A construction method and device of a generalized MET-LDPC code suitable for CV-QKD

Abstract

The application discloses a construction method and device of a generalized MET-LDPC code suitable for CV-QKD. G The MET-LDPC code is constructed, wherein R is the code rate of the MET-LDPC code to be constructed, and R>R G ; S2: all check nodes of the MET-LDPC code are sorted to determine the priority of replacement of each check node; S3: after the priority of replacement of all check nodes is determined, the first P check nodes are selected to replace the linear block code corresponding to the check nodes; S4: the check matrix of the linear block code selected in step S3 is used to replace the row of the check matrix of the MEET-LDPC code corresponding to the linear block code, so that the required generalized MET-LDPC code is obtained. The negative influence caused by the reduction of the code rate is reduced while the error correction performance is improved.

Description

Technical Field

[0001] This invention belongs to the field of communication technology, and in particular relates to a method and apparatus for constructing a generalized MET-LDPC code suitable for CV-QKD. Background Technology

[0002] With the development of quantum physics and quantum information theory, quantum cryptography, based on the principles of quantum mechanics, has been proven to possess unconditional security in the information theory sense. Among these technologies, quantum key distribution (QKD) is the most representative. QKD mainly includes two approaches: discrete variable and continuous variable. Continuous variable quantum key distribution (CV-QKD) uses orthogonal components of the quantum optical field as the information carrier, offering advantages such as high secure code rates over short to medium transmission distances and compatibility with most devices in traditional optical communication. It represents a significant direction for the development of quantum key distribution technology.

[0003] The CV-QKD system includes the main steps of quantum information generation, transmission, detection, and data post-processing, and its overall block diagram is shown below. Figure 1 As shown. The data post-processing process significantly affects the overall security of the system and the key generation rate. After data post-processing on the classic channel, Alice and Bob obtain a completely identical set of security keys. The data post-processing flowchart is shown below. Figure 2 As shown, the error correction step is crucial to the system's performance. Currently, the commonly used error correction code in CV-QKD systems at typical transmission distances is the Multi-Edge Type LDPC (MET-LDPC) code. Error correction is achieved by iteratively decoding the received data, and Alice and Bob obtained an identical sequence of binary bits.

[0004] When the transmission distance is short, the signal-to-noise ratio (SNR) of the raw data to be corrected in the CV-QKD system is relatively high, making error correction using MET-LDPC codes easy to implement. However, as the transmission distance increases, the SNR decreases sharply, resulting in a large number of residual errors after decoding with MET-LDPC codes, leading to a high frame error rate (FER) and severely limiting the system's secure bit rate. Under extremely low SNR conditions, the error correction performance of MET-LDPC codes can no longer meet the practical requirements of the CV-QKD system.

[0005] Generalized LDPC (GLDPC) codes are a special type of LDPC code, typically obtained by replacing some or all rows of the LDPC code's parity-check matrix with the parity-check matrix of a linear block code. The process of replacing a row with a linear block code is as follows: Figure 3 As shown. Since GLDPC codes replace the single parity check codes represented by a row in the original LDPC code parity-check matrix with linear block codes, increasing the parity capability of the replaced rows, they can provide more accurate decoding information during iterative decoding, thereby reducing the number of residual errors after decoding and improving error correction performance. Therefore, constructing a generalized MET-LDPC code based on the MET-LDPC code can effectively improve the error correction performance of CV-QKD under extremely low signal-to-noise ratio conditions. However, compared to the original LDPC code, the generalized LDPC code obtained through replacement has an increased number of rows in the parity-check matrix while the number of columns remains unchanged. Therefore, the code rate of the generalized LDPC code decreases, and the more rows replaced, the lower the code rate of the obtained generalized LDPC code. In CV-QKD systems, the code rate of the error correction code also affects the final security code rate of the system. Summary of the Invention

[0006] The purpose of this invention is to overcome the problems of the prior art by disclosing a method and apparatus for constructing a generalized MET-LDPC code suitable for CV-QKD. The method or apparatus of this invention improves the error correction performance of the generalized MET-LDPC code while reducing the negative impact of its code rate reduction.

[0007] The objective of this invention is achieved through the following technical solution:

[0008] A method for constructing a generalized MET-LDPC code suitable for CV-QKD, the method comprising:

[0009] S1: Based on the input code rate R and code length N G Construct a MET-LDPC code, where R is the code rate of the MET-LDPC code to be constructed, and R > R G R G Let N be the target code rate of the generalized MET-LDPC code to be constructed. G The code length is the same as the proposed generalized MET-LDPC code;

[0010] S2: Sort all check nodes of the MET-LDPC code and determine the priority of each check node to be replaced;

[0011] S3: After determining the priority of all check nodes to be replaced, select the linear block codes corresponding to the first P check nodes for replacement;

[0012] S4: Replace the rows of the parity-check matrix of the corresponding MEET-LDPC code with the parity-check matrix of the linear block code selected in step S3 to obtain the desired generalized MET-LDPC code.

[0013] According to a preferred embodiment, step S1 includes: generating an optimal degree distribution at the input code rate R, and then generating a MET-LDPC code using the PEG algorithm.

[0014] According to a preferred embodiment, step S2, determining the priority of each verification node being replaced, includes the following steps:

[0015] S21: Decode the error-correcting code obtained in step S1 several times, and use vector t to record the number of times each check node fails to satisfy the check relationship;

[0016] S22: After each decoding, if the product of the current decoding result and the i-th row of the test matrix H is not equal to 0, then t[i] is incremented by 1;

[0017] S23: After the entire decoding process is completed, sort all elements of vector t, and the row with the larger t[i] value is used for replacement first.

[0018] According to a preferred embodiment, in step S3, the selected linear block codes are sequentially denoted by N. i The bitrates are R in order. i .

[0019] According to a preferred embodiment, in step S4, the code rate R of the generalized MET-LDPC code obtained after replacement is... P Represented as:

[0020]

[0021] Furthermore, the choice of parameter P satisfies:

[0022] On the other hand, the present invention also discloses:

[0023] A construction apparatus for a generalized MET-LDPC code suitable for CV-QKD, wherein the generalized MET-LDPC code construction apparatus completes the construction of the generalized MET-LDPC code using the aforementioned generalized MET-LDPC code construction method.

[0024] According to a preferred embodiment, the construction apparatus includes: a MET-LDPC code construction module, a check node selection module, a linear block code selection module, and a generalized MET-LDPC code generation module.

[0025] The MET-LDPC code construction module is configured to generate MET-LDPC codes according to step S1.

[0026] The verification node selection module is configured to determine the priority of each verification node to be replaced according to step S2.

[0027] The linear block code selection module is configured to select the linear block codes corresponding to the first P check nodes for replacement according to step S3.

[0028] The generalized MET-LDPC code generation module is configured to replace the rows of the check matrix of the corresponding MEET-LDPC code with the check matrix of the linear block code selected by the linear block code selection module in step S4, so as to obtain the desired generalized MET-LDPC code.

[0029] According to a preferred embodiment, the MET-LDPC code construction module includes a degree distribution optimization module and a PEG algorithm module.

[0030] The degree distribution optimization module is configured to generate the optimal degree distribution for the input code rate R.

[0031] The PEG algorithm module is configured to use the PEG algorithm to generate MET-LDPC codes.

[0032] The aforementioned main solution of the present invention and its various further alternative solutions can be freely combined to form multiple solutions, all of which are solutions that can be adopted and are claimed by the present invention. Those skilled in the art, after understanding the solution of the present invention, will realize that there are many combinations based on existing technology and common knowledge, all of which are technical solutions to be protected by the present invention, and will not be exhaustively listed here.

[0033] The beneficial effects of this invention are:

[0034] Under extremely low signal-to-noise ratio conditions, using MET-LDPC codes for error correction results in a large number of residual errors after decoding, leading to a high FER (Failure Error Rate). Its performance cannot meet the long-distance transmission requirements of the CV-QKD system.

[0035] This invention proposes a method and apparatus for constructing a generalized MET-LDPC code suitable for CV-QKD. While improving decoding performance by using a check node with stronger check capability in the generalized MET-LDPC code, it reduces the negative impact of changes in the code rate of the generalized MET-LDPC code on the final secure code rate of the system. Attached Figure Description

[0036] Figure 1 This is a flowchart of the CV-QKD system;

[0037] Figure 2This is a flowchart of the CV-QKD system data post-processing.

[0038] Figure 3 This is a diagram of the generalized LDPC code replacement process;

[0039] Figure 4 This is a diagram of the generalized MET-LDPC code construction device of the present invention;

[0040] Figure 5 This is a diagram of the MET-LDPC code construction module in the device of the present invention;

[0041] Figure 6 This is the MET-LDPC code verification matrix diagram of the present invention. Detailed Implementation

[0042] The following specific examples illustrate the implementation of the present invention. Those skilled in the art can easily understand other advantages and effects of the present invention from the content disclosed in this specification. The present invention can also be implemented or applied through other different specific embodiments, and various details in this specification can also be modified or changed based on different viewpoints and applications without departing from the spirit of the present invention. It should be noted that, unless otherwise specified, the following embodiments and features described therein can be combined with each other.

[0043] It should be noted that similar labels and letters in the following figures indicate similar items. Therefore, once an item is defined in one figure, it does not need to be further defined and explained in subsequent figures.

[0044] In the description of this invention, it should also be noted that, unless otherwise explicitly specified and limited, the terms "set," "install," "connect," and "link" should be interpreted broadly. For example, they can refer to a fixed connection, a detachable connection, or an integral connection; they can refer to a mechanical connection or an electrical connection; they can refer to a direct connection or an indirect connection through an intermediate medium; and they can refer to the internal connection of two components. Those skilled in the art can understand the specific meaning of the above terms in this invention based on the specific circumstances.

[0045] Furthermore, it should be noted that, unless otherwise specified, the structures, connections, positions, power sources, etc. involved in this invention are all things that a person skilled in the art can know without creative effort based on the prior art.

[0046] Example

[0047] refer to Figures 4 to 6This embodiment discloses a method for constructing a generalized MET-LDPC code suitable for CV-QKD. The method for constructing the generalized MET-LDPC code includes the following steps.

[0048] Step S1: Based on the input code rate R and code length N G Construct a MET-LDPC code, where R is the code rate of the MET-LDPC code to be constructed, and R > R G R G Let N be the target code rate of the generalized MET-LDPC code to be constructed. G It has the same code length as the proposed generalized MET-LDPC code.

[0049] Specifically, step S1 includes: generating the optimal degree distribution at the input code rate R, and then using the PEG (Progressive Edge Growth) algorithm to generate the MET-LDPC code.

[0050] The MET-LDPC code parity check matrix is ​​typically as follows: Figure 6 As shown, the upper right corner is an all-zero matrix, and the lower right corner is an identity matrix. The row weights of the two parts differ significantly, and the length of the linear block code used for replacement needs to be the same as the row weight of the replaced row. Therefore, in the process of constructing the generalized MET-LDPC code, it is necessary to select the corresponding linear block code based on the position of the replaced check node.

[0051] Step S2: Sort all check nodes of the MET-LDPC code and determine the priority of each check node to be replaced.

[0052] Specifically, step S2 determines the priority of each verification node being replaced, including the following steps:

[0053] S21: Decode the error-correcting code obtained in step S1 several times, and use vector t to record the number of times each check node fails to satisfy the check relationship;

[0054] S22: After each decoding, if the product of the current decoding result and the i-th row of the test matrix H is not equal to 0, then t[i] is incremented by 1;

[0055] S23: After the entire decoding process is completed, sort all elements of vector t, and the row with the larger t[i] value is used for replacement first.

[0056] Step S3: After determining the priority of replacing all check nodes, select the linear block codes corresponding to the first P check nodes for replacement. This ensures that the code rate of the generalized MET-LDPC code obtained after replacing these selected linear block codes is close to or even the same as the target code rate. Let the code length of the selected linear block codes be N, sequentially...i The bitrates are R in order. i .

[0057] Step S4: Replace the rows of the parity check matrix of the corresponding MEET-LDPC code with the parity check matrix of the linear block code selected in step S3 to obtain the desired generalized MET-LDPC code.

[0058] Specifically, in step S4, the code rate R of the generalized MET-LDPC code obtained after the replacement is... P Represented as:

[0059]

[0060] Furthermore, to minimize the impact of the decrease in error correction code rate caused by constructing generalized MET-LDPC codes on the system's security code rate, R P The value needs to be consistent with R G The closest, that is, the choice of parameter P, needs to satisfy:

[0061] Example 2

[0062] Based on Embodiment 1, this embodiment discloses a construction apparatus for a generalized MET-LDPC code applicable to CV-QKD. The construction apparatus for the generalized MET-LDPC code uses the construction method of the generalized MET-LDPC code as described in Embodiment 1 to complete the construction of the generalized MET-LDPC code.

[0063] The generalized MET-LDPC code construction device includes: a MET-LDPC code construction module, a check node selection module, a linear block code selection module, and a generalized MET-LDPC code generation module.

[0064] Preferably, the MET-LDPC code construction module is configured to generate MET-LDPC codes according to step S1.

[0065] Furthermore, the MET-LDPC code construction module includes a degree distribution optimization module and a PEG algorithm module. The degree distribution optimization module is configured to generate the optimal degree distribution under the input code rate R. The PEG algorithm module is configured to generate MET-LDPC codes using the PEG algorithm.

[0066] Preferably, the verification node selection module is configured to determine the priority of each verification node to be replaced according to step S2.

[0067] Preferably, the linear block code selection module is configured to select the linear block codes corresponding to the first P check nodes for replacement according to step S3.

[0068] Preferably, the generalized MET-LDPC code generation module is configured to replace the rows of the check matrix of the corresponding MEET-LDPC code with the check matrix of the linear block code selected by the linear block code selection module in step S4 to obtain the desired generalized MET-LDPC code.

[0069] Under extremely low signal-to-noise ratio conditions, using MET-LDPC codes for error correction results in a large number of residual errors after decoding, leading to a high FER (Failure Error Rate). Its performance cannot meet the long-distance transmission requirements of the CV-QKD system.

[0070] This invention proposes a method and apparatus for constructing a generalized MET-LDPC code suitable for CV-QKD. While improving decoding performance by using a check node with stronger check capability in the generalized MET-LDPC code, it reduces the negative impact of changes in the code rate of the generalized MET-LDPC code on the final secure code rate of the system.

[0071] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A method for constructing a generalized MET-LDPC code suitable for CV-QKD, characterized in that, The method for constructing the generalized MET-LDPC code includes: S1: Based on the input bitrate R and code length Construct the MET-LDPC code, where R Given the required MET-LDPC code rate, and R > , The target code rate and code length of the generalized MET-LDPC code to be constructed are given by [reference to code rate and code length]. The code length is the same as the proposed generalized MET-LDPC code; S2: Sort all check nodes of the MET-LDPC code and determine the priority of each check node to be replaced; Step S2 includes the following steps: S21: Decode the error-correcting code obtained in step S1 several times, using vector... t Record the number of times each verification node fails to meet the verification relationship; S22: After each decoding step, if the current decoding result matches the test matrix... H The i If the product of rows is not equal to 0, then t [ i Add 1; S23: After the entire decoding process is completed, for the vector... t Sort all elements. t [ i Rows with larger values ​​are replaced first; S3: After determining the priority of all check nodes to be replaced, select the first... P The linear block code corresponding to each check node is used for replacement; Let the selected linear block code lengths be as follows: The bitrates are as follows: ; S4: Replace the rows of the parity check matrix of the corresponding MET-LDPC code with the parity check matrix of the linear block code selected in step S3 to obtain the desired generalized MET-LDPC code. In step S4, the code rate of the generalized MET-LDPC code obtained after replacement is... Represented as: Furthermore, the choice of parameter P satisfies: .

2. The method for constructing the generalized MET-LDPC code as described in claim 1, characterized in that, Step S1 includes: based on the input bitrate R The optimal degree distribution at this code rate is generated, and then the MET-LDPC code is generated using the PEG algorithm.

3. A device for constructing a generalized MET-LDPC code suitable for CV-QKD, characterized in that, The apparatus for constructing the generalized MET-LDPC code is used to construct the generalized MET-LDPC code by means of any one of claims 1 to 2.

4. The apparatus for constructing a generalized MET-LDPC code as described in claim 3, characterized in that, The constructing device includes: a MET-LDPC code construction module, a check node selection module, a linear block code selection module, and a generalized MET-LDPC code generation module. The MET-LDPC code construction module is configured to generate MET-LDPC codes according to step S1. The verification node selection module is configured to determine the priority of each verification node to be replaced according to step S2. The linear block code selection module is configured to select the previous linear block code according to step S3. P The linear block code corresponding to each check node is used for replacement; The generalized MET-LDPC code generation module is configured to replace the rows of the check matrix of the corresponding MET-LDPC code with the check matrix of the linear block code selected by the linear block code selection module in step S4, so as to obtain the desired generalized MET-LDPC code.

5. The apparatus for constructing a generalized MET-LDPC code as described in claim 4, characterized in that, The MET-LDPC code construction module includes a degree distribution optimization module and a PEG algorithm module. The degree distribution optimization module is configured to optimize the input bit rate. R Generate the optimal degree distribution at this code rate; The PEG algorithm module is configured to use the PEG algorithm to generate MET-LDPC codes.

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