CN111884759A - A Channel Security Coding Method Against Joint Eavesdropping in Relay Transmission - Google Patents

一种中继传输中抗联合窃听的信道安全编码方法A Channel Security Coding Method Against Joint Eavesdropping in Relay Transmission

技术领域technical field

本发明属于无线通信技术领域，涉及一种中继传输中抗联合窃听的信道安全编码方法。The invention belongs to the technical field of wireless communication, and relates to a channel security coding method for resisting joint eavesdropping in relay transmission.

背景技术Background technique

在无线通信系统中，由于发送端的功率限制，或者信源节点和目的节点的距离较远，两者之间不能直接进行传输信息。因此当信源节点和目的节点之间不具备信息的直接传输条件时，我们可以借助中继转发技术来实现信息的传递。中继节点将接收到信源节点发送的信息进行处理后再转发给目的节点。In a wireless communication system, due to the power limitation of the transmitter or the long distance between the source node and the destination node, information cannot be directly transmitted between the two. Therefore, when there is no direct information transmission condition between the source node and the destination node, we can realize the transmission of information by means of relay and forwarding technology. The relay node processes the information sent by the source node and then forwards it to the destination node.

在中继解码转发通信系统中，信息传输的安全性同样值得重视。目前在中继传输系统中，常用的抗窃听手段为人工噪声与波束成形技术，尚无相关的安全编码系统。假设合法链路拥有信道质量优势，在一跳传输中，根据信息论，可以传输一定速率的，完全无法被窃听用户窃取的信息。但是，关于多跳传输，窃听者可以根据两跳窃听到的信号经最大比合并后，可以获得3dB的增益。由于合法链路采用译码转发(Decode-and-Forward，DF)，最后的目的接收机客观上只能根据第二跳信号进行译码。此时，合法链路对于窃听链路的优势就被完全抹平，可以获得的安全速率为0。In the relay decoding and forwarding communication system, the security of information transmission is also worthy of attention. At present, in the relay transmission system, the commonly used anti-eavesdropping methods are artificial noise and beamforming technology, and there is no relevant security coding system. Assuming that the legitimate link has the advantage of channel quality, in one-hop transmission, according to information theory, information at a certain rate can be transmitted, and information that cannot be stolen by eavesdropping users at all. However, regarding multi-hop transmission, the eavesdropper can obtain a gain of 3dB after combining the signals overheard by the two hops by the maximum ratio. Since the legal link adopts decoding and forwarding (Decode-and-Forward, DF), the final destination receiver can only perform decoding according to the second hop signal objectively. At this point, the advantage of the legitimate link over the eavesdropping link is completely wiped out, and the security rate that can be obtained is 0.

如果合法用户采用理想的，两个独立的码本进行两跳传输，那么每跳都可以安全的传输一定速率的信息。这样，最终，整个中继传输系统也可以获得>0的安全速率。因此，我们提出一种编码策略，使得能够有效抑制窃听者联合窃听能力。If legitimate users use ideal, two independent codebooks for two-hop transmission, each hop can safely transmit a certain rate of information. In this way, in the end, the entire relay transmission system can also obtain a safe rate > 0. Therefore, we propose an encoding strategy that can effectively suppress the eavesdropper's joint eavesdropping ability.

发明内容SUMMARY OF THE INVENTION

本发明的目的在于克服上述现有技术的缺点，提供了一种中继传输中抗联合窃听的信道安全编码方法，该方法能够有效的提高信息传输的安全性。The purpose of the present invention is to overcome the above-mentioned shortcomings of the prior art, and to provide a channel security coding method for resisting joint eavesdropping in relay transmission, which can effectively improve the security of information transmission.

为达到上述目的，本发明所述的中继传输中抗联合窃听的信道安全编码方法包括以下步骤：In order to achieve the above object, the channel security coding method for resisting joint eavesdropping in relay transmission according to the present invention comprises the following steps:

1)源节点S将原始信息序列

通过一个维度为M⁽¹⁾×N校验矩阵的LDPC码进行编码，得到长度为N的系统码传输码字c⁽¹⁾，然后再将得到的系统码传输码字c⁽¹⁾调制传输给中继节点R；1) The source node S converts the original information sequence

Encoding is performed by an LDPC code with a dimension of M ⁽¹⁾ ×N check matrix to obtain a systematic code transmission code word c ⁽¹⁾ of length N, and then the obtained systematic code transmission code word c ^{(1) is} modulated and transmitted to the relay node R;

2)中继节点R对接收数据进行译码，得原始信息序列

再将原始信息序列

通过一个维度为M⁽²⁾×N校验矩阵的LDPC码进行编码，得到长度为N的系统码传输码字c⁽²⁾，然后将系统码传输码字c⁽²⁾调制传输给目的节点D；2) The relay node R decodes the received data to obtain the original information sequence

Then sequence the original information

Encoding is performed by an LDPC code with a dimension of M ⁽²⁾ ×N check matrix to obtain a systematic code transmission code word c ⁽²⁾ of length N, and then the systematic code transmission code word c ^{(2) is} modulated and transmitted to the destination node D;

3)目的节点D根据接收到的信息以及传输所使用的码本进行译码求解，以恢复出原始信息序列

3) The destination node D performs decoding and solving according to the received information and the codebook used for transmission to recover the original information sequence

步骤1)中，In step 1),

M⁽¹⁾×N校验矩阵H⁽¹⁾的分块形式为：The block form of the M ⁽¹⁾ ×N check matrix H ⁽¹⁾ is:

校验矩阵H⁽¹⁾对应的生成矩阵G⁽¹⁾为：The generator matrix G ^{(1 ) corresponding to the check matrix H (} 1) is:

系统码传输码字c⁽¹⁾为：The system code transmission code word c ⁽¹⁾ is:

其中，p⁽¹⁾为该码字的校验比特。Among them, p ⁽¹⁾ is the check bit of the codeword.

步骤2)中，In step 2),

M⁽²⁾×N校验矩阵H⁽²⁾的分块形式为：The block form of the M ⁽²⁾ ×N check matrix H ⁽²⁾ is:

校验矩阵H⁽²⁾对应的生成矩阵G⁽²⁾为：The generator matrix G ^{(2 ) corresponding to the check matrix H (} 2) is:

系统码传输码字c⁽²⁾为：The system code transmission code word c ⁽²⁾ is:

其中，p⁽²⁾为系统码传输码字c⁽²⁾的校验比特。Among them, p ⁽²⁾ is the check bit of the systematic code transmission code word c ⁽²⁾ .

步骤1)中使用的LDPC码为系统码，源节点S传输给中继节点R使用的LDPC码的校验矩阵H⁽¹⁾中，前K列对应信息位上的比特序列，后N-K列对应校验位上的比特序列。The LDPC code used in step 1) is a system code, and in the check matrix H ⁽¹⁾ of the LDPC code used by the source node S to transmit the LDPC code used by the relay node R, the first K columns correspond to the bit sequence on the information bits, and the latter NK columns correspond to The sequence of bits on the parity bit.

步骤2)中使用的LDPC码为系统码，中继节点R转发给目的节点D使用的LDPC码校验矩阵H⁽²⁾中，前K列对应信息位上的比特序列，后N-K列对应校验位上的比特序列。The LDPC code used in step 2) is a system code, and the relay node R forwards it to the LDPC code check matrix H ⁽²⁾ used by the destination node D. The first K columns correspond to the bit sequence on the information bits, and the latter NK columns correspond to the check matrix. bit sequence on the parity bit.

当目的节点D只接收到中继节点R的转发信息y_D时，则利用中继节点R转发使用的LDPC码码本H进行译码，以恢复出原始信息序列d＝(d₁,d₂,…,d_k)^T；When the destination node D only receives the forwarding information y _D of the relay node R, the LDPC codebook H used by the relay node R for forwarding is used for decoding to restore the original information sequence d=(d ₁ , d ₂ ,…,d _k ) ^T ;

当接收机接收到源节点S发送的信息

同时接收到中继节点R的转发信息

时，则利用两跳使用的M⁽¹⁾×N校验矩阵H⁽¹⁾及M⁽²⁾×N校验矩阵H⁽²⁾，通过联合译码的方式进行译码，以恢复出原始信息序列d＝(d₁,d₂,…,d_k)^T。When the receiver receives the information sent by the source node S

At the same time, the forwarding information of the relay node R is received

, then use the M ⁽¹⁾ ×N check matrix H ⁽¹⁾ and M ⁽²⁾ ×N check matrix H ⁽²⁾ used by two hops to decode by joint decoding to restore the original Information sequence d=(d ₁ , d ₂ , . . . , d _k ) ^T .

当M⁽¹⁾×N校验矩阵H⁽¹⁾与M⁽²⁾×N校验矩阵H⁽²⁾不同时，则采用耦合拼接方案，接收机采用等效校验矩阵直接译码的直接法及基于联合Tanner图的迭代法进行译码。When the M ⁽¹⁾ ×N check matrix H ⁽¹⁾ is different from the M ⁽²⁾ ×N check matrix H ⁽²⁾ , the coupling splicing scheme is adopted, and the receiver adopts the direct decoding method of the equivalent check matrix directly. method and iterative method based on joint Tanner graph for decoding.

当M⁽¹⁾×N校验矩阵H⁽¹⁾与M⁽²⁾×N校验矩阵H⁽²⁾相同时，则采用耦合插入方案，接收机采用联合Tanner图的方式进行译码。When the M ⁽¹⁾ ×N check matrix H ⁽¹⁾ is the same as the M ⁽²⁾ ×N check matrix H ⁽²⁾ , the coupling insertion scheme is used, and the receiver uses the joint Tanner graph for decoding.

本发明具有以下有益效果：The present invention has the following beneficial effects:

本发明所述的中继传输中抗联合窃听的信道安全编码方法在具体操作时，通过对信息传输时的编码方案进行相关设计，以降低窃听端的窃听性能，继而提高信息传输的安全性，具体的，源节点通过维度为M⁽¹⁾×N校验矩阵的LDPC码进行编码，中继节点维度为M⁽²⁾×N校验矩阵的LDPC码进行编码，目的节点D根据接收到的信息以及传输所使用的码本进行译码求解，与传统的基于人工噪声波束成形的安全策略不同，本发明依靠对传输过程信道编码的相关设计，不需要消耗额外的能量，提高了能量利用效率。The channel security coding method for anti-joint eavesdropping in relay transmission according to the present invention reduces the eavesdropping performance of the eavesdropping end and improves the security of information transmission through the relevant design of the coding scheme during information transmission during the specific operation. , the source node is encoded by an LDPC code with a dimension of M ⁽¹⁾ ×N check matrix, the relay node is encoded by an LDPC code with a dimension of M ⁽²⁾ ×N check matrix, and the destination node D is based on the received information. And the codebook used for transmission is decoded and solved. Different from the traditional security strategy based on artificial noise beamforming, the present invention relies on the relevant design of channel coding in the transmission process, does not need to consume extra energy, and improves the energy utilization efficiency.

附图说明Description of drawings

图1为本发明的系统模型图；Fig. 1 is a system model diagram of the present invention;

图2为耦合拼接方案下的联合Tanner图；Figure 2 is a joint Tanner diagram under the coupling splicing scheme;

图3为耦合插入方案下的联合Tanner图；Fig. 3 is the joint Tanner diagram under the coupling insertion scheme;

图4为耦合拼接方案下两种译码算法的性能比较图；Fig. 4 is a performance comparison diagram of two decoding algorithms under the coupled splicing scheme;

图5为耦合拼接方案与传统方案的性能对比图；Figure 5 is a performance comparison diagram between the coupling and splicing scheme and the traditional scheme;

图6为耦合插入方案与传统方案的性能对比图。Figure 6 is a performance comparison diagram between the coupling insertion scheme and the traditional scheme.

具体实施方式Detailed ways

下面结合附图对本发明做进一步详细描述：Below in conjunction with accompanying drawing, the present invention is described in further detail:

参考图1，本发明所述的中继传输中抗联合窃听的信道安全编码方法包括以下步骤：Referring to FIG. 1 , the method for channel security coding for anti-joint eavesdropping in relay transmission according to the present invention includes the following steps:

1)源节点S将原始信息序列

通过一个维度为M⁽¹⁾×N校验矩阵的LDPC码进行编码，得到长度为N的系统码传输码字c⁽¹⁾，然后再将得到的系统码传输码字c⁽¹⁾调制传输给中继节点R；1) The source node S converts the original information sequence

Encoding is performed by an LDPC code with a dimension of M ⁽¹⁾ ×N check matrix to obtain a systematic code transmission code word c ⁽¹⁾ of length N, and then the obtained systematic code transmission code word c ^{(1) is} modulated and transmitted to the relay node R;

步骤1)中使用的LDPC码为系统码，源节点S传输给中继节点R使用的LDPC码的校验矩阵H⁽¹⁾中，前K列对应信息位上的比特序列，后N-K列对应校验位上的比特序列。The LDPC code used in step 1) is a system code, and in the check matrix H ⁽¹⁾ of the LDPC code used by the source node S to transmit the LDPC code used by the relay node R, the first K columns correspond to the bit sequence on the information bits, and the latter NK columns correspond to The sequence of bits on the parity bit.

M⁽¹⁾×N校验矩阵H⁽¹⁾的分块形式为：The block form of the M ⁽¹⁾ ×N check matrix H ⁽¹⁾ is:

校验矩阵H⁽¹⁾对应的生成矩阵G⁽¹⁾为：The generator matrix G ^{(1 ) corresponding to the check matrix H (} 1) is:

系统码传输码字c⁽¹⁾为：The system code transmission code word c ⁽¹⁾ is:

其中，p⁽¹⁾为该码字的校验比特。Among them, p ⁽¹⁾ is the check bit of the codeword.

2)中继节点R对接收数据进行译码，得原始信息序列

再将原始信息序列

通过一个维度为M⁽²⁾×N校验矩阵的LDPC码进行编码，得到长度为N的系统码传输码字c⁽²⁾，然后将系统码传输码字c⁽²⁾调制传输给目的节点D；2) The relay node R decodes the received data to obtain the original information sequence

Then sequence the original information

Encoding is performed by an LDPC code with a dimension of M ⁽²⁾ ×N check matrix to obtain a systematic code transmission code word c ⁽²⁾ of length N, and then the systematic code transmission code word c ^{(2) is} modulated and transmitted to the destination node D;

步骤2)中使用的LDPC码为系统码，中继节点R转发给目的节点D使用的LDPC码校验矩阵H⁽²⁾中，前K列对应信息位上的比特序列，后N-K列对应校验位上的比特序列。The LDPC code used in step 2) is a system code, and the relay node R forwards it to the LDPC code check matrix H ⁽²⁾ used by the destination node D. The first K columns correspond to the bit sequence on the information bits, and the latter NK columns correspond to the check matrix. bit sequence on the parity bit.

M⁽²⁾×N校验矩阵H⁽²⁾的分块形式为：The block form of the M ⁽²⁾ ×N check matrix H ⁽²⁾ is:

校验矩阵H⁽²⁾对应的生成矩阵G⁽²⁾为：The generator matrix G ^{(2 ) corresponding to the check matrix H (} 2) is:

系统码传输码字c⁽²⁾为：The system code transmission code word c ⁽²⁾ is:

其中，p⁽²⁾为系统码传输码字c⁽²⁾的校验比特。Among them, p ⁽²⁾ is the check bit of the systematic code transmission code word c ⁽²⁾ .

3)目的节点D根据接收到的信息以及传输所使用的码本进行译码求解，以恢复出原始信息序列

3) The destination node D performs decoding and solving according to the received information and the codebook used for transmission to recover the original information sequence

当接收机只接收到中继节点R的转发信息y_D时，则利用中继节点R转发使用的LDPC码码本H进行译码，以恢复出原始信息序列d＝(d₁,d₂,…,d_k)^T；当接收机接收到源节点S发送的信息

同时接收到中继节点R的转发信息

时，则利用两跳使用的M⁽¹⁾×N校验矩阵H⁽¹⁾及M⁽²⁾×N校验矩阵H⁽²⁾，通过联合译码的方式进行译码，以恢复出原始信息序列d＝(d₁,d₂,…,d_k)^T。When the receiver only receives the forwarding information y _D of the relay node R, the LDPC codebook H used by the relay node R for forwarding is used for decoding to recover the original information sequence d=(d ₁ , d ₂ , ...,d _k ) ^T ; when the receiver receives the information sent by the source node S

At the same time, the forwarding information of the relay node R is received

, then use the M ⁽¹⁾ ×N check matrix H ⁽¹⁾ and M ⁽²⁾ ×N check matrix H ⁽²⁾ used by two hops to decode by joint decoding to restore the original Information sequence d=(d ₁ , d ₂ , . . . , d _k ) ^T .

当M⁽¹⁾×N校验矩阵H⁽¹⁾与M⁽²⁾×N校验矩阵H⁽²⁾不同时，则采用耦合拼接方案，接收机采用等效校验矩阵直接译码的直接法及基于联合Tanner图的迭代法进行译码。When the M ⁽¹⁾ ×N check matrix H ⁽¹⁾ is different from the M ⁽²⁾ ×N check matrix H ⁽²⁾ , the coupling splicing scheme is adopted, and the receiver adopts the direct decoding method of the equivalent check matrix directly. method and iterative method based on joint Tanner graph for decoding.

采用耦合拼接方案具有以下特征：The coupling splicing scheme has the following characteristics:

对于源节点S传输给中继节点R使用的LDPC码的校验矩阵H⁽¹⁾，中继节点R转发给目的节点D使用的LDPC码的校验矩阵H⁽²⁾，构造一个等效校验矩阵For the check matrix H ⁽¹⁾ of the LDPC code used by the source node S to transmit to the relay node R, the relay node R forwards the check matrix H ⁽²⁾ of the LDPC code used by the destination node D to construct an equivalent check matrix H (2). test matrix

将两个码本的对应信息比特上前K列按列拼接，将对应于校验比特上的N-K列对角拼接，其维度为(M⁽¹⁾+M⁽²⁾)×(2N-K)，与将两跳码字进行重新排列后的码字序列

满足校验方差

同时由于等效校验矩阵是两个码本的分割拼接，仍然具有稀疏特性。The first K columns on the corresponding information bits of the two codebooks are spliced by column, and the NK columns corresponding to the check bits are spliced diagonally, and its dimension is (M ⁽¹⁾ +M ⁽²⁾ )×(2N-K ), and the codeword sequence after rearranging the two-hop codewords

Satisfy the check variance

At the same time, since the equivalent parity check matrix is the division and splicing of two codebooks, it still has the sparse characteristic.

对于源节点S传输给中继节点R使用的LDPC码的校验矩阵H⁽¹⁾与中继节点R转发给目的节点D使用的LDPC码的校验矩阵H⁽²⁾中，块矩阵Λ⁽¹⁾、Λ⁽²⁾中自身并无环状结构，而对于矩阵Λ⁽¹⁾与Λ⁽²⁾拼接而成的矩阵For the check matrix H ⁽¹⁾ of the LDPC code used by the source node S to transmit to the relay node R and the check matrix H ⁽²⁾ of the LDPC code used by the relay node R to forward to the destination node D, the block matrix Λ ^{( 1)} , Λ ⁽²⁾ itself has no ring structure, but for the matrix formed by the splicing of matrices Λ ⁽¹⁾ and Λ ⁽²⁾

其存在两列之间位置相同的1的个数大于1，即根据矩阵

生成对应Tanner图中存在大量4环严重影响LDPC码的译码性能。It exists that the number of 1s in the same position between two columns is greater than 1, that is, according to the matrix

There are a large number of 4-loops in the generated corresponding Tanner graph, which seriously affects the decoding performance of LDPC codes.

当M⁽¹⁾×N校验矩阵H⁽¹⁾与M⁽²⁾×N校验矩阵H⁽²⁾相同时，则采用耦合插入方案，目的节点D采用联合Tanner图的方式进行译码。When the M ⁽¹⁾ ×N check matrix H ⁽¹⁾ is the same as the M ⁽²⁾ ×N check matrix H ⁽²⁾ , the coupling insertion scheme is used, and the destination node D uses a joint Tanner graph for decoding.

耦合插入方案具有以下特征：The coupling insertion scheme has the following characteristics:

a)对于源节点S传输给中继节点R使用的LDPC码的校验矩阵H⁽¹⁾，中继节点R转发给目的节点D使用的LDPC码的校验矩阵H⁽²⁾，两个码本相同，记为H＝H⁽¹⁾＝H⁽²⁾；a) For the check matrix H ⁽¹⁾ of the LDPC code used by the source node S to transmit to the relay node R, the relay node R forwards the check matrix H ⁽²⁾ of the LDPC code used by the destination node D, two codes This is the same, denoted as H=H ⁽¹⁾ =H ⁽²⁾ ;

b)中继节点R能够正确接收源节点S传输的信息

在中继节点R对信息

进行转发时，采用一个耦合插入矩阵M将信息序列映射为另一组信息序列

第二跳传输的信息比特与第一跳信息序列满足b) The relay node R can correctly receive the information transmitted by the source node S

Pair information at relay node R

When forwarding, a coupling insertion matrix M is used to map the information sequence to another set of information sequences

The information bits transmitted by the second hop satisfies the information sequence of the first hop

耦合插入矩阵M是一个满秩方阵，其维度K×K，其逆矩阵记为M^-1。The coupling insertion matrix M is a full-rank square matrix, its dimension is K×K, and its inverse matrix is denoted as M ^-1 .

直接法的具体过程为：The specific process of the direct method is as follows:

第一步：对于两跳接收信息c⁽¹⁾＝dG⁽¹⁾＝[d p⁽¹⁾]_1×N、c⁽²⁾＝dG⁽²⁾＝[d p⁽²⁾]_1×N对其信息位进行最大比合并，校验位进行顺序排列，得到新的等效接受序列

Step 1: For two-hop reception information c ⁽¹⁾ = dG ⁽¹⁾ = [dp ⁽¹⁾ ] _1×N , c ⁽²⁾ = dG ⁽²⁾ = [dp ⁽²⁾ ] _1×N The information bits are combined with the maximum ratio, and the check bits are arranged in order to obtain a new equivalent acceptance sequence.

第二步：利用等效校验矩阵

对等效接收序列

做常规BP算法，进行译码恢复私密数据d＝(d₁,d₂,…,d_k)^T。Step 2: Use the Equivalent Check Matrix

For the equivalent receive sequence

Do the conventional BP algorithm, and perform decoding to restore the private data d=(d ₁ , d ₂ , . . . , d _k ) ^T .

迭代法的具体过程为：The specific process of the iterative method is as follows:

迭代法为基于联合Tanner图的BP译码算法。由于两跳传输均采用系统码，两跳码字的信息位比特序列拥有相同值，在使用BP算法时，可以进行信息的互相传递。在两个码本使用BP算法时，在计算位于信息位上的第j变量节点(variable nodes，VN)传递给第i个校验节点的信息值L_j→i时，需要加上从另一个码本获得额外信息值；同样的，在更新第j个变量节点的LLR值时，需要加上从另一个码本获得额外信息值。该额外信息值为另一个码本相同位上的信息位变量节点获得的所有校验信息值。The iterative method is a BP decoding algorithm based on the joint Tanner graph. Since the two-hop transmission adopts the systematic code, the information bit sequences of the two-hop codewords have the same value, and the information can be transmitted to each other when the BP algorithm is used. When the BP algorithm is used in the two codebooks, when calculating the information value L _j→i transmitted to the i-th check node from the j-th variable node (VN) located on the information bit, it is necessary to add the information value from the other The codebook obtains additional information values; similarly, when updating the LLR value of the jth variable node, additional information values obtained from another codebook need to be added. The extra information value is all check information values obtained by the information bit variable node on the same bit of another codebook.

对于码本1而言，用于判决的的软信息

变为：For codebook 1, the soft information used for decision

becomes:

H⁽¹⁾Tanner图中信息位第j个变量节点VN传递给第i个检验节点的信息值L_j→i变为：H ⁽¹⁾ The information value L _j→i that the j-th variable node VN of the information bit in the Tanner graph passes to the i-th check node becomes:

基于该Tanner图的耦合拼接方案联合BP算法如表1所示：The coupling splicing scheme and BP algorithm based on the Tanner graph are shown in Table 1:

表1Table 1

插入方案，可以使用基于联合Tanner图的BP译码算法。由于两跳传输采用了相同码本，两跳码字的信息位比特序列满足：For the insertion scheme, the BP decoding algorithm based on the joint Tanner graph can be used. Since the two-hop transmission uses the same codebook, the information bit sequence of the two-hop codeword satisfies:

在使用BP算法时，可以进行信息的互相传递。在两个码本使用BP算法时，在计算位于信息位上的第j变量节点(variable nodes，VN)传递给第i个校验节点的信息值L_j→i时，需要加上从另一个码本获得额外信息值；同样的，在更新第j个变量节点的LLR值时，需要加上从另一个码本获得额外信息值。该额外信息值为另一个码本相同位上的信息位变量节点获得的所有校验信息值。When using the BP algorithm, information can be transmitted to each other. When the BP algorithm is used in the two codebooks, when calculating the information value L _j→i transmitted to the i-th check node from the j-th variable node (VN) located on the information bit, it is necessary to add the information value from the other The codebook obtains additional information values; similarly, when updating the LLR value of the jth variable node, additional information values obtained from another codebook need to be added. The extra information value is all check information values obtained by the information bit variable node on the same bit of another codebook.

码本H⁽¹⁾传递给H⁽²⁾的第j个变量节点的额外信息值为：The additional information value passed by codebook H ⁽¹⁾ to the jth variable node of H ⁽²⁾ is:

其中，N(j)为耦合插入矩阵M中第j行行向量1的位置的集合，

为校验矩阵H⁽¹⁾中第j'个变量节点的上轮迭代LLR值。Among them, N(j) is the set of positions of the row vector 1 of the jth row in the coupled insertion matrix M,

is the LLR value of the previous iteration of the j'th variable node in the check matrix H ⁽¹⁾ .

对于码本H⁽²⁾而言，用于判决的的软信息

变为：For codebook H ⁽²⁾ , the soft information used for decision

becomes:

H⁽²⁾码本Tanner图中信息位第j个变量节点VN传递给第i个检验节点的信息值L_j→i变为：H ⁽²⁾ The information value L _j→i that the j-th variable node VN of the information bit in the Tanner graph of the codebook passes to the i-th check node becomes:

基于该Tanner图的耦合插入方案联合BP算法如表2所示：The coupling insertion scheme combined with BP algorithm based on the Tanner graph is shown in Table 2:

表2Table 2

仿真实验：Simulation:

采用信息序列长度为504，码字长度为1008，码率为1/2的LDPC码，BP算法的最大迭代次数为20次。合法接收端只能接收到中继的转发信息，且合法链路的信道增益h_RD＝1；窃听端同时窃听源节点S与中继节点R，窃听链路的信道增益h_SE＝h_RE＝0.707，调制方式选取BPSK。The length of the information sequence is 504, the length of the code word is 1008, and the code rate is 1/2 LDPC code, and the maximum number of iterations of the BP algorithm is 20 times. The legitimate receiving end can only receive the forwarding information of the relay, and the channel gain of the legitimate link is h _RD =1; the eavesdropping end eavesdrops on the source node S and the relay node R at the same time, and the channel gain of the eavesdropping link is h _SE = h _RE = 0.707, select BPSK as the modulation method.

图4表示耦合拼接方案下两种译码算法的误码率随信噪比的变化曲线，由此可以看出，两种译码算法拥有相同的译码性能。Figure 4 shows the variation curve of the bit error rate with the signal-to-noise ratio of the two decoding algorithms under the coupled splicing scheme. From this, it can be seen that the two decoding algorithms have the same decoding performance.

图5表示耦合拼接方案与传统方案的性能对比图，对于两跳传输采用不同码本的中继传输系统，窃听端可以通过构造等效校验矩阵的方式，减小与合法接收端的译码性能差距，在该实验中，对于相同误码率下，传统方案下合法接收端与窃听端仅有0.2dB的译码性能差距。通过耦合拼接设计，使其等效校验矩阵出现环状结构，能抑制窃听端的译码性能，在耦合拼接方案下，对于相同误码率下，窃听端相比合法接收端译码性能差距被拉大到0.3dB。Figure 5 shows the performance comparison between the coupling and splicing scheme and the traditional scheme. For a relay transmission system using different codebooks for two-hop transmission, the eavesdropping end can reduce the decoding performance with the legitimate receiving end by constructing an equivalent check matrix. In this experiment, for the same bit error rate, there is only a 0.2dB difference in decoding performance between the legitimate receiving end and the eavesdropping end under the traditional scheme. Through the coupling and splicing design, the equivalent parity check matrix has a ring structure, which can suppress the decoding performance of the eavesdropping end. Pull up to 0.3dB.

图6为耦合插入方案与传统方案的性能对比图，对于两跳传输采用相同码本的中继传输系统，窃听端可以通过最大比合并的方式获得更优的信噪比条件，从而获得最佳的窃听性能。在该实验中，对于相同误码率下，传统方案下合法接收端与窃听端译码性能十分接近。通过耦合插入设计，将信息序列映射为另一组信息序列，能够有效的抑制窃听端使用最大比合并的方式进行联合窃听，其只能采用基于联合Tanner图的方式来获取最优的译码性能。尽管如此，在耦合插入方案下，对于相同误码率下，窃听端与合法接收端约有2dB的译码性能差距，能有效的保证信息的安全传输。Figure 6 is a performance comparison diagram between the coupling insertion scheme and the traditional scheme. For a relay transmission system using the same codebook for two-hop transmission, the eavesdropping end can obtain better SNR conditions by means of maximum ratio combining, so as to obtain the best signal-to-noise ratio condition. eavesdropping performance. In this experiment, for the same bit error rate, the decoding performance of the legitimate receiver and the eavesdropper under the traditional scheme is very close. Through the coupling insertion design, the information sequence is mapped to another group of information sequences, which can effectively suppress the eavesdropping end using the maximum ratio combining method to conduct joint eavesdropping, which can only obtain the optimal decoding performance based on the joint Tanner graph . Nevertheless, under the coupling insertion scheme, under the same bit error rate, the decoding performance gap between the eavesdropping end and the legitimate receiving end is about 2dB, which can effectively ensure the safe transmission of information.