CN112600568B - Code modulation transmission method combining nonstandard 6-order modulation and LDPC code - Google Patents

Code modulation transmission method combining nonstandard 6-order modulation and LDPC code Download PDF

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CN112600568B
CN112600568B CN202011412567.1A CN202011412567A CN112600568B CN 112600568 B CN112600568 B CN 112600568B CN 202011412567 A CN202011412567 A CN 202011412567A CN 112600568 B CN112600568 B CN 112600568B
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ldpc code
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CN112600568A (en
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韩昌彩
代锁蕾
杨晋生
陈为刚
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Tianjin University
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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

Abstract

The invention discloses a code modulation transmission method combining non-standard 6-order modulation and LDPC codes, which comprises the following steps: at a sending end, performing serial-parallel conversion on an information sequence; performing Galois field GF (2) Low Density Parity Check (LDPC) code encoding and GF (3) LDPC code encoding in layers; combining the GF (2) LDPC code word with the GF (3) LDPC code word to obtain a 6-system code word through mapping; carrying out 6-QAM modulation on the 6-ary code word according to a 6-order quadrature amplitude modulation 6-QAM constellation diagram, and sending a modulation signal to an additive white Gaussian noise AWGN channel; at a receiving end, carrying out soft demodulation on the received signal according to a 6-QAM constellation diagram; according to the 6-system demodulation information, iterative decoding of a GF (3) LDPC code is firstly executed, iterative decoding of the GF (2) LDPC code is executed, decoding information of the GF (2) LDPC code is transmitted to the GF (3) LDPC code, and iterative decoding of the GF (3) LDPC code is executed to realize integral iteration between two LDPC codes; and obtaining the recovered information sequence through parallel-serial conversion.

Description

Code modulation transmission method combining nonstandard 6-order modulation and LDPC code
Technical Field
The invention relates to the field of coding modulation, in particular to a coding modulation transmission method combining nonstandard 6-order modulation and LDPC codes.
Background
With the rapid development of communication technology, the requirement of data transmission rate has been raised to 400Gb/s, however, the limited bandwidth in the communication system and the loss of various noises, filtering effects, etc. existing in the information transmission process are the main factors that restrict the performance of the communication system. From the physical layer perspective of communication transmission, a high-order modulation technique and a channel coding technique are effective means for improving these problems. Compared with the current advanced signal processing technology, the coded modulation technology combining Forward Error Correction (FEC) coding and high-order modulation can achieve higher spectral efficiency and a reliable transmission Error rate. Therefore, under the constraint of limited bandwidth, how to select an efficient code modulation combination scheme has important research significance. Low-Density Parity-Check (LDPC) codes are one of the candidates for third-generation FEC coding schemes due to their advantages of high throughput, Low error-level, and small decoding delay. Compared with a binary LDPC code, the multi-system LDPC code has more excellent error correction performance under medium and short code lengths, is easy to combine with high-order modulation, and can realize transmission with higher spectral efficiency, thereby providing a new thought for high-reliability transmission of information.
The modulation technology moves the frequency spectrum of a signal to an expected position and can be combined with multi-system transmission to improve the transmission rate, so that the frequency spectrum efficiency of the system is improved. The high-order Modulation scheme is mainly classified into Phase-Shift Keying (PSK), Amplitude Phase-Shift Keying (APSK), and Quadrature Amplitude Modulation (QAM). The current research work is focused on 2p(p ≧ 4) high-order or high-dimensional constellation design of constellation points. PSK modulation is more advantageous in terms of peak-to-average power ratio, but its euclidean distance decreases rapidly with increasing constellation size, so that high-order PSK modulation is rarely used in practice. Compared with other high-order modulation, the QAM has better noise resistance and higher bandwidth utilization rate, but has higher sensitivity to nonlinear distortion at the cost of higher peak-to-average power ratio. In addition to the above three common modulation methods, the regular hexagonal constellation modulation is widely focused on its advantage of being able to retain the minimum euclidean distance under the high-order modulation of the relatively low Peak-to-Average Power Ratio (PAPR). In addition, for 3 × 2pThe design method of the binary self-adaptive QAM constellation diagram is also concerned. According to the constellation scheme, 2p +3 bits are mapped into 2 symbols for information transmission, finer granularity is allocated to the bits, the flexibility of adaptive modulation is improved, and only the error rate performance without coding is concerned. Researchers have proposed a coding scheme for 6-PSK that converts 5 bits into 2 symbols, but this method suffers from a certain conversion efficiency loss because some information transmission is discarded during the conversion process. Researchers have proposed an orthogonal coding method for 6-PSK, which searches 18-dimensional codewords, and generates 72-symbol orthogonal codes by repeating four consecutive cycles for each symbol, but in practical cases, a certain error occurs due to random mismatch of symbol values. Communication system channels are typically subject to non-linear effectsDue to the effect, the power is limited and the performance desired for the corresponding modulation order cannot be achieved. As the modulation order increases, the tolerance to signal impairments decreases, which will lead to a deterioration of the system performance. In this case, it is necessary to design in conjunction with FEC coding to further increase the transmission capacity of the communication system.
The combination of the multi-system LDPC code and the high-order modulation of the corresponding order can further optimize the performance of the error rate, thereby ensuring the reliability of information transmission. The combination of the two has the advantages that the order of the multilevel symbol is the same as that of the modulation symbol, the symbol mapping can be directly carried out, the operation is simple, and the decoding performance is excellent. The combination of multilevel LDPC codes and high-order modulation is mainly divided into two categories, Galois field GF (2)p) LDPC codes and 2pCombination of order higher order modulation and GF (q) (≠ 2)p) LDPC codes are combined with q-order higher order modulations, q representing the size of the galois field. The first type combines a bit interleaving method, a multilevel trellis coding method or a method combining non-uniform constellation modulation and a multilevel LDPC code, and fuses coded bits and a high-order modulation constellation together to obtain performance optimization. However, with the increase of the modulation order q, the coding and decoding complexity of the multi-system LDPC code is greatly increased, which results in too long decoding time and low feasibility. The second type of combining method is generally aimed at lower modulation orders, and the coding and decoding complexity of the corresponding multi-system LDPC code is lower. The current research on the second kind of combining method mainly focuses on the combination of 5-QAM, 7-QAM, 9-QAM and the LDPC code corresponding to galois field. Researchers put forward a constellation diagram design algorithm of 5-QAM and 7-QAM applied to a self-adaptive optical network based on Huffman coding, the algorithm adopts Huffman coding for precoding, inputs information bits of LDPC codes, maps the information bits to corresponding constellation points in groups, sets different probabilities for the constellation points to realize probability forming, and saves transmitting power. And further, 5-QAM and 7-QAM are respectively combined with GF (5) NB-LDPC codes and GF (7) NB-LDPC codes, so that excellent decoding performance is realized. The algorithm considers the code rate of the non-uniform shaping and the LDPC code when designing the constellation diagram, and improves the coding gain and the overall performance. Non-uniform 9-QAM constellation is proposed and combined with corresponding binary LDPC code in the same spectrum effectAnd the performance is 0.8dB higher than that of the multi-system LDPC code combined with 8-QAM. Researchers put forward a method for combining 7-QAM and GF (7) NB-LDPC codes suitable for satellite channels, the method designs a constellation diagram with an original point plus a regular hexagon configuration, and further combines the 7-QAM and the LDPC codes of a corresponding system, so that good anti-noise performance is obtained, and compared with 8-PSK, the demodulation threshold of the 7-QAM is lower, and the sensitivity to nonlinear distortion is effectively reduced. In addition, researchers have proposed a multilevel coded modulation scheme combining 18-HSM and Turbo coding, which is a regular hexagonal shell constellation modulation in 18 systems. The regular hexagon constellation modulation can fully utilize two-dimensional plane space, and the 18-HSM has higher resistance to the nonlinearity of a power amplifier compared with the square 16-QAM. However, the HSM modulation is suitable for modulation with three or more levels, and for modulation with low order such as 6-HSM, the performance of the HSM is equivalent to that of 6-PSK, and no obvious advantage is provided. Furthermore, for modulation order of 3 × 2pThe research on the QAM modulation mode is relatively mature, but how to realize 3 x 2pThere is still a great deal of research space for matching the higher order modulation of the order with the multilevel LDPC code.
Disclosure of Invention
The invention provides a coding modulation transmission method combining non-standard 6-order modulation and LDPC codes, which can realize high-efficiency coding and decoding operation, reduce the error rate of transmission data and ensure the reliability of high-speed information transmission, and is described in detail as follows:
a coded modulation transmission method combining non-standard 6 th order modulation with LDPC codes, the method comprising the steps of:
(1) at a sending end, performing serial-parallel conversion on an information sequence; performing Galois field GF (2) Low Density Parity Check (LDPC) code encoding and GF (3) LDPC code encoding in layers; combining the GF (2) LDPC code word with the GF (3) LDPC code word to obtain a 6-system code word through mapping;
(2) carrying out 6-QAM modulation on the 6-ary code word according to a 6-order quadrature amplitude modulation 6-QAM constellation diagram, and sending a modulation signal to an additive white Gaussian noise AWGN channel;
(3) at a receiving end, carrying out soft demodulation on the received signal according to a 6-QAM constellation diagram; according to the 6-system demodulation information, iterative decoding of a GF (3) LDPC code is firstly executed, iterative decoding of the GF (2) LDPC code is executed, decoding information of the GF (2) LDPC code is transmitted to the GF (3) LDPC code, and iterative decoding of the GF (3) LDPC code is executed to realize integral iteration between two LDPC codes; and obtaining the recovered information sequence through parallel-serial conversion.
Wherein the step (1) is as follows:
(1.1) the information sequence U is converted into an information sequence U with the length of k 2-system symbols by serial-parallel conversionBInformation sequence U with length of k 3-ary symbolsT；
(1.2) transmitting the information sequence UBInputting GF (2) LDPC code encoder, generating code word C of GF (2) LDPC code with code length of n 2-system symbolsBTo convert the information sequence UTInputting GF (3) LDPC code encoder, generating code word C of GF (3) LDPC code with code length of n 3-system symbolsT；
(1.3) according to GF (2) symbols
Figure BDA0002818842590000031
With GF (3) symbols
Figure BDA0002818842590000032
Value of (A) CBAnd CTThe mapping is a 6-ary codeword, and the mapping rule is 00 → 0, 01 → 1, 02 → 2, 10 → 3, 11 → 4, 12 → 5.
Wherein the step (2) is as follows:
(2.1) constructing a 6-QAM constellation diagram, wherein 1 constellation point is distributed at the origin of the constellation point and corresponds to 0 element in a 6-system, and the other 5 constellation points are equidistantly distributed on an excircle with a radius of R by a phase difference phi of 2 pi/5 and correspond to 5 non-zero elements in the 6-system;
and (2.2) carrying out 6-QAM modulation on the 6-ary code word C, and sending the obtained modulation signal to an AWGN channel.
Wherein the step (3) is as follows:
(3.1) Complex coordinates y from the l-th received symbollAnd the complex coordinate x of the a-th constellation pointaCalculating to obtain the likelihood information of the 6-system symbol; normalizing symbol likelihood information to obtain the l-th receivedProbability that the 6-ary symbol is a;
(3.2) initializing integral iteration times Iter between GF (3) LDPC codes and GF (2) LDPC codes;
(3.3) GF (3) LDPC decoder based on probability P of l 6 th symboll aCalculating decoding prior probability P of GF (3) LDPC codeT；
(3.4) GF (3) LDPC code decoder performs iterative decoding of GF (3) LDPC codes by a prior probability PTCalculating posterior probability post of GF (3) LDPC code decoding with probability information of iterative decoding post variable nodeTAnd judging to obtain the decoding code word of the GF (3) LDPC code
Figure BDA0002818842590000041
If code word
Figure BDA0002818842590000042
And 3-ary check matrix HTSatisfy the requirement of
Figure BDA0002818842590000043
Or if the decoding iteration times of the GF (3) LDPC code reach the maximum value, the decoding is finished;
(3.5) GF (2) LDPC decoder based on probability P of l 6 th symboll aPosterior probability post for decoding GF (3) LDPC codeTCalculating prior probability P of GF (2) LDPC code decodingB；
(3.6) GF (2) LDPC code decoder performs iterative decoding of GF (2) LDPC codes by a prior probability PBCalculating posterior probability post of GF (2) LDPC code decoding with probability information of iterative decoding post variable nodeBAnd judging to obtain the decoding code word of GF (2) LDPC code
Figure BDA0002818842590000044
If code word
Figure BDA0002818842590000045
And 2-ary check matrix HBSatisfy the requirement of
Figure BDA0002818842590000046
Or GF (2) LDPC codesIf the iteration number of decoding reaches the maximum value, the decoding is ended;
(3.7) increasing the integral iteration number Iter by 1 time, and judging whether the maximum integral iteration number Iter is reachedoutIf Iter > -outIf not, executing the step (3.9), otherwise, executing the step (3.8);
(3.8) GF (3) LDPC code decoder according to probability of 6-system symbol and posterior probability post of GF (2) LDPC code decodingBUpdating GF (3) LDPC code decoding prior probability PTAnd returning to the step (3.4) to continue execution;
(3.9) decoding GF (2) LDPC code
Figure BDA0002818842590000047
And GF (3) LDPC code decoding code word
Figure BDA0002818842590000048
Obtaining the recovered information sequence by parallel-to-serial conversion
Figure BDA0002818842590000049
The technical scheme provided by the invention has the beneficial effects that:
1. the invention realizes the matching of non-standard 6-system modulation and error correction coding, and obtains superior decoding performance; the method adopts two LDPC codes to carry out layered coding, and divides the coding of the LDPC codes into a mode of combining GF (2) LDPC code coding and GF (3) LDPC code coding;
2. the invention designs an iterative decoding method between two layers of LDPC codes, which realizes iterative decoding between two layers of codes by a mode of mutually transmitting GF (2) LDPC code decoding information and GF (3) LDPC code decoding information and improves the error correction performance of a system.
Drawings
FIG. 1 is a block diagram of a coded modulation transmission method that combines non-standard 6 th order modulation with LDPC codes;
FIG. 2 is a mapping diagram of GF (2) symbols, GF (3) symbols and 6-ary symbols;
FIG. 3 is a schematic diagram of a 6-QAM constellation;
FIG. 4 is a flow chart of a method for iterative decoding of 6-ary code;
FIG. 5 is a schematic diagram of error code performance of the 6-ary code iterative decoding method under different overall iteration times;
fig. 6 is a performance comparison of the method according to the embodiment of the present invention and a coding transmission method based on a GF (7) LDPC code, a coding modulation transmission method based on a GF (5) LDPC code, and a coding modulation transmission method combining a 6-ary code with 6-PSK.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, embodiments of the present invention are described in further detail below.
For 3X 2pAnd the coding is difficult to realize because the coding modulation is not based on the extension of 2 systems. In order to perfectly match the constellation size with the codes, the embodiment of the invention researches an LDPC code layered coding method matched with 6-QAM, and provides a code modulation transmission method combining non-standard 6-QAM and LDPC codes. The method not only increases the flexibility of the system, but also realizes excellent decoding performance. Firstly, a 6-QAM constellation diagram is provided, and then a coded modulation transmission method which is matched with 6-QAM and combines binary coding and ternary coding is provided. At a transmitting end, firstly, the layered coding of the GF (2) LDPC code and the GF (3) LDPC code is executed, the code words of the GF (2) LDPC code and the code words of the GF (3) LDPC code are respectively obtained, and then the two code words are mapped according to the designed mapping rule to obtain the six-system code words. At a receiving end, according to the structural characteristics of the six-system code, an iterative processing method aiming at the six-system code modulation is provided, the method realizes the mutual transmission of GF (2) LDPC code decoding information and GF (3) LDPC code decoding information, the decoding success rate of the LDPC code is improved through the iterative decoding between two layers of codes, and further the integral decoding performance of the system is improved. Finally, simulation analysis is performed on Symbol Error Rate (SER) performance of the proposed coded modulation transmission scheme under the AWGN channel.
In order to ensure the reliability of high-speed information transmission, the embodiment of the invention provides a code modulation transmission method combining nonstandard 6-order modulation and LDPC codes. The method designs an LDPC code layered coding method based on GF (2) LDPC codes and GF (3) LDPC codes, and provides an iterative decoding method between double-layer LDPC codes according to the coding characteristics of the LDPC codes. Further, 6-system codes and 6-QAM are combined to realize integral matching transmission. The method not only increases the flexibility of the system, but also realizes excellent decoding performance. Embodiments of the present invention will be described in detail below with reference to the accompanying drawings.
The present embodiment describes in detail a transmission method combining non-standard 6-order modulation and LDPC code coded modulation proposed in an embodiment of the present invention, and with reference to fig. 1, the method specifically includes the following steps:
(1) at a sending end, firstly, serial-parallel conversion is carried out on an information sequence; then, performing GF (2) LDPC code coding and GF (3) LDPC code coding in a layered mode; further, combining the code word of the GF (2) LDPC code with the code word of the GF (3) LDPC code to obtain a 6-system code word through mapping; finally, 6-QAM modulation is carried out on the 6-ary code word according to a 6-QAM constellation diagram, and a modulation signal is sent to an AWGN channel;
(2) at a receiving end, firstly, carrying out soft demodulation on a received signal according to a 6-QAM constellation diagram; then, according to the 6-system demodulation information, firstly, iterative decoding of the GF (3) LDPC code is executed, further, iterative decoding of the GF (2) LDPC code is executed, then the decoding information of the GF (2) LDPC code is transmitted to the GF (3) LDPC code, and the iterative decoding of the GF (3) LDPC code is continuously executed to realize integral iteration between the two LDPC codes; and finally, obtaining the recovered information sequence through parallel-serial conversion.
The specific steps of hierarchically executing the GF (2) LDPC code encoding and the GF (3) LDPC code encoding, combining codewords of the GF (2) LDPC code and codewords of the GF (3) LDPC code, and obtaining 6-ary codewords through mapping are as follows:
(1.1) the information sequence U is converted into an information sequence with the length of k 2-system symbols by serial-parallel conversion
Figure BDA0002818842590000061
Information sequence with length of k 3-ary symbols
Figure BDA0002818842590000062
Two parts;
(1.2) sequencing the information
Figure BDA0002818842590000063
Inputting GF (2) LDPC code encoder, generating GF (2) LDPC code word with code length of n 2-system symbols
Figure BDA0002818842590000064
Information sequence
Figure BDA0002818842590000065
Inputting GF (3) LDPC code encoder, generating GF (3) LDPC code word with code length of n 3-system symbols
Figure BDA0002818842590000066
Referring to fig. 2, the mapping relationship between codewords of the GF (2) LDPC code and codewords of the GF (3) LDPC code and codewords of the 6 system is as follows:
the first column in fig. 2 represents GF (2) elements, i.e. 0 and 1, and the second column represents GF (3) elements 0, 1 and 2. Each 6-ary codeword is composed of two-bit symbols, where the first bit is a codeword of a GF (2) LDPC code and the second bit is a codeword of a GF (3) LDPC code. The total number of element combinations of GF (2) and GF (3) is 6. These 6 combinations correspond one-to-one to 6-ary elements 0 to 5.
(1.3) according to GF (2) symbols
Figure BDA0002818842590000071
With GF (3) symbols
Figure BDA0002818842590000072
Value of (A) CBAnd CTMapping to 6-ary code word
Figure BDA0002818842590000073
The specific mapping rule is, if
Figure BDA0002818842590000074
Then c isi0, i.e. 00 → 0, similarly 01 → 1, 02 → 2, 10 → 3, 11 → 4, 12 → 5.
The method comprises the following steps of carrying out 6-QAM modulation on a 6-ary code word, and sending a modulation signal to an AWGN channel, wherein the specific steps are as follows:
(2.1) constructing a 6-QAM constellation diagram;
(2.2) carrying out 6-QAM modulation on the 6-ary code word C to obtain a modulation signal;
(2.3) transmitting the modulated signal over an AWGN channel.
Referring to fig. 3, the distribution of the 6-QAM constellation is:
(3.1)1 constellation point is distributed at the origin of the constellation point and corresponds to 0 element in the 6-system;
(3.2) the other 5 constellation points are equidistantly distributed on an excircle with the radius of R by a phase difference phi of 2 pi/5, and correspond to 5 non-zero elements in a 6-system;
(3.3) radius of 6-QAM constellation is R, wherein the radius
Figure BDA0002818842590000075
Referring to fig. 4, at a receiving end, first, a received signal is soft-demodulated according to a 6-QAM constellation; then, according to the 6-system demodulation information, firstly, iterative decoding of the GF (3) LDPC code is executed, further, iterative decoding of the GF (2) LDPC code is executed, then the decoding information of the GF (2) LDPC code is transmitted to the GF (3) LDPC code, and the iterative decoding of the GF (3) LDPC code is continuously executed to realize integral iteration between the two LDPC codes; and finally, obtaining an information sequence through parallel-serial conversion, wherein the specific steps are as follows:
(4.1) at the receiving end, according to the complex coordinate y of the l-th received symbol l1,2, …, n and the complex coordinate x of the a-th constellation pointa6-system symbol likelihood information is obtained through calculation:
Figure BDA0002818842590000076
normalizing the symbol likelihood information to obtain the probability P that the ith received 6-system symbol is al a，Pl aThe calculation formula of (a) is as follows:
Figure BDA0002818842590000081
wherein σ2Representing the variance of white gaussian noise.
(4.2) initializing integral iteration times Iter between GF (3) LDPC codes and GF (2) LDPC codes;
(4.3) GF (3) LDPC decoder based on probability P of l 6 th symboll aCalculating decoding prior probability of GF (3) LDPC code
Figure BDA0002818842590000082
Wherein, the decoding prior probability of the l 3-th symbol
Figure BDA0002818842590000083
The calculation formula of (a) is as follows,
Figure BDA0002818842590000084
and
Figure BDA0002818842590000085
respectively representing the probabilities that the ith 3-ary symbol is 0, 1 and 2:
Figure BDA0002818842590000086
(4.4) GF (3) LDPC code decoder performs iterative decoding of GF (3) LDPC code by prior probability PTProbability information calculation of GF (3) LDPC code decoding posterior probability with iterative decoding post-variable node
Figure BDA0002818842590000087
Wherein, the posterior probability of the l 3 th symbol
Figure BDA0002818842590000088
Figure BDA0002818842590000089
And
Figure BDA00028188425900000810
respectively representing the posterior probabilities that the l 3-th symbol is judged to be 0, 1 and 2, and obtaining the decoding code word of the GF (3) LDPC code through judgment
Figure BDA00028188425900000811
If code word
Figure BDA00028188425900000812
And 3-ary check matrix HTSatisfy the requirement of
Figure BDA00028188425900000813
Or if the decoding iteration times of the GF (3) LDPC code reach the maximum value, the decoding is finished;
(4.5) GF (2) LDPC decoder based on probability P of l 6 th symboll aPosterior probability post for decoding GF (3) LDPC codeTCalculating prior probability of GF (2) LDPC code decoding
Figure BDA00028188425900000814
Prior probability of the l 2-th symbol
Figure BDA00028188425900000815
The calculation formula of (a) is as follows, wherein,
Figure BDA00028188425900000816
representing the probability that the ith 2-ary symbol is 0,
Figure BDA00028188425900000817
represents the probability that the ith 2-ary symbol is 1:
Figure BDA00028188425900000818
(4.6) GF (2) LDPC code decoder performs iterative decoding of GF (2) LDPC codes by a prior probability PBProbability information calculation of GF (2) LDPC code decoding posterior probability with iterative decoding post-variable node
Figure BDA0002818842590000091
Decoding code word of GF (2) LDPC code obtained by judgment
Figure BDA0002818842590000092
If code word
Figure BDA0002818842590000093
And 2-ary check matrix HBSatisfy the requirement of
Figure BDA0002818842590000094
Or if the decoding iteration times of the GF (2) LDPC code reach the maximum value, the decoding is finished;
(4.7) increasing the integral iteration number Iter by 1 time, and judging whether the maximum integral iteration number Iter is reachedoutIf Iter > -outIf not, executing the step (4.9), otherwise, executing the step (4.8);
(4.8) GF (3) LDPC decoder according to probability of 6-system symbol and posterior probability post of GF (2) LDPC decodingBUpdating GF (3) LDPC code decoding prior probability PTAnd returns to the step (4.4) to continue the execution, specifically,
Figure BDA0002818842590000095
and
Figure BDA0002818842590000096
respectively representing the posterior probability that the l 2-th 2-system symbol is 0 and 1 and the probability of the l 3-system symbol after the decoding of the GF (2) LDPC code in the step (4.6)
Figure BDA0002818842590000097
And
Figure BDA0002818842590000098
the update rule of (2) is as follows:
Figure BDA0002818842590000099
(4.9) decoding GF (2) LDPC code
Figure BDA00028188425900000910
And GF (3) LDPC code decoding code word
Figure BDA00028188425900000911
Obtaining the recovered information sequence by parallel-to-serial conversion
Figure BDA00028188425900000912
DETAILED DESCRIPTION OF EMBODIMENT (S) OF INVENTION
A specific embodiment is given below to illustrate the feasibility of the coded modulation transmission method combining non-standard 6 th order modulation and LDPC code according to the present invention. This example verifies the invention under AWGN channel.
In the 6-ary code constructed in this embodiment, the codeword length is 6000 6-ary symbols, the code rate is 1/2, the check matrix structures adopted by the GF (2) LDPC code and the GF (3) LDPC code are the same, the row subset is {7,8}, and the column subset is {12,3,2,1 }.
As shown in the model of fig. 1, at the transmitting end, the LDPC code division layer encoding process specifically includes:
(1) the information sequence U is converted into 3000 symbols in 2 system by serial-parallel conversion
Figure BDA00028188425900000913
Information sequence with length of 3000 3-system symbols
Figure BDA00028188425900000914
(2) Information sequence
Figure BDA0002818842590000101
Inputting GF (2) LDPC code encoder, generating code word of GF (2) LDPC code with code length of 6000 2-system symbols
Figure BDA0002818842590000102
Information sequence
Figure BDA0002818842590000103
Inputting GF (3) LDPC code encoder, generating code word of GF (3) LDPC code with code length of 6000 3-system symbols
Figure BDA0002818842590000104
(3) According to GF (2) symbols
Figure BDA0002818842590000105
With GF (3) symbols
Figure BDA0002818842590000106
Value of (A) CBAnd CTMapping to 6-ary code word
Figure BDA0002818842590000107
The specific mapping rule is, if
Figure BDA0002818842590000108
Figure BDA0002818842590000109
Then c isi0, i.e. 00 → 0, similarly 01 → 1, 02 → 2, 10 → 3, 11 → 4, 12 → 5.
(4) The 6-ary codeword C is 6-QAM modulated and the modulated signal is transmitted to an AWGN channel.
After passing through the AWGN channel, the 6-system code iterative decoding method at the receiving end specifically comprises the following steps:
(1) from the complex coordinate y of the l-th received symbol l1,2, …,6000 and the complex coordinate x of the a-th constellation pointaObtaining the likelihood information of the 6-system symbol by calculation
Figure BDA00028188425900001010
Normalizing the symbol likelihood information to obtain the probability P that the l-th received symbol is al a，Pl aIs calculated as follows
Figure BDA00028188425900001011
(2) Initializing integral iteration times Iter between GF (3) LDPC codes and GF (2) LDPC codes;
(3) GF (3) LDPC code decoder according to probability P of l 6-th symboll aCalculating decoding prior probability of GF (3) LDPC code
Figure BDA00028188425900001012
Wherein, the decoding initial probability of the l 3 th symbol
Figure BDA00028188425900001013
The calculation formula of (a) is as follows,
Figure BDA00028188425900001014
and
Figure BDA00028188425900001015
respectively representing the initial probabilities of the ith 3-ary symbol being 0, 1 and 2,
Figure BDA00028188425900001016
(4) the GF (3) LDPC code decoder performs iterative decoding of the GF (3) LDPC code by a prior probability PTProbability information calculation of GF (3) LDPC code decoding posterior probability with iterative decoding post-variable node
Figure BDA0002818842590000111
Posterior probability of the l 3 th symbol
Figure BDA0002818842590000112
Figure BDA0002818842590000113
And
Figure BDA0002818842590000114
respectively representing the l < th > 3-ary symbol judgmentJudging to obtain the decoding code word of GF (3) LDPC code according to the posterior probability of 0, 1 and 2
Figure BDA0002818842590000115
If code word
Figure BDA0002818842590000116
And 3-ary check matrix HTSatisfy the requirement of
Figure BDA0002818842590000117
Or if the decoding iteration times of the GF (3) LDPC code reach 20 times, the decoding is finished;
(5) GF (2) LDPC code decoder according to probability P of l 6-th system symboll aPosterior probability post for decoding GF (3) LDPC codeTCalculating prior probability of GF (2) LDPC code decoding
Figure BDA0002818842590000118
Prior probability of the l 2-th symbol
Figure BDA0002818842590000119
The calculation formula of (a) is as follows, wherein,
Figure BDA00028188425900001110
representing the probability that the ith 2-ary symbol is 0,
Figure BDA00028188425900001111
representing the probability that the ith 2-ary symbol is 1,
Figure BDA00028188425900001112
(6) the GF (2) LDPC code decoder performs iterative GF (2) LDPC code decoding with a prior probability PBProbability information calculation of GF (2) LDPC code decoding posterior probability with iterative decoding post-variable node
Figure BDA00028188425900001113
Decoding code for obtaining GF (2) LDPC code by decision
Figure BDA00028188425900001114
If code word
Figure BDA00028188425900001115
And 2-ary check matrix HBSatisfy the requirement of
Figure BDA00028188425900001116
Or if the decoding iteration times of the GF (2) LDPC code reach 20 times, the decoding is finished;
(7) increasing the integral iteration number Iter by 1 time, and judging whether the maximum integral iteration number Iter is reachedout3, if Iter > - [ Iter ]outIf not, executing the step (8);
(8) the decoder of GF (3) LDPC code decodes the posterior probability post according to the probability of the 6-system symbol and the GF (2) LDPC codeBUpdating GF (3) LDPC code decoding initial probability PTAnd returning to the step (4) to continue the execution, specifically,
Figure BDA00028188425900001117
and
Figure BDA00028188425900001118
respectively representing the posterior probability that the l 2-th 2-system symbol is 0 and 1 and the probability of the l 3-system symbol after the GF (2) LDPC code is decoded in the step (6)
Figure BDA00028188425900001119
And
Figure BDA00028188425900001120
is as follows
Figure BDA0002818842590000121
(9) Decoding codewords from GF (2) LDPC codes
Figure BDA0002818842590000122
And GF (3) LDPC codingCode word
Figure BDA0002818842590000123
Performing parallel-to-serial conversion to obtain recovered information sequence
Figure BDA0002818842590000124
And will follow the same mapping rule as the transmitting end
Figure BDA0002818842590000125
And
Figure BDA0002818842590000126
mapping to 6-ary code word
Figure BDA0002818842590000127
Under an AWGN channel, first, the SER performance of the 6-ary code iterative decoding method in the embodiment of the present invention is verified. The simulation result is shown in fig. 5, where Iter represents the overall number of iterations of the GF (2) LDPC code and the GF (3) LDPC code. SER was 10 compared to the SER performance of 1 iteration as a whole-6When the whole is iterated for 2 times, the performance gain of the embodiment is about 0.2 dB. Secondly, simulating the SER performance of a coding modulation method combining 5-QAM and GF (5) NB-LDPC codes, a coding modulation method based on 7-QAM and a 6-PSK transmission method combining 6-ary codes, and comparing with the embodiment. The simulation results are shown in FIG. 6, where SER is 10-6Compared with the 6-QAM without the code, the proposed code modulation scheme obtains about 9.8dB of code gain; when the iteration is carried out for 3 times, compared with a code modulation method based on 7-QAM, the gain of the embodiment is 0.8 dB. This embodiment has a performance gain of about 1.6dB compared to a 6-PSK transmission method incorporating a 6-ary code. Compared with the coding modulation method based on 5-QAM, the SER performance difference is only 0.3dB, namely the effectiveness of the method is verified.
The embodiment of the invention does not limit the types of other devices except the types of the devices which are specially explained,
any device capable of performing the above functions may be used.
Those skilled in the art will appreciate that the drawings are only schematic illustrations of preferred embodiments, and the above-described embodiments of the present invention are merely provided for description and do not represent the merits of the embodiments.
The above description is only for the purpose of illustrating the preferred embodiments of the present invention and is not to be construed as limiting the invention, and any modifications, equivalents, improvements and the like that fall within the spirit and principle of the present invention are intended to be included therein.

Claims (1)

1. A coded modulation transmission method combining non-standard 6 th order modulation with LDPC codes, the method comprising the steps of:
(1) at a sending end, performing serial-parallel conversion on an information sequence; performing Galois field GF (2) Low Density Parity Check (LDPC) code encoding and GF (3) LDPC code encoding in layers; combining the GF (2) LDPC code word with the GF (3) LDPC code word to obtain a 6-system code word through mapping;
(2) carrying out 6-QAM modulation on the 6-ary code word according to a 6-order quadrature amplitude modulation 6-QAM constellation diagram, and sending a modulation signal to an additive white Gaussian noise AWGN channel;
(3) at a receiving end, carrying out soft demodulation on the received signal according to a 6-QAM constellation diagram; according to the 6-system demodulation information, iterative decoding of a GF (3) LDPC code is firstly executed, iterative decoding of the GF (2) LDPC code is executed, decoding information of the GF (2) LDPC code is transmitted to the GF (3) LDPC code, and iterative decoding of the GF (3) LDPC code is executed to realize integral iteration between two LDPC codes; obtaining a recovered information sequence through parallel-serial conversion;
wherein the step (1) is as follows:
(1.1) the information sequence U is converted into an information sequence U with the length of k 2-system symbols by serial-parallel conversionBInformation sequence U with length of k 3-ary symbolsT；
(1.2) transmitting the information sequence UBInputting GF (2) LDPC code encoder, generating code word C of GF (2) LDPC code with code length of n 2-system symbolsBTo convert the information sequence UTInputting GF (3) LDPC code encoder, generating code word C of GF (3) LDPC code with code length of n 3-system symbolsT；
(1.3) according to GF (2) symbols
Figure FDA0003145739170000011
With GF (3) symbols
Figure FDA0003145739170000012
Value of (A) CBAnd CTMapping is carried out on a 6-system code word, and the mapping rule is 00 → 0, 01 → 1, 02 → 2, 10 → 3, 11 → 4, 12 → 5;
wherein the step (2) is as follows:
(2.1) constructing a 6-QAM constellation diagram, wherein 1 constellation point is distributed at the origin of the constellation point and corresponds to 0 element in a 6-system, and the other 5 constellation points are equidistantly distributed on an excircle with a radius of R by a phase difference phi of 2 pi/5 and correspond to 5 non-zero elements in the 6-system;
(2.2) carrying out 6-QAM modulation on the 6-ary code word C, and sending the obtained modulation signal to an AWGN channel;
wherein the step (3) is as follows:
(3.1) Complex coordinates y from the l-th received symbollAnd the complex coordinate x of the a-th constellation pointaCalculating to obtain the likelihood information of the 6-system symbol; normalizing the symbol likelihood information to obtain the probability that the l-th received 6-system symbol is a;
(3.2) initializing integral iteration times Iter between GF (3) LDPC codes and GF (2) LDPC codes;
(3.3) GF (3) LDPC decoder based on probability P of l 6 th symboll aCalculating decoding prior probability P of GF (3) LDPC codeT；
(3.4) GF (3) LDPC code decoder performs iterative decoding of GF (3) LDPC codes by a prior probability PTCalculating posterior probability post of GF (3) LDPC code decoding with probability information of iterative decoding post variable nodeTAnd judging to obtain the decoding code word of the GF (3) LDPC code
Figure FDA0003145739170000021
If code word
Figure FDA0003145739170000022
And 3-ary check matrix HTSatisfy the requirement of
Figure FDA0003145739170000023
Or if the decoding iteration times of the GF (3) LDPC code reach the maximum value, the decoding is finished;
(3.5) GF (2) LDPC decoder based on probability P of l 6 th symboll aPosterior probability post for decoding GF (3) LDPC codeTCalculating prior probability P of GF (2) LDPC code decodingB；
(3.6) GF (2) LDPC code decoder performs iterative decoding of GF (2) LDPC codes by a prior probability PBCalculating posterior probability post of GF (2) LDPC code decoding with probability information of iterative decoding post variable nodeBAnd judging to obtain the decoding code word of GF (2) LDPC code
Figure FDA0003145739170000024
If code word
Figure FDA0003145739170000025
And 2-ary check matrix HBSatisfy the requirement of
Figure FDA0003145739170000026
Or if the decoding iteration times of the GF (2) LDPC code reach the maximum value, the decoding is finished;
(3.7) increasing the integral iteration number Iter by 1 time, and judging whether the maximum integral iteration number Iter is reachedoutIf Iter > -outIf not, executing the step (3.9), otherwise, executing the step (3.8);
(3.8) GF (3) LDPC code decoder according to probability of 6-system symbol and posterior probability post of GF (2) LDPC code decodingBUpdating GF (3) LDPC code decoding prior probability PTAnd returning to the step (3.4) to continue execution;
(3.9) decoding GF (2) LDPC code
Figure FDA0003145739170000027
And GF (3) LDPC code decoding code word
Figure FDA0003145739170000028
Obtaining the recovered information sequence by parallel-to-serial conversion
Figure FDA0003145739170000029
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