CN116015538A - Non-orthogonal multiple access communication method based on Polar codes - Google Patents

Abstract

The invention discloses a non-orthogonal multiple access communication method based on Polar codes, wherein information sent from a source is encoded by the Polar codes, then modulated by GMSK and enters a channel; the signal is demodulated at the receiving end, then Polar code decoding is carried out, and finally the signal is sent to the information sink. Gaussian Approximation (GA) construction and the Tal-Vardy (TV) construction are used in Polar code construction. The invention uses GMSK to modulate through Polar code encoding and decoding, thereby reducing error rate and improving NOMA system performance; the reliability of the communication system can be effectively improved by performing error control through Polar codes.

Description

Non-orthogonal multiple access communication method based on Polar codes

Technical Field

The invention belongs to the technical field of communication, and particularly relates to a non-orthogonal multiple access communication method.

Background

Both LDPC codes and Turbo codes have long been the dominant coding schemes for channel error control. For LDPC and Turbo codes which also adopt iterative decoding algorithms, error floor (error floor) is an important problem in the related research field, namely after passing through a waterfall area, the error code performance curves of the LDPC code and the Turbo code under the condition of higher signal to noise ratio tend to be flat until the decline is stopped. Actually reducing the error floor is also one of the starting points in the research of improved algorithms of LDPC and Turbo.

Polarization codes (polar codes) are a new type of channel coding proposed by turkish scientist Erdal Arikan. It has been demonstrated at the beginning of the proposal that when the code rate does not exceed the channel capacity, there is no error floor in the polarization code, and when the code length N is sufficiently large, the Bit Error Rate (BER) of the polarization code can be arbitrarily small, and the performance of the code can reach the shannon limit. In fact, polar codes are also the only channel coding technique currently proven to be able to reach shannon's limit.

Therefore, combining Polar coding and decoding technology with NOMA, designing NOMA coding and decoding scheme in accordance with multi-user scene has important meaning for improving error code performance of 5G system.

Disclosure of Invention

In order to overcome the defects of the prior art, the invention provides a non-orthogonal multiple access communication method based on Polar codes, wherein information sent from a source is firstly encoded by using the Polar codes, then modulated by GMSK and enters a channel; the signal is demodulated at the receiving end, then Polar code decoding is carried out, and finally the signal is sent to the information sink. Gaussian Approximation (GA) construction and the Tal-Vardy (TV) construction are used in Polar code construction. The invention uses GMSK to modulate through Polar code encoding and decoding, thereby reducing error rate and improving NOMA system performance; the reliability of the communication system can be effectively improved by performing error control through Polar codes.

The technical scheme adopted by the invention for solving the technical problems comprises the following steps:

step 1: constructing Polar codes; respectively adopting a Tal-Vardy structure and a Gaussian approximate GA structure;

step 1-1: tal-Vardy construction: considering the transition probability matrix of the polarized channel WN (i)

The output maximum likelihood decision result on the left side of the division line is specified to be 0, the output maximum likelihood decision result on the right side is specified to be 1, and the output maximum likelihood decision results are arranged in ascending order according to likelihood ratio;

for polarized channels, the output alphabet size increases exponentially with codeword length; the capacity of the channel W is denoted as C (W), and for the BI-DMSC channel W, by combining and outputting, i.e., adding and combining the values of two columns of the transition probability matrix and the values of two columns symmetrical thereto, the new channel is Q, and the capacity is denoted as C (Q), then Q is the statistical degradation of W, and the statistical degradation property is: c (Q) is less than or equal to C (W);

step 1-2: gaussian approximation GA structure: the Gaussian approximation GA construction algorithm adopts the expected value of the log-likelihood ratio LLR as the measurement parameter of the channel reliability, and specifies that the input is a full zero sequence and is formed by noise single-side power spectral density n ₀ As can be seen from the definition of (a) there is delta for Gaussian white noise ² ＝n ₀ 2; when the input x=0 is considered, the output bit is y, and y to (1, δ) ² ) The method comprises the steps of carrying out a first treatment on the surface of the Taking the channel transition probability as a likelihood function:

for AWGN channel, when x=0 is input, LLR (y) obeys normal distribution with variance twice the mean;

step 2: the Polar code encoding process is summarized as X _N ＝U _N G _N Wherein X is _N Representing a codeword sequence of length N generated after encoding, U _N ＝U _A U _r Then it is the input bit sequence; length N is fixed at a time G _N Is also certain;

step 3: polar encoding the uncoded bit sequence of each user, the encoded bit sequence being denoted B _j ＝[b _j1 ,b _j2 ,…,b _ji ,…,b _jn ]In which b _ji The ith coded bit symbol, b, of the jth user _ji The value of (2) is 0 or 1, and the length of the coded bit sequence of all users is fixed to be n; interleaving the bit sequence after each user code according to the Polar codebook, and the bit sequence after interleaving is expressed as S _j ＝[s _j1 ,s _j2 ,…,s _ji ,…,s _jn ]In s _ji The ith interleaved bit symbol, s, of the jth user _ji The value of (2) is 0 or 1, and the lengths are fixed to n;

step 4: NOMA modulation based on GMSK modulation is performed on Polar coded information of all users, and the modulated signal is transmitted. The power intensity allocated to each user is decreased in sequence, namely, the power allocated to the user 1 is half, the power allocated to the user 2 is quarter, and so on, and the power allocated to the user N is the smallest;

step 5: the receiving end adopts the SIC technology, and the receiving bit sequence S of each user is obtained in turn according to the power intensity distributed by each user _j ＝[s _j1 ,s _j2 ,…,s _ji ,…,s _jn ]Demodulating according to the received signal; wherein s is _ji The ith symbol, s, of the jth user _ji The value of (1) is 0 or 1, the initial value of j is 1, and the length of the received bit sequences of all users is fixed to be n;

step 6: received bit sequence R for each user _j Decoding according to the specific Polar codebook corresponding to the user, wherein the Polar codebook set of N users is represented as Ite= [ Ite ] ₁ ,Ite ₂ ,…,Ite _j ,…,Ite _N ]Ite in _j Polar codebook, which is the jth user; representation of the bit sequence after decodingIs R _j ＝[r _j1 ,r _j2 ,…,r _ji ,…,r _jn ]Wherein r is _ji The ith Polar decoded bit symbol, r, of the jth user _ji The value of (2) is 0 or 1, and the Polar decoding bit sequence length of all users is fixed to be n;

step 7: polar decoding bit sequence R for each user _j Decoding according to the specific Polar codebook corresponding to the user, wherein the decoded bit sequence is expressed as U _j ＝[u _j1 ,u _j2 ,…,u _ji ,…,u _jk ]In the following

The ith decoded bit symbol, u, of the jth user _ji The value of (1) is 0 or 1, and the decoding bit sequence length of all users is fixed to k;

step 8: if the jth user is not the last user, decoding the bit sequence U _j Polar coding and modulation are carried out, and the received signal is updated, and the step 5 is returned; otherwise, all decoding processes are completed.

The beneficial effects of the invention are as follows:

the Polar coding and decoding method suitable for NOMA is provided in the aspect, and the Polar coding and decoding technology is combined with the NOMA, so that the NOMA system can obtain the capability of correcting error information, and the error code performance of the NOMA system is improved; and in the decoding process, a serial interference cancellation SIC technology is adopted, so that the signal detection capability in the multi-user NOMA system is improved, and the error code performance of the NOMA system is further enhanced. Polarization codes have potential competitiveness in bit error performance compared with tip coding schemes such as LDPC and Turbo codes.

Drawings

Fig. 1 is an overall flowchart of a NOMA communication method based on Polar codes according to the present invention.

Fig. 2 is a flow chart of operation of the Polar decoding based technique for serial interference cancellation SIC of the present invention.

FIG. 3 shows the G with bit substitution according to the present invention ₈ And (5) a polarization code coding model.

Fig. 4 is a graph of simulated packet error rate performance in a four-user NOMA system using a code length 1024 and a code rate of about 0.5 using the method of the present invention, and a comparison of TV and GA polarization code construction methods.

Fig. 5 is a graph of simulated packet error rate performance in an eight user NOMA system using codes of 1024 code length and about 0.5 code rate using the method of the present invention, and a comparison of TV and GA polarization code construction methods.

Detailed Description

The invention will be further described with reference to the drawings and examples.

The invention provides a Polar coding and decoding method suitable for NOMA based on the existing NOMA technology and combined with the Polar coding and decoding technology.

A non-orthogonal multiple access communication method based on Polar codes comprises the following steps:

step 1: constructing Polar codes; respectively adopting a Tal-Vardy structure and a Gaussian approximate GA structure;

step 1-1: tal-Vardy construction: considering the transition probability matrix of the polarized channel WN (i)

The output maximum likelihood decision result on the left side of the division line is specified to be 0, the output maximum likelihood decision result on the right side is specified to be 1, and the output maximum likelihood decision results are arranged in ascending order according to likelihood ratio;

for polarized channels, the output alphabet size increases exponentially with codeword length; for the BI-DMSC channel W, through merging output, namely adding and merging the values of two columns of the transition probability matrix and the values of two columns symmetrical to the transition probability matrix, the obtained new channel is Q, and the Q is the statistical degradation of W, wherein the statistical degradation property is as follows: c (Q) is less than or equal to C (W);

step 1-2: gaussian approximation GA structure: the Gaussian approximation GA construction algorithm adopts the expected value of the log-likelihood ratio LLR as the measurement parameter of the channel reliability, and specifies that the input is a full zero sequence and is formed by noise single-side power spectral density n ₀ As can be seen from the definition of (a) there is delta for Gaussian white noise ² ＝n ₀ 2; when the input x=0 is considered, the output bit is y, and y is equal to%1,δ ² ) The method comprises the steps of carrying out a first treatment on the surface of the Taking the channel transition probability as a likelihood function:

for AWGN channel, when x=0 is input, LLR (y) obeys normal distribution with variance twice the mean;

step 2: the Polar code encoding process is summarized as X _N ＝U _N G _N Wherein X is _N Representing a codeword sequence of length N generated after encoding, U _N ＝U _A U _r Then it is the input bit sequence; length N is fixed at a time G _N Is also certain;

step 3: polar encoding the uncoded bit sequence of each user, the encoded bit sequence being denoted B _j ＝[b _j1 ,b _j2 ,…,b _ji ,…,b _jn ]In which b _ji The ith coded bit symbol, b, of the jth user _ji The value of (2) is 0 or 1, and the length of the coded bit sequence of all users is fixed to be n; interleaving the bit sequence after each user code according to the Polar codebook, and the bit sequence after interleaving is expressed as S _j ＝[s _j1 ,s _j2 ,…,s _ji ,…,s _jn ]In s _ji The ith interleaved bit symbol, s, of the jth user _ji The value of (2) is 0 or 1, and the lengths are fixed to n;

step 4: NOMA modulation based on GMSK modulation is performed on Polar coded information of all users, and the modulated signal is transmitted. The power intensity allocated to each user is decreased in sequence, namely, the power allocated to the user 1 is half, the power allocated to the user 2 is quarter, and so on, and the power allocated to the user N is the smallest;

step 5: as shown in fig. 2, the receiving end adopts a serial interference cancellation SIC technology to sequentially obtain a received bit sequence S of each user according to the power intensity allocated to each user _j ＝[s _j1 ,s _j2 ,…,s _ji ,…,s _jn ]Demodulating according to the received signal; wherein s is _ji The ith symbol, s, of the jth user _ji Has a value of 0Or the initial value of 1, j is 1, and the length of the received bit sequences of all users is fixed to be n;

step 6: received bit sequence R for each user _j Decoding according to the specific Polar codebook corresponding to the user, wherein the Polar codebook set of N users is represented as Ite= [ Ite ] ₁ ,Ite ₂ ,…,Ite _j ,…,Ite _N ]Ite in _j Polar codebook, which is the jth user; the decoded bit sequence is denoted as R _j ＝[r _j1 ,r _j2 ,…,r _ji ,…,r _jn ]Wherein r is _ji The ith Polar decoded bit symbol, r, of the jth user _ji The value of (2) is 0 or 1, and the Polar decoding bit sequence length of all users is fixed to be n;

step 7: polar decoding bit sequence R for each user _j Decoding according to the specific Polar codebook corresponding to the user, wherein the decoded bit sequence is expressed as U _j ＝[u _j1 ,u _j2 ,…,u _ji ,…,u _jk ]In the following

The ith decoded bit symbol, u, of the jth user _ji The value of (1) is 0 or 1, and the decoding bit sequence length of all users is fixed to k;

step 8: if the jth user is not the last user, decoding the bit sequence U _j Polar coding and modulation are carried out, and the received signal is updated, and the step 5 is returned; otherwise, all decoding processes are completed.

Specific examples:

referring to fig. 1, a Polar coding and decoding method suitable for NOMA is disclosed, comprising the steps of:

step 1: the construction of Polar codes is first performed, here two methods are used together, the Tal-Vardy (TV) construction and the Gaussian Approximation (GA) construction, respectively.

Tal-Vardy (TV) architecture: considering the transition probability matrix of the polarized channel WN (i)

The output maximum likelihood decision result on the left of the division line is specified as 0, and on the right as 1, and is arranged in ascending order of likelihood ratio. For polarized channels, the output alphabet size increases exponentially with codeword length. If go through->

The ML decision error rate of the channel is directly calculated, and the algorithm complexity becomes very high in case of long codes. For the BI-DMSC channel W, through merging output, namely adding and merging the values of two columns of the transition probability matrix and the values of two columns symmetrical to the transition probability matrix, the obtained new channel is Q, and the Q is the statistical degradation of W, wherein the statistical degradation property is as follows: c (Q) is less than or equal to C (W).

Gaussian Approximation (GA) construction: since the GA construction algorithm uses the expected value of the log-likelihood ratio (LLR) as a measure of channel reliability, since the input is defined as an all-zero sequence, the larger the expected value of the log-likelihood ratio (LLR) is, the more likely the final decision result is 0, i.e., the more reliable the channel is. When the input x=0 is considered, the output bit is y, and y is (1, delta 2), and the channel transition probability is taken as a likelihood function:

for an AWGN channel, when x=0 is input, the LLR (y) obeys a normal distribution with variance twice the mean.

Step 2: the polarization code is used as a grouping and gathering code, and the coding process of the polarization code can be summarized as X _N ＝U _N G _N Wherein X is _N Representing a codeword sequence of length N generated after encoding, U _N ＝U _A U _r Then it is the input bit sequence. Length N is fixed at a time G _N Is also determined. Polar encoder G using n=8 as an example ₈ The model is shown in fig. 3, which illustrates the process of three-layer channel combining as (u _2i-1 ,u _2i ) F, where (u) _2i-1 ,u _2i ) Represents two adjacent bits, and has:

where F is the Arikan polarization kernel and bit permutation operations are performed between every two layers of channel combinations. Can be given ₈ , ₄ And (3) with ₂ The relation between them is

And->

Wherein->

Represents tensor product (Kronecker product), E _n Representing an n x n identity matrix. Thus, the general recurrence relation between the matrixes can be summarized

Further introducing the concept of a "shuffling matrix". Defining an mn×mn matrix Shuffle (m, n), defined by R _N The nature of (1) and the definition of the Shuffle matrix are known as R _N The properties of the Shuffle matrix are Shuffle (m, N) ^-1 ＝Shuffle(m,n) ^T =shuffle (nm). And +.>

The preparation method has the following properties:

thereby can obtain

Wherein the method comprises the steps of

Can be seen as an accumulation of several base column permutations. Thus, it is possible to obtain:>

the reduced generator matrix expression is +.>

Step 3: polar encoding the uncoded bit sequence of each user, the encoded bit sequence being denoted B _j ＝[b _j1 ,b _j2 ,…,b _ji ,…,b _jn ]In which b _ji The ith coded bit symbol, b, of the jth user _ji The coded bit sequence length of all users is fixed to n, with a value of 0 or 1. Interleaving the bit sequence after each user code according to the Polar codebook, and the bit sequence after interleaving is expressed as S _j ＝[s _j1 ,s _j2 ,…,s _ji ,…,s _jn ]In s _ji The ith interleaved bit symbol, s, of the jth user _ji The value of (2) is 0 or 1, and the length is fixed to n.

Step 4: NOMA modulation based on GMSK modulation is performed on all users and Polar coded information, and the modulated signal is transmitted. The power intensity allocated to each user is decreased in turn, i.e. the power allocated to user 1 is one half, the power allocated to user 2 is one quarter, and so on, and the power allocated to user N is the smallest.

Step 5: the receiving end adopts the SIC technology, and the receiving bit sequence S of each user is obtained in turn according to the power intensity distributed by each user _j ＝[s _j1 ,s _j2 ,…,s _ji ,…,s _jn ]Demodulation is performed in accordance with the received signal. Wherein s is _ji The ith symbol, s, of the jth user _ji The initial value of (1) is 0 or 1, and the received bit sequence length of all users is fixed to n. First, the first user is subjected to the following Polar decoding and other works.

Step 6: received bit sequence R for each user _j Decoding according to the specific Polar codebook corresponding to the user, wherein the Polar codebook set of N users is represented as Ite= [ Ite ] ₁ ,Ite ₂ ,…,Ite _j ,…,Ite _N ]Ite in _j Is the Polar codebook for the jth user. The decoded bit sequence is denoted as R _j ＝[r _j1 ,r _j2 ,…,r _ji ,…,r _jn ]Wherein r is _ji The ith Polar decoded bit symbol, r, of the jth user _ji The Polar decoding bit sequence length of all users is fixed to n with a value of 0 or 1.

Step 7: polar decoding bit sequence R for each user _j Decoding according to the specific Polar codebook corresponding to the user, wherein the decoded bit sequence is expressed as U _j ＝[u _j1 ,u _j2 ,…,u _ji ,…,u _jk ]In the following

The ith decoded bit symbol, u, of the jth user _ji The value of (1) is 0 or 1, and the decoding bit sequence length of all users is fixed to k;

step 8: if the jth user is not the last user, decoding the bit sequence U _j Polar coding and modulation are carried out, and the received signal is updated, and the step 5 is returned; otherwise, all decoding processes are completed.

With reference to FIG. 3, G with bit permutation is described ₈ And (5) a polarization code coding model.

Fig. 4 is a graph of simulated packet error rate performance in a four-user NOMA system using codes of 1024 code length and about 0.5 code rate using the method of the present invention, and a comparison of TV and GA polarization code construction methods.

Fig. 5 is a graph of simulated packet error rate performance in an eight user NOMA system using codes of 1024 code length and about 0.5 code rate using the method of the present invention, and a comparison of TV and GA polarization code construction methods.

Claims (1)

1. The non-orthogonal multiple access communication method based on Polar codes is characterized by comprising the following steps:

step 1: constructing Polar codes; respectively adopting a Tal-Vardy structure and a Gaussian approximate GA structure;

step 1-1: tal-Vardy construction: considering the transition probability matrix of the polarized channel WN (i)

The output maximum likelihood decision result on the left side of the division line is specified to be 0, the output maximum likelihood decision result on the right side is specified to be 1, and the output maximum likelihood decision results are arranged in ascending order according to likelihood ratio;

for polarized channels, the output alphabet size increases exponentially with codeword length; the capacity of the channel W is denoted as C (W), and for the BI-DMSC channel W, by combining and outputting, i.e., adding and combining the values of two columns of the transition probability matrix and the values of two columns symmetrical thereto, the new channel is Q, and the capacity is denoted as C (Q), then Q is the statistical degradation of W, and the statistical degradation property is: c (Q) is less than or equal to C (W);

step 1-2: gaussian approximation GA structure: the Gaussian approximation GA construction algorithm adopts the expected value of the log-likelihood ratio LLR as the measurement parameter of the channel reliability, and specifies that the input is a full zero sequence and is formed by noise single-side power spectral density n ₀ As can be seen from the definition of (a) there is delta for Gaussian white noise ² ＝n ₀ 2; when the input x=0 is considered, the output bit is y, and y to (1, δ) ² ) The method comprises the steps of carrying out a first treatment on the surface of the Taking the channel transition probability as a likelihood function:

for AWGN channel, when x=0 is input, LLR (y) obeys normal distribution with variance twice the mean;

step 2: the Polar code encoding process is summarized as X _N ＝U _N G _N Wherein X is _N Representing a codeword sequence of length N generated after encoding, U _N ＝U _A U _r Then is the inputEntering a bit sequence; length N is fixed at a time G _N Is also certain;

step 3: polar encoding the uncoded bit sequence of each user, the encoded bit sequence being denoted B _j ＝[b _j1 ,b _j2 ,…,b _ji ,…,b _jn ]In which b _ji The ith coded bit symbol, b, of the jth user _ji The value of (2) is 0 or 1, and the length of the coded bit sequence of all users is fixed to be n; interleaving the bit sequence after each user code according to the Polar codebook, and the bit sequence after interleaving is expressed as S _j ＝[s _j1 ,s _j2 ,…,s _ji ,…,s _jn ]In s _ji The ith interleaved bit symbol, s, of the jth user _ji The value of (2) is 0 or 1, and the lengths are fixed to n;

step 4: performing NOMA modulation based on GMSK modulation on Polar coded information of all users, and transmitting the modulated signals; the power intensity allocated to each user is decreased in sequence, namely, the power allocated to the user 1 is half, the power allocated to the user 2 is quarter, and so on, and the power allocated to the user N is the smallest;

step 5: the receiving end adopts the SIC technology, and the receiving bit sequence S of each user is obtained in turn according to the power intensity distributed by each user _j ＝[s _j1 ,s _j2 ,…,s _ji ,…,s _jn ]Demodulating according to the received signal; wherein s is _ji The ith symbol, s, of the jth user _ji The value of (1) is 0 or 1, the initial value of j is 1, and the length of the received bit sequences of all users is fixed to be n;

step 6: received bit sequence R for each user _j Decoding according to the specific Polar codebook corresponding to the user, wherein the Polar codebook set of N users is represented as Ite= [ Ite ] ₁ ,[Ite ₂ ,…,Ite _j ,…,Ite _N ]Ite in _j Polar codebook, which is the jth user; the decoded bit sequence is denoted as R _j ＝[r _j1 ,r _j2 ,…,r _ji ,…,r _jn ]Wherein r is _ji The ith Polar decoded bit symbol, r, of the jth user _ji The value of (2) is 0 or 1, and the Polar decoding bit sequence length of all users is fixed to be n;

step 7: polar decoding bit sequence R for each user _j Decoding according to the specific Polar codebook corresponding to the user, wherein the decoded bit sequence is expressed as U _j ＝[u _j1 ,u _j2 ,…,u _ji ,…,u _jk ]In the following

The ith decoded bit symbol, u, of the jth user _ji The value of (1) is 0 or 1, and the decoding bit sequence length of all users is fixed to k;

step 8: if the jth user is not the last user, decoding the bit sequence U _j Polar coding and modulation are carried out, and the received signal is updated, and the step 5 is returned; otherwise, all decoding processes are completed.

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