A non-orthogonal multiple access communication method based on Polar code

Abstract

The present invention discloses a non-orthogonal multiple access communication method based on Polar code. The information sent from the source is first encoded with Polar code, then modulated with GMSK and enters the channel; the signal is demodulated at the receiving end, then Polar code is decoded, and finally sent to the destination. Gaussian approximation (GA) structure and Tal-Vardy (TV) structure are used in Polar code construction. The present invention reduces the bit error rate and improves the performance of the NOMA system by encoding and decoding Polar code and modulating with GMSK; error control by Polar code can effectively improve the reliability of the communication system.

Description

Technical Field

[0001] The invention belongs to the technical field of communications, and in particular relates to a non-orthogonal multiple access communication method. Background Art

[0002] For a long time, LDPC codes and Turbo codes have been the mainstream coding schemes for channel error control. For LDPC and Turbo codes, which both use iterative decoding algorithms, the error floor is an important issue in the relevant research field. That is, after passing through the waterfall region, the error performance curves of LDPC and Turbo codes under higher signal-to-noise ratio conditions tend to be flat until they stop decreasing. In fact, reducing the error floor is also one of the starting points for the research on improved algorithms for LDPC and Turbo.

[0003] Polar codes are a new type of channel coding proposed by Turkish scientist Erdal Arikan. It has been proven since its inception that when the code rate does not exceed the channel capacity, polar codes do not have an error floor. When the code length N is large enough, the bit error rate (BER) of polar codes can be arbitrarily small, and the code performance can reach the Shannon limit. In fact, polar codes are currently the only channel coding technology that has been proven to reach the Shannon limit.

[0004] Therefore, combining Polar coding and decoding technology with NOMA and designing a NOMA coding and decoding scheme that meets multi-user scenarios is of great significance for improving the error performance of 5G systems. Summary of the invention

[0005] In order to overcome the shortcomings of the prior art, the present invention provides a non-orthogonal multiple access communication method based on Polar code, in which the information sent from the source is first encoded with Polar code, then modulated with GMSK and enters the channel; the signal is demodulated at the receiving end, then Polar code is decoded, and finally sent to the destination. Gaussian approximation (GA) structure and Tal-Vardy (TV) structure are used in Polar code construction. The present invention reduces the bit error rate and improves the performance of the NOMA system by encoding and decoding Polar code and modulating with GMSK; error control through Polar code can effectively improve the reliability of the communication system.

[0006] The technical solution adopted by the present invention to solve the technical problem includes the following steps:

[0007] Step 1: Construct Polar code by using Tal-Vardy construction and Gaussian approximation GA construction respectively;

[0008] Step 1-1: Tal-Vardy construction: Consider the transition probability matrix of the polarized channel WN(i) The maximum likelihood decision result on the left side of the dividing line is specified to be 0, and the maximum likelihood decision result on the right side of the dividing line is specified to be 1, and the results are arranged in ascending order of likelihood ratio;

[0009] For polarized channels, the size of the output alphabet increases exponentially with the length of the codeword. The capacity of channel W is denoted by C(W). For BI-DMSC channel W, the new channel Q is obtained by merging the values ​​of the two columns of the transition probability matrix and the values ​​of the two columns symmetrical to it. The capacity is denoted by C(Q). Then Q is the statistical degradation of W. According to the statistical degradation property, C(Q)≤C(W).

[0010] Step 1-2: Gaussian approximation GA construction: The Gaussian approximation GA construction algorithm uses the expected value of the log-likelihood ratio LLR as the measurement parameter of the channel reliability. The input is specified as an all-zero sequence. From the definition of the noise unilateral power spectrum density n0, it can be seen that for Gaussian white noise, there is δ 2 =n0 / 2; when the input x=0, the output bit is y, then y~(1,δ 2 );Take the channel transfer probability as the likelihood function: For the AWGN channel, when the input x = 0, LLR(y) follows a normal distribution with a variance twice the mean;

[0011] Step 2: The Polar code encoding process can be summarized as X N =U N G N , where X N Represents the codeword sequence of length N generated after encoding, U N =U A U r is the input bit sequence; when the length N is constant, G N It is also certain;

[0012] Step 3: Polar code the uncoded bit sequence of each user. The coded bit sequence is represented as B j =[b j1 ,b j2 ,…,b ji ,…,b jn ], where b ji is the ith coded bit symbol of the jth user, b ji The value of is 0 or 1, and the length of the encoded bit sequence of all users is fixed to n. The encoded bit sequence of each user is interleaved according to the Polar codebook, and the interleaved bit sequence is represented as S j =[s j1 ,s j2,…,s ji ,…,s jn ], where s ji is the i-th interleaved bit symbol of the j-th user, s ji The value of is 0 or 1, and the length is fixed to n;

[0013] Step 4: Perform NOMA modulation based on GMSK modulation on the Polar coded information of all users and send the modulated signal. The power intensity allocated to each user decreases in sequence, that is, user 1 is allocated half of the power, user 2 is allocated one quarter of the power, and so on. User N is allocated the smallest power.

[0014] Step 5: The receiving end uses the serial interference cancellation (SIC) technology to obtain the received bit sequence S of each user in turn according to the power intensity allocated to each user. j =[s j1 ,s j2 ,…,s ji ,…,s jn ], demodulate according to the received signal; where s ji is the i-th codeword of the j-th user, s ji The value of is 0 or 1, the initial value of j is 1, and the length of the received bit sequence of all users is fixed to n;

[0015] Step 6: For each user's received bit sequence R j Decoding is performed according to the specific Polar codebook corresponding to the user. The Polar codebook set of N users is represented as Ite = [Ite1, Ite2, ..., Ite j ,…,It N ], where Ite j is the Polar codebook of the jth user; the decoded bit sequence is represented by R j =[r j1 ,r j2 ,…,r ji ,…,r jn ], where r ji is the i-th Polar decoded bit symbol of the j-th user, r ji The value of is 0 or 1, and the length of the Polar decoding bit sequence of all users is fixed to n;

[0016] Step 7: Decode the Polar bit sequence R for each user j Decoding is performed according to the specific Polar codebook corresponding to the user, and the decoded bit sequence is represented as U j =[u j1 ,u j2 ,…,uji ,…,u jk ], where is the i-th decoded bit symbol of the j-th user, u ji The value of is 0 or 1, and the length of the decoding bit sequence of all users is fixed to k;

[0017] Step 8: If the jth user is not the last user, decode the bit sequence U j Polar coding and modulation are performed, and the received signal is updated, and the process returns to step 5; otherwise, all decoding processes are completed.

[0018] The beneficial effects of the present invention are as follows:

[0019] This aspect proposes a Polar coding and decoding method suitable for NOMA, which combines Polar coding and decoding technology with NOMA, so that the NOMA system can correct erroneous information and improve the error performance of the NOMA system; the serial interference cancellation SIC technology is used in the decoding process to improve the signal detection capability in the multi-user NOMA system and further enhance the error performance of the NOMA system. Polar codes have potential competitiveness in error performance compared with top coding schemes such as LDPC and Turbo codes. BRIEF DESCRIPTION OF THE DRAWINGS

[0020] Figure 1 This is an overall flow chart of a NOMA communication method based on Polar code proposed in the present invention.

[0021] Figure 2 The figure is a working flow chart of the serial interference cancellation SIC technology based on Polar decoding of the present invention.

[0022] Figure 3 This is the G8 polar code coding model with bit replacement of the present invention.

[0023] Figure 4 The packet error rate performance simulation results of the coding method of the present invention with a code length of 1024 and a code rate of about 0.5 in a four-user NOMA system are shown, and a comparison chart of the TV and GA polar code construction methods is used.

[0024] Figure 5 The packet error rate performance simulation results of the coding with a code length of 1024 and a code rate of about 0.5 in an eight-user NOMA system using the method of the present invention are shown, and a comparison chart of the TV and GA polar code construction methods is used. DETAILED DESCRIPTION

[0025] The present invention is further described below in conjunction with the accompanying drawings and embodiments.

[0026] The present invention is based on the existing NOMA technology and combines the Polar coding and decoding technology to propose a Polar coding and decoding method suitable for NOMA.

[0027] A non-orthogonal multiple access communication method based on Polar code comprises the following steps:

[0028] Step 1: Construct Polar code by using Tal-Vardy construction and Gaussian approximation GA construction respectively;

[0029] Step 1-1: Tal-Vardy construction: Consider the transition probability matrix of the polarized channel WN(i) The maximum likelihood decision result on the left side of the dividing line is specified to be 0, and the maximum likelihood decision result on the right side of the dividing line is specified to be 1, and the results are arranged in ascending order of likelihood ratio;

[0030] For polarized channels, the size of the output alphabet increases exponentially with the length of the codeword. For the BI-DMSC channel W, the new channel is Q obtained by combining the values ​​of the two columns of the transfer probability matrix and the values ​​of the two columns symmetrical to it. Then Q is the statistical degradation of W. According to the statistical degradation property, C(Q)≤C(W).

[0031] Step 1-2: Gaussian approximation GA construction: The Gaussian approximation GA construction algorithm uses the expected value of the log-likelihood ratio LLR as the measurement parameter of the channel reliability. The input is specified as an all-zero sequence. From the definition of the noise unilateral power spectrum density n0, it can be seen that for Gaussian white noise, there is δ 2 =n0 / 2; when the input x=0, the output bit is y, then y~(1,δ 2 );Take the channel transfer probability as the likelihood function: For the AWGN channel, when the input x = 0, LLR(y) follows a normal distribution with a variance twice the mean;

[0032] Step 2: The Polar code encoding process can be summarized as X N =U N G N , where X N Represents the codeword sequence of length N generated after encoding, U N =U A U r is the input bit sequence; when the length N is constant, G N It is also certain;

[0033] Step 3: Polar code the uncoded bit sequence of each user. The coded bit sequence is represented as B j =[b j1 ,b j2 ,…,b ji,…,b jn ], where b ji is the ith coded bit symbol of the jth user, b ji The value of is 0 or 1, and the length of the encoded bit sequence of all users is fixed to n. The encoded bit sequence of each user is interleaved according to the Polar codebook, and the interleaved bit sequence is represented as S j =[s j1 ,s j2 ,…,s ji ,…,s jn ], where s ji is the i-th interleaved bit symbol of the j-th user, s ji The value of is 0 or 1, and the length is fixed to n;

[0034] Step 4: Perform NOMA modulation based on GMSK modulation on the Polar coded information of all users and send the modulated signal. The power intensity allocated to each user decreases in sequence, that is, user 1 is allocated half of the power, user 2 is allocated one quarter of the power, and so on. User N is allocated the smallest power.

[0035] Step 5: Figure 2 As shown, the receiving end adopts the serial interference cancellation SIC technology to obtain the received bit sequence S of each user in turn according to the power intensity allocated to each user. j =[s j1 ,s j2 ,…,s ji ,…,s jn ], demodulate according to the received signal; where s ji is the i-th codeword of the j-th user, s ji The value of is 0 or 1, the initial value of j is 1, and the length of the received bit sequence of all users is fixed to n;

[0036] Step 6: For each user's received bit sequence R j Decoding is performed according to the specific Polar codebook corresponding to the user. The Polar codebook set of N users is represented as Ite = [Ite1, Ite2, ..., Ite j ,…,It N ], where Ite j is the Polar codebook of the jth user; the decoded bit sequence is represented by R j =[r j1 ,r j2 ,…,r ji ,…,r jn ], where r ji is the i-th Polar decoded bit symbol of the j-th user, rji The value of is 0 or 1, and the length of the Polar decoding bit sequence of all users is fixed to n;

[0037] Step 7: Decode the Polar bit sequence R for each user j Decoding is performed according to the specific Polar codebook corresponding to the user, and the decoded bit sequence is represented as U j =[u j1 ,u j2 ,…,u ji ,…,u jk ], where is the i-th decoded bit symbol of the j-th user, u ji The value of is 0 or 1, and the length of the decoding bit sequence of all users is fixed to k;

[0038] Step 8: If the jth user is not the last user, decode the bit sequence U j Polar coding and modulation are performed, and the received signal is updated, and the process returns to step 5; otherwise, all decoding processes are completed. Specific embodiment:

[0040] Reference Figure 1 , discloses a Polar encoding and decoding method suitable for NOMA, comprising the following steps:

[0041] Step 1: First, construct the Polar code. Two methods are used here, namely Tal-Vardy (TV) construction and Gaussian approximation (GA) construction.

[0042] Tal-Vardy (TV) construction: Consider the transition probability matrix of the polarized channel WN(i) The maximum likelihood decision result on the left side of the dividing line is set to 0, and on the right side to 1, and they are arranged in ascending order of likelihood ratio. For polarized channels, the size of the output alphabet increases exponentially with the length of the codeword. Directly calculating the ML decision error rate of the channel will make the algorithm complexity very high in the case of long code length. For the BI-DMSC channel W, the new channel is Q obtained by merging the values ​​of the two columns of the transfer probability matrix and the values ​​of the two columns symmetrical to it. Then Q is the statistical degradation of W. According to the statistical degradation property, C(Q)≤C(W).

[0043] Gaussian approximation (GA) construction: The GA construction algorithm uses the expected value of the log-likelihood ratio (LLR) as a measurement parameter of channel reliability, and stipulates that the input is an all-zero sequence. Therefore, the larger the expected value of the log-likelihood ratio (LLR), the more likely the final decision result is 0, that is, the more reliable the channel is. Considering that when the input x = 0, the output bit is y, then y~(1,δ2), take the channel transfer probability as the likelihood function: For the AWGN channel, when the input x=0, LLR(y) follows a normal distribution with a variance twice the mean.

[0044] Step 2: As a group matching code, the encoding process of polar code can be summarized as X N =U N G N Where X N Represents the codeword sequence of length N generated after encoding, U N =U A U r is the input bit sequence. When the length N is constant, G N Taking N=8 as an example, the polar code encoder G8 model is as follows: Figure 3 As shown in the figure, the process of three-layer channel merging is shown as (u 2i-1 ,u 2i )·F, where (u 2i-1 ,u 2i ) represents two adjacent bits, and there are: Where F is the Arikan polarization kernel, and a bit permutation operation is performed between each two-layer channel merging. The relationship between 8, 4 and 2 can be given as and in represents the tensor product (Kronecker product), E n represents the n×n identity matrix. Thus, the general recursive relationship between the generator matrices can be summarized as The concept of "shuffle matrix" is further introduced. It is specified that the mn×mn matrix Shuffle(m,n) is composed of R N From the properties of and the definition of the Shuffle matrix, we know that R N =Shuffle(N / 2,2), the properties of the Shuffle matrix are:Shuffle(m,n) -1 =Shuffle(m,n) T =Shuffle(nm). For the tensor product It has the following properties: Thus we can get in It can be seen as the accumulation of several basic column permutations. So far, we can get: The simplified generator matrix expression is:

[0045] Step 3: Polar code the uncoded bit sequence of each user. The coded bit sequence is represented as B j =[b j1 ,b j2 ,…,b ji ,…,b jn ], where b ji is the ith coded bit symbol of the jth user, b ji The value of is 0 or 1, and the length of the encoded bit sequence of all users is fixed to n. The encoded bit sequence of each user is interleaved according to the Polar codebook, and the interleaved bit sequence is represented as S j =[s j1 ,s j2 ,…,s ji ,…,s jn ], where s ji is the i-th interleaved bit symbol of the j-th user, s ji The value of is 0 or 1, and the length is fixed to n.

[0046] Step 4: Perform NOMA modulation based on GMSK modulation on all users and the Polar encoded information, and send the modulated signal. The power intensity allocated to each user decreases in sequence, that is, user 1 is allocated half of the power, user 2 is allocated one quarter of the power, and so on. User N is allocated the smallest power.

[0047] Step 5: The receiving end uses the serial interference cancellation (SIC) technology to obtain the received bit sequence S of each user in turn according to the power intensity allocated to each user. j =[s j1 ,s j2 ,…,s ji ,…,s jn ], demodulate according to the received signal. ji is the i-th codeword of the j-th user, s ji The value of is 0 or 1, the initial value of j is 1, and the length of the received bit sequence of all users is fixed to n. First, the subsequent Polar decoding and other work are performed on the first user.

[0048] Step 6: For each user's received bit sequence R jDecoding is performed according to the specific Polar codebook corresponding to the user. The Polar codebook set of N users is represented as Ite = [Ite1, Ite2, ..., Ite j ,…,It N ], where Ite j is the Polar codebook of the jth user. The decoded bit sequence is represented by R j =[r j1 ,r j2 ,…,r ji ,…,r jn ], where r ji is the i-th Polar decoded bit symbol of the j-th user, r ji The value of is 0 or 1, and the length of the Polar decoding bit sequence of all users is fixed to n.

[0049] Step 7: Decode the Polar bit sequence R for each user j Decoding is performed according to the specific Polar codebook corresponding to the user, and the decoded bit sequence is represented as U j =[u j1 ,u j2 ,…,u ji ,…,u jk ], where is the i-th decoded bit symbol of the j-th user, u ji The value of is 0 or 1, and the length of the decoding bit sequence of all users is fixed to k;

[0050] Step 8: If the jth user is not the last user, decode the bit sequence U j Polar coding and modulation are performed, and the received signal is updated, and the process returns to step 5; otherwise, all decoding processes are completed.

[0051] Reference Figure 3 , describes the G8 polar code coding model with bit permutation.

[0052] like Figure 4 The packet error rate performance simulation results of the coding method of the present invention with a code length of 1024 and a code rate of about 0.5 in a four-user NOMA system are shown, and a comparison chart of the TV and GA polar code construction methods is used.

[0053] like Figure 5 The packet error rate performance simulation results of the coding with a code length of 1024 and a code rate of about 0.5 in an eight-user NOMA system using the method of the present invention are shown, and a comparison chart of the TV and GA polar code construction methods is used.

Claims

1. A non-orthogonal multiple access communication method based on Polar code, characterized in that: The steps include: Step 1: Construct Polar code by using Tal-Vardy construction and Gaussian approximation GA construction respectively; Step 1-1: Tal-Vardy construction: Consider the transition probability matrix of the polarized channel WN(i) The maximum likelihood decision result of the output on the left side of the dividing line is specified to be 0, and the maximum likelihood decision result of the output on the right side is specified to be 1, and they are arranged in ascending order of likelihood ratio; For polarized channels, the size of the output alphabet increases exponentially with the length of the codeword. The capacity of channel W is denoted by C(W). For BI-DMSC channel W, the new channel Q is obtained by merging the values ​​of the two columns of the transition probability matrix and the values ​​of the two columns symmetrical to it. The capacity is denoted by C(Q). Then Q is the statistical degradation of W. According to the statistical degradation property, C(Q)≤C(W). Step 1-2: Gaussian approximation GA construction: The Gaussian approximation GA construction algorithm uses the expected value of the log-likelihood ratio LLR as the measurement parameter of the channel reliability. The input is specified as an all-zero sequence. From the definition of the noise unilateral power spectrum density n0, it can be seen that for Gaussian white noise, there is δ 2 =n0 / 2; when the input x=0, the output bit is y, then y~(1,δ 2 );Take the channel transfer probability as the likelihood function: For the AWGN channel, when the input x = 0, LLR(y) follows a normal distribution with a variance twice the mean; Step 2: The Polar code encoding process can be summarized as X N =U N G N , where X N Represents the codeword sequence of length N generated after encoding, U N =U A U r is the input bit sequence; when the length N is constant, G N It is also certain; Step 3: Polar code the uncoded bit sequence of each user. The coded bit sequence is represented as B j =[b j1 ,B j2 ,…,B ji ,…,b jn ], where B ji is the ith coded bit symbol of the jth user, b ji The value of is 0 or 1, and the length of the encoded bit sequence of all users is fixed to n. The encoded bit sequence of each user is interleaved according to the Polar codebook, and the interleaved bit sequence is represented as S j =[s j1 ,s j2 ,…,s ji ,…,s jn ], where s ji is the i-th interleaved bit symbol of the j-th user, s ji The value of is 0 or 1, and the length is fixed to n; Step 4: Perform NOMA modulation based on GMSK modulation on the Polar coded information of all users and send the modulated signal. The power intensity allocated to each user decreases in sequence, that is, user 1 is allocated half of the power, user 2 is allocated one quarter of the power, and so on. User N is allocated the smallest power. Step 5: The receiving end uses the serial interference cancellation (SIC) technology to obtain the received bit sequence S of each user in turn according to the power intensity allocated to each user. j =[s j1 ,s j2 ,…,s ji ,…,s jn ], demodulate according to the received signal; where s ji is the i-th codeword of the j-th user, s ji The value of is 0 or 1, the initial value of j is 1, and the length of the received bit sequence of all users is fixed to n; Step 6: Receive bit sequence S for each user j Decoding is performed according to the specific Polar codebook corresponding to the user. The Polar codebook set of N users is represented as Ite = [Ite1, Ite2, ..., Ite j ,…,It N ], where Ite j is the Polar codebook of the jth user; the decoded bit sequence is represented by R j =[rj j1 ,r j2 ,…,r ji ,…,r jn ], where r ji is the i-th Polar decoded bit symbol of the j-th user, r ji The value of is 0 or 1, and the length of the Polar decoding bit sequence of all users is fixed to n; Step 7: Decode the Polar bit sequence R for each user j Decoding is performed according to the specific Polar codebook corresponding to the user, and the decoded bit sequence is represented as U j =[u j1 ,u j2 ,…,u ji ,…,u jk ], where u ji is the i-th decoded bit symbol of the j-th user, u ji The value of is 0 or 1, and the length of the decoding bit sequence of all users is fixed to k; Step 8: If the jth user is not the last user, decode the bit sequence U j Polar coding and modulation are performed, and the received signal is updated, and the process returns to step 5; otherwise, all decoding processes are completed.

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