Error code correction method and device suitable for long-distance CV-QKD

Abstract

The invention provides an error code correction method and device suitable for long-distance CV-QKD, and the method is realized based on an LDPC code and a binary linear block code, a 01 bit sequence randomly generated in an error code correction process is multiplied by a linear block code generation matrix to obtain a linear block code check bit sequence, and the linear block code check bit sequence is used in an iterative decoding process of the LDPC code, so that the linear block code check bit sequence is obtained. Therefore, the check capability of the LDPC code check node is enhanced, the LDPC code check node can provide more accurate decoding information in the iterative decoding process, the purpose of improving the error code correction performance of the long-distance CV-QKD system is achieved, and the safe code rate of the CV-QKD system is ensured.

Description

Technical Field

[0001] The present invention relates to the technical field of continuous variable quantum key distribution (CV-QKD), and in particular to a method and device for error correction suitable for long-distance CV-QKD. Background Art

[0002] With the development of quantum physics and quantum information theory, quantum cryptography based on the principles of quantum mechanics has been proven to have unconditional security in the sense of information theory. Among them, the most representative technology is quantum key distribution (QKD). QKD mainly includes two major technical approaches: discrete variables and continuous variables. Among them, continuous variable quantum key distribution (CV-QKD) uses the orthogonal components of the quantum light field as the information carrier, has the advantages of high security code rate within medium and short transmission distances, and good compatibility with the traditional optical communication industry chain. It is an important development direction of quantum key distribution technology.

[0003] The CV-QKD system includes the preparation, transmission, detection and classical data post-processing of quantum states. The overall block diagram is as follows: Figure 1 The data post-processing process significantly affects the overall security of the system and the key generation rate. After data post-processing, Alice (sender) and Bob (receiver) obtain a set of completely consistent security keys. The data post-processing flow chart is shown in Figure 2 As shown in the figure, the error correction step is the key to determine the system performance. At present, the error correction code commonly used in CV-QKD systems at typical transmission distances is LDPC (Low density parity-check, LDPC) code. Error correction is completed by iteratively decoding the error correction data. Alice and Bob obtain a string of exactly the same binary bit sequences.

[0004] When the transmission distance is short, the signal-to-noise ratio of the original data to be corrected in the CV-QKD system is relatively high, and error correction is easy to implement when using LDPC codes for iterative decoding. However, as the transmission distance increases, the signal-to-noise ratio drops sharply, and there are a large number of residual errors after decoding using LDPC codes. The frame error rate (FER) is very high, and the system security code rate is severely limited. Under long-distance transmission, the error correction performance of LDPC codes cannot fully meet the actual needs of CV-QKD systems. Summary of the invention

[0005] As the transmission distance of the CV-QKD system increases, under extremely low signal-to-noise ratio conditions, the error correction based on the LDPC code has a large number of residual errors after iterative decoding, and its error correction performance can no longer meet the requirements of the long-distance CV-QKD system. In order to achieve efficient error correction of the CV-QKD system over long distances, the present invention aims to provide an error correction method and device suitable for long-distance CV-QKD, multiplying the 01 bit sequence randomly generated during the error correction process with the linear block code check matrix to obtain a linear block code check bit sequence, and using it in the iterative decoding process of the LDPC code, thereby enhancing the check capability of the LDPC code check node, so that the LDPC code check node can provide more accurate decoding information during the iterative decoding process, thereby achieving the purpose of improving the error correction performance.

[0006] In the error correction method for long-distance CV-QKD provided by the present invention, it is assumed that the LDPC code check matrix H used for error correction has m rows and n columns, each row has a row weight of k, and the matrix element is h i,j (1≤i≤m,1≤j≤n); the binary linear block code generator matrix G0 is k rows and L columns, the check matrix H0 is Lk rows and L columns, and its check bit sequence length is Lk; the random 01 bit sequence generated during the data negotiation process is C={c1,c2,…,c n};

[0007] The error correction method comprises the following steps:

[0008] (1) constructing an LDPC code check matrix H;

[0009] (2) For each row i of the LDPC code check matrix H, a sequence p with a sequence length k is generated i ={c j |h i,j =1};

[0010] (3) Using sequence p i Generate a linear block code check bit sequence q i , where {p i ,q i =p i *G0,q i The length is Lk;

[0011] (4) The linear block code check bit sequence q i After being added to the random 01-bit sequence C, a new sequence C0 = {C, q1, q2, …, q m};

[0012] (5) Use sequence C0 to perform data negotiation and generate data LLRs to be error corrected;

[0013] (6) Based on the LDPC code check matrix H, the belief propagation decoding algorithm is used to iteratively decode the first n data in the data LLR; for the information update of the i-th check node in the iterative process, the data LLR corresponding to {p i ,q i The corresponding data is implemented using the posterior probability decoding algorithm;

[0014] (7) The sequence obtained after decoding is u = {u1,u2,…,u n}.

[0015] Furthermore, when constructing the LDPC code check matrix H:

[0016] According to the final required error correction rate R, the error correction sequence length N and the linear block code related parameters L and k used, the number of rows m and the number of columns n of the check matrix H are calculated;

[0017] On the basis that the row weight of the LDPC code check matrix H is k, the corresponding degree distribution optimization is performed in combination with the calculated number of rows m and columns n of the LDPC code check matrix H, and then the LDPC code generation algorithm is used to construct the LDPC code check matrix H according to the optimized degree distribution function.

[0018] Furthermore, the error correction code rate is

[0019] The present invention also provides an error correction device suitable for long-distance CV-QKD. Assume that the LDPC code check matrix H used for error correction has m rows and n columns, each row has a row weight of k, and the matrix element is h i,j (1≤i≤m,1≤j≤n); the binary linear block code generator matrix G0 is k rows and L columns, the check matrix H0 is Lk rows and L columns, and its check bit sequence length is Lk; the random 01 bit sequence generated during the data negotiation process is C={c1,c2,…,c n};

[0020] The error correction device comprises:

[0021] An LDPC code check matrix generation module, used for constructing an LDPC code check matrix H;

[0022] A random bit sequence generation module, used for generating a random 01 bit sequence C;

[0023] The linear block code check bit generation module is used to generate a sequence p with a sequence length of k for each row i of the LDPC code check matrix H. i ={c j |h i,j =1}; and use the sequence p iGenerate a linear block code check bit sequence q i , where {p i ,q i =p i *G0,q i The length is Lk;

[0024] The sequence reassembly module is used to reconstruct the linear block code check bit sequence q i After being added to the random 01-bit sequence C, a new sequence C0 = {C, q1, q2, …, q m};

[0025] A data negotiation module, used for performing data negotiation using sequence C0 to generate data LLRs to be error corrected;

[0026] The iterative decoding module is used to iteratively decode the first n data in the data LLR using the belief propagation decoding algorithm based on the LDPC code check matrix H. The sequence obtained after decoding is u={u1,u2,…,u n};

[0027] The a posteriori probability decoding module is used to update the information of the i-th check node in the iteration process, based on the check matrix H0, to decode the LLR of the data corresponding to {p i ,q i The corresponding data is implemented using the posterior probability decoding algorithm.

[0028] Furthermore, when constructing the LDPC code check matrix H, the LDPC code check matrix generation module:

[0029] According to the final required error correction rate R, the error correction sequence length N and the linear block code related parameters L and k used, the number of rows m and the number of columns n of the check matrix H are calculated;

[0030] On the basis that the row weight of the LDPC code check matrix H is k, the corresponding degree distribution optimization is performed in combination with the calculated number of rows m and columns n of the LDPC code check matrix H, and then the LDPC code generation algorithm is used to construct the LDPC code check matrix H according to the optimized degree distribution function.

[0031] Furthermore, the error correction code rate is

[0032] In summary, due to the adoption of the above technical solution, the beneficial effects of the present invention are:

[0033] Under long-distance transmission conditions, the signal-to-noise ratio of the CV-QKD system is extremely low. If the LDPC code is used directly for error correction, there will be a large number of residual errors after decoding, resulting in a high FER, and its performance cannot meet the long-distance transmission requirements of the CV-QKD system. The method of the present invention is based on LDPC code and binary linear block code. The 01 bit sequence randomly generated in the error correction process is multiplied by the linear block code generation matrix to obtain the linear block code check bit sequence, and it is used in the iterative decoding process of the LDPC code, thereby enhancing the check capability of the LDPC code check node, so that the LDPC code check node can provide more accurate decoding information during the iterative decoding process, achieving the purpose of improving the error correction performance of the long-distance CV-QKD system, thereby ensuring the security code rate of the CV-QKD system. BRIEF DESCRIPTION OF THE DRAWINGS

[0034] Figure 1 This is the flow chart of the CV-QKD system.

[0035] Figure 2 This is the data post-processing flow chart of the CV-QKD system.

[0036] Figure 3 The figure is a flow chart of a method for correcting bit errors applicable to long-distance CV-QKD in an embodiment of the present invention.

[0037] Figure 4 It is the Tanner graph of the LDPC code in the embodiment of the present invention.

[0038] Figure 5 It is a structural diagram of a bit error correction device suitable for long-distance CV-QKD in an embodiment of the present invention. DETAILED DESCRIPTION

[0039] In order to make the purpose, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are part of the embodiments of the present invention, not all of the embodiments. Generally, the components of the embodiments of the present invention described and shown in the drawings here can be arranged and designed in various different configurations.

[0040] Therefore, the following detailed description of the embodiments of the present invention provided in the accompanying drawings is not intended to limit the scope of the invention claimed for protection, but merely represents selected embodiments of the present invention. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0041] Example

[0042] As the transmission distance of the CV-QKD system increases, under extremely low signal-to-noise ratio conditions, the error correction based on the LDPC code has a large number of residual errors after iterative decoding, and its error correction performance can no longer meet the requirements of the long-distance CV-QKD system. In order to achieve efficient error correction of the CV-QKD system over long distances, this embodiment proposes an error correction method suitable for long-distance CV-QKD, which multiplies the 01 bit sequence randomly generated during the error correction process with the linear block code check matrix to obtain a linear block code check bit sequence, and uses it in the iterative decoding process of the LDPC code, thereby enhancing the check capability of the LDPC code check node, so that the LDPC code check node can provide more accurate decoding information during the iterative decoding process, thereby achieving the purpose of improving the error correction performance.

[0043] Assume that the LDPC code check matrix H used for error correction has m rows and n columns, each row has a row weight of k, and the matrix element is h i,j (1≤i≤m,1≤j≤n). The binary linear block code generator matrix G0 is k rows and L columns, the check matrix H0 is Lk rows and L columns, and its check bit sequence length is Lk. The random 01 bit sequence generated during the data negotiation process is C={c1,c2,…,c n}.like Figure 3 As shown, the present embodiment proposes a method for correcting errors in long-distance CV-QKD, comprising the following steps:

[0044] (1) constructing an LDPC code check matrix H;

[0045] (2) For each row i of the LDPC code check matrix H, a sequence p with a sequence length k is generated i ={c j |h i,j =1};

[0046] (3) Using sequence p i Generate a linear block code check bit sequence q i , where {p i ,q i =p i *G0,q i The length is Lk;

[0047] (4) The linear block code check bit sequence q i After being added to the random 01-bit sequence C, a new sequence C0 = {C, q1, q2, …, q m};

[0048] (5) Use sequence C0 to perform data negotiation and generate data LLRs to be error corrected;

[0049] (6) Based on the LDPC code check matrix H, the belief propagation decoding algorithm is used to iteratively decode the first n data in the data LLR; for the information update of the i-th check node in the iterative process, the data LLR corresponding to {p i ,q i The corresponding data is implemented using the posterior probability decoding algorithm;

[0050] (7) The sequence obtained after decoding is u = {u1,u2,…,u n}.

[0051] In the above error correction method, since the linear block code check bit sequence is introduced, the actual sequence length N=n+m(Lk) used for error correction is, and the error correction code rate is:

[0052]

[0053] The final Tanner diagram of the LDPC code used for error correction is as follows: Figure 4 shown.

[0054] When constructing the LDPC code check matrix H, the number of rows m and the number of columns n of the check matrix H can be calculated according to the final required error correction rate R, the sequence length N of the error correction, and the linear block code related parameters L and k used. Based on the assumption that the row weight of the LDPC code check matrix H is k, the present invention can perform corresponding degree distribution optimization in combination with the calculated number of rows m and the number of columns n of the LDPC code check matrix H, and then use the LDPC code generation algorithm to construct the LDPC code check matrix H according to the optimized degree distribution function.

[0055] The implementation device corresponding to the error correction method proposed in the present invention is as follows Figure 5 As shown,

[0056] Corresponding to the above error correction method, such as Figure 5 As shown, this embodiment also provides an error correction device suitable for long-distance CV-QKD, including:

[0057] An LDPC code check matrix generation module, used for constructing an LDPC code check matrix H;

[0058] A random bit sequence generation module, used for generating a random 01 bit sequence C;

[0059] The linear block code check bit generation module is used to generate a sequence p with a sequence length of k for each row i of the LDPC code check matrix H. i ={c j |h i,j =1}; and use the sequence p iGenerate a linear block code check bit sequence q i , where {p i ,q i =p i *G0,q i The length is Lk;

[0060] The sequence reassembly module is used to reconstruct the linear block code check bit sequence q i After being added to the random 01-bit sequence C, a new sequence C0 = {C, q1, q2, …, q m};

[0061] A data negotiation module, used for performing data negotiation using sequence C0 to generate data LLRs to be error corrected;

[0062] The iterative decoding module is used to iteratively decode the first n data in the data LLR using the belief propagation decoding algorithm based on the LDPC code check matrix H. The sequence obtained after decoding is u={u1,u2,…,u n};

[0063] The a posteriori probability decoding module is used to update the information of the i-th check node in the iteration process, based on the check matrix H0, to decode the LLR of the data corresponding to {p i ,q i The corresponding data is implemented using the posterior probability decoding algorithm.

[0064] The working principle of each functional module in the above-mentioned error correction device refers to the above-mentioned error correction method, which will not be repeated here.

[0065] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. For those skilled in the art, the present invention may have various modifications and variations. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention shall be included in the protection scope of the present invention.

Claims

1. A method for error correction for long-distance CV-QKD, characterized in that: Assume that the LDPC code check matrix H used for error correction has m rows and n columns, each row has a row weight of k, and the matrix element is h i,j (1≤i≤m,1≤j≤n); the binary linear block code generator matrix G0 is k rows and L columns, the check matrix H0 is Lk rows and L columns, and its check bit sequence length is Lk; the random 01 bit sequence generated during the data negotiation process is C={c1,c2,…,c n }; The error correction method comprises the following steps: (1) constructing an LDPC code check matrix H; (2) For each row i of the LDPC code check matrix H, a sequence p with a sequence length k is generated. i ={c j |h i,j =1}; (3) Using sequence p i Generate a linear block code check bit sequence q i , where {p i ,q i =p i *G0,q i The length is Lk; (4) The linear block code check bit sequence q i After being added to the random 01-bit sequence C, a new sequence C0 = {C, q1, q2, …, q m }; (5) Use sequence C0 to perform data negotiation and generate data LLRs to be error corrected; (6) Based on the LDPC code check matrix H, the belief propagation decoding algorithm is used to iteratively decode the first n data in the data LLR; for the information update of the i-th check node in the iterative process, the data LLR corresponding to {p i ,q i The corresponding data is implemented using the posterior probability decoding algorithm; (7) The sequence obtained after decoding is u = {u1,u2,…,u n }.

2. The error correction method for long-distance CV-QKD according to claim 1, characterized in that: When constructing the LDPC code check matrix H, the number of rows m and the number of columns n of the check matrix H are calculated according to the final required error correction rate R, the error correction sequence length N, and the linear block code related parameters L and k used; On the basis that the row weight of the LDPC code check matrix H is k, the corresponding degree distribution optimization is performed in combination with the calculated number of rows m and columns n of the LDPC code check matrix H, and then the LDPC code generation algorithm is used to construct the LDPC code check matrix H according to the optimized degree distribution function.

3. The error correction method for long-distance CV-QKD according to claim 2, characterized in that: The error correction code rate is 4. An error correction device suitable for long-distance CV-QKD, characterized in that: Assume that the LDPC code check matrix H used for error correction has m rows and n columns, each row has a row weight of k, and the matrix element is h i,j (1≤i≤m,1≤j≤n); the binary linear block code generator matrix G0 is k rows and L columns, the check matrix H0 is Lk rows and L columns, and its check bit sequence length is Lk; the random 01 bit sequence generated during the data negotiation process is C={c1,c2,…,c n }; The error correction device comprises: An LDPC code check matrix generation module, used for constructing an LDPC code check matrix H; A random bit sequence generation module, used for generating a random 01 bit sequence C; The linear block code check bit generation module is used to generate a sequence p with a sequence length of k for each row i of the LDPC code check matrix H. i ={c j |h i,j =1}; and use the sequence p i Generate a linear block code check bit sequence q i , where {p i ,q i =p i *G0,q i The length is Lk; The sequence reassembly module is used to reconstruct the linear block code check bit sequence q i After being added to the random 01-bit sequence C, a new sequence C0 = {C, q1, q2, …, q m }; A data negotiation module, used for performing data negotiation using sequence C0 to generate data LLRs to be error corrected; The iterative decoding module is used to iteratively decode the first n data in the data LLR using the belief propagation decoding algorithm based on the LDPC code check matrix H. The sequence obtained after decoding is u={u1,u2,…,u n }; The a posteriori probability decoding module is used to update the information of the i-th check node in the iteration process, based on the check matrix H0, to decode the LLR of the data corresponding to {p i ,q i The corresponding data is implemented using the posterior probability decoding algorithm.

5. The error correction device for long-distance CV-QKD according to claim 4, characterized in that: When constructing the LDPC code check matrix H, the LDPC code check matrix generation module calculates the number of rows m and the number of columns n of the check matrix H according to the final required error correction code rate R, the error correction sequence length N, and the linear block code related parameters L and k used; On the basis that the row weight of the LDPC code check matrix H is k, the corresponding degree distribution optimization is performed in combination with the calculated number of rows m and columns n of the LDPC code check matrix H, and then the LDPC code generation algorithm is used to construct the LDPC code check matrix H according to the optimized degree distribution function.

6. The error correction device for long-distance CV-QKD according to claim 5, characterized in that: The error correction code rate is

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