Y through an AWGN channel.
3. The method for iterative receiving of BICM-ID based on LDPC code as claimed in claim 2, wherein: the implementation method of the second step is that,
the channel output symbol sequence is represented by z= { Z 1 ,z 2 ,…,z t When deriving soft bit information using initial symbol information of a received channel, the source can be regarded as an equal probability distribution, so that the probability of each bit node initially being 0 or 1 is equal, i.e.:
wherein x is i A value representing the i-th bit in the transmission sequence; mapping symbols in constellation mapping spaceThe probability of (2) is also the same, namely:
the probability information of each transmission symbol is:
wherein y is t Representing the t-th symbol, z in the sequence of transmitted symbols t Representing the t-th symbol in the received symbol sequence;middle "]" represents its estimated value;
based on the additive white gaussian noise channel, the probability density function is:
whereas for complex gaussian channels, the probability density function is:
wherein sigma 2 Representing the variance of the gaussian channel; y is I And y Q Representing the real and imaginary parts, z, respectively, of the channel transmit symbol y I And z Q Representing the real and imaginary parts of the channel received symbol z, respectively;
substituting the initial probability information into the above mode and simplifying the initial probability information to obtain the initial probability information of each transmission symbol as follows:
wherein,and->Respectively representing the real part and the imaginary part, z, of the kth constellation mapping point in the constellation mapping space re And z im Representing the real and imaginary parts of the channel received symbol z, respectively;
deriving probability information of each bit from the symbol probability information:
wherein the method comprises the steps ofConstellation point +.f representing bit b at ith position of constellation map χ>Is a collection of (3);
the above formula is expressed in the logarithmic domain as:
4. the method for iterative receiving of BICM-ID based on LDPC code as claimed in claim 3, wherein: the implementation method of the third step is that,
the de-interleaving only changes the bit order, has no effect on the probability information, and therefore has no effect onAnd->No distinction is made;
constructing a factor graph model G= (VNs U CNs, xi) with a check constraint relation according to a check matrix of the LDPC code, wherein VNs represents a variable node set, CNs represents a check node set, and xi represents a variable node and an edge set of the check node, and corresponds to the position of 1 in the check matrix H;
channel received symbol sequence z= { Z 1 ,Z 2 ,…,Z t The bit stream sequence X= { X is obtained through the joint mapping module phi 1 ,X 2 ,…,X n And obtaining a sequence C= { C by a de-interleaving module pi 1 ,C 2 ,…,C n Corresponding to the variable node set VNs in the G= (VNs U.CNs, xi) model, the first k variable nodes correspondingly output a decoding final result sequence M= { M 1 ,M 2 ,…,M k }；
On the basis, the added check node satisfies the probability detection node G= { G 1 ,g 2 ,…,g n-k Normalized meeting probability statistic node G of check node sum The method comprises the steps of carrying out a first treatment on the surface of the Check node CNs= { h 1 ,h 2 ,…,h n-k Meeting probability check node g= { G to check node connected thereto 1 ,g 2 ,…,g n-k One-way transfer of information, where h i Represents the ith check node, g i Representing the ith detection node, which are in one-to-one correspondence.
5. The method for iterative receiving of BICM-ID based on LDPC codes as claimed in claim 4, wherein: the implementation method of the fourth step is that,
by r ji (x i ) Represents the j-th check node C j A probability density function with a corresponding bit of "0" or "1" passed to the ith variable node; with q ij (x i ) Represents the ith variable node V i A probability density function with a corresponding bit of "0" or "1" passed to the jth check node; the check node update process is expressed as:
the variable node update process is expressed as:
wherein, set R j\i Set C representing the set of positions except for the ith 1 in the jth row of the check matrix H i\j Representing a set of positions except for the jth 1 in the ith row in the check matrix H;
the node update procedure is expressed in the logarithmic domain as:
the primary node updating process is regarded as an internal iteration process; repeating the node updating process until a stopping criterion is reached; by Q i (x i ) Representing the posterior likelihood probability of the ith variable node, namely the probability value to be finally calculated in the iterative decoding process;
the above formula is expressed in the logarithmic domain as:
6. the method for iterative receiving of BICM-ID based on LDPC codes as claimed in claim 5, wherein: the implementation method of the fifth step is that,
the interleaver only changes the sequence, does not affect probability information, does not distinguish between x and c, uses p a (x i ) A priori information representing the next demodulation process:
p a (x i ＝0)＝Q i (x i ＝0)
p a (x i ＝1)＝Q i (x i ＝1)
the above formula is expressed in the logarithmic domain as:
7. the method for iterative receiving of BICM-ID based on LDPC code as claimed in claim 6, wherein: the implementation method of the step six is that,
using the symbol information from the channel calculated in step twoAnd the prior information p obtained by feedback in the step five a (x i The method comprises the steps of (a) updating information of each bit together, completing an outer iteration process, and obtaining updated probability information of each bit as follows:
the above formula is expressed in the logarithmic domain as:
wherein,the ith bit, b e {0,1}, y, representing the t-th symbol t T-th symbol representing channel transmission, < >>Constellation point +.f representing bit b at ith position of constellation map χ>Set of->Represents the j-th bit value corresponding to the k-th constellation mapping point.
8. The method for iterative receiving of BICM-ID based on LDPC code as claimed in claim 7, wherein: the implementation method of the step seven is that,
node g i Representing whether the ith check equation is satisfied, we can use the probability p (g i =0) represents a probability mass function of whether an i-th equation is satisfied or not among the check equations; check node h i To the detection node g i The information of (a) needs to be calculated through the information of all variable nodes connected with the ith check node, and the information is representedThe method comprises the following steps:
wherein,representation of other than g i Summation of functions of all variable nodes except V m′ ∈N(C i )\g i Represents V m′ Belonging to check node C i Connected, but not including node g i All variable node sets, f i (x) Immediate indication function I C (C i ) =δ (·) representing that when the modulo two addition of all variable nodes connected to the check node is 0, the function value is 1;
the output of the detection node G is the check node satisfaction probability p (G i =0|h, Y), indicating that the check equation detection node outputs a check relationship g under the condition that the received channel sequence Y and the check matrix H are known i A probability of 0, expressed as:
check node normalized satisfaction probability node G sum Output p (G) sum ) To normalize the output values of all the detection nodes G:
with p (G) sum ) As a confidence coefficient parameter, the change trend in the inner and outer iterative processes can know that if the confidence coefficient parameter gradually tends to 1 from 0.5 and converges, the codeword is a correctly decodable codeword; if the confidence parameter converges to about 0.5 during the decoding process, it is indicated that the error codeword is converged during the decoding process, the next outer iteration process can be performed, and the channel is reintroducedThe information re-decodes the frame; if the confidence level continuously oscillates between 0.5 and 1, the codeword is in a non-converging pattern;
based on the above description, the stopping criteria are expressed as: (one) when the check node normalizes the satisfaction probability p (G) sum ) Stopping the iteration of the current frame when the decoding success threshold is reached, and considering that the decoding is successful; (II) when the check node normalizes the satisfaction probability p (G) sum ) Stopping the current decoding iteration when the symbol convergence threshold value is threshold value, and entering an outer iteration process; stopping iteration when the inner iteration and the outer iteration reach the maximum inner iteration and the outer iteration times;
three threshold parameters T, gamma and eta are given by a stopping criterion and used for judgment; wherein T represents a decoding success threshold, gamma represents a converged continuous period threshold, and eta represents a variation range threshold;
the specific implementation process of the stopping criterion is as follows: first, the confidence coefficient p (G) sum ) If the value of (2) is greater than the decoding success threshold value T, when p (G sum ) If the T is greater than the T, the frame processed by the current decoder already finds the correct codeword, the decoding process of the system is stopped immediately, and the bit posterior probability output by the decoder is judged; next, the current iteration period p (G sum ) If the difference value is smaller than the threshold eta of the threshold of the set change range, the counter is added with 1, otherwise, the counter is set to 0; when the counter reaches a continuous period threshold gamma with convergence, judging that the current decoding process is converged and then the decoding iteration is invalid, wherein the decoding inner iteration process is also immediately terminated and the updating process of the outer iteration is started; in addition to the above two cases, when the iterative decoding process exceeds the preset number of iterations and the correct codeword cannot be found, the decoder stops the current iterative process and proceeds to the iterative process of the next frame.
9. The method for iterative receiving of BICM-ID based on LDPC codes as claimed in claim 8, wherein: the implementation method of the step eight is that,
judging the first k bits according to the decoding output posterior probability information, if Q i (x i ＝0)＞Q i (x i =1), then m i And judging to be 0, otherwise, judging to be 1, so as to obtain a received code word sequence, and finishing the demodulation-decoding process.
CN202310994227.1A 2023-08-08 2023-08-08 BICM-ID iterative receiving method based on LDPC code Pending CN117040545A (en)

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* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN117792475A (en) * 2023-12-29 2024-03-29 深圳市安信达存储技术有限公司 Instruction detection and error correction method based on satellite running state
CN117792475B (en) * 2023-12-29 2024-06-18 深圳市安信达存储技术有限公司 Instruction detection and error correction method based on satellite running state

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