技术领域Technical Field
本发明属于编码技术领域，尤其涉及一种大圈长准循环半随机LDPC码设计方法。The invention belongs to the field of coding technology, and in particular relates to a large-cycle-length quasi-cyclic semi-random LDPC code design method.
背景技术Background technique
信道编码在通信中的作用是通过在发送端引入冗余信息，以增强对噪声和信道干扰的容错能力，从而提高通信系统的可靠性和性能。通过编码，原始数据被转换为编码字，其中包含了冗余信息，这使得接收端能够检测和纠正由信道导致的错误。The role of channel coding in communication is to enhance the tolerance to noise and channel interference by introducing redundant information at the sending end, thereby improving the reliability and performance of the communication system. Through coding, the original data is converted into a coded word, which contains redundant information, which enables the receiving end to detect and correct errors caused by the channel.
LDPC码是由Gallager在20世纪60年代初发明的，然而在接下来的几十年里被忽视，直到1999年Mackay重新发现。LDPC码是由稀疏检验矩阵定义的，在通过置信传播(BP)算法迭代解码时能够展现出接近香农极限的卓越误码率(BER)性能。如果Tanner图中存在短环，经过几步迭代后外部信息会相关联，从而阻止迭代的收敛。另一个常见的影响解码的问题是陷阱集，它们同样由环组成，小陷阱集通常由小环构成，随着环长的增加，小陷阱集通常也随之消失。因此为了提高LDPC的纠错性能，通常将尽可能增大圈长作为LDPC码的构造目标。LDPC codes were invented by Gallager in the early 1960s, but were neglected for decades until they were rediscovered by Mackay in 1999. LDPC codes are defined by a sparse check matrix and can exhibit excellent bit error rate (BER) performance close to the Shannon limit when iteratively decoded using the belief propagation (BP) algorithm. If there are short cycles in the Tanner graph, external information will be correlated after a few iterations, preventing the iterations from converging. Another common problem that affects decoding is trap sets, which are also composed of cycles. Small trap sets are usually composed of small cycles, and as the length of the cycle increases, small trap sets usually disappear. Therefore, in order to improve the error correction performance of LDPC, it is usually necessary to increase the cycle length as much as possible as the construction goal of LDPC codes.
发明内容Summary of the invention
针对现有技术存在的问题，本发明提供了一种大圈长准循环半随机LDPC码设计方法。In view of the problems existing in the prior art, the present invention provides a method for designing a large-cycle-length quasi-cyclic semi-random LDPC code.
本发明是这样实现的，一种基于准循环半随机结构的LDPC码设计方法，用于在通信系统中提高数据传输的可靠性，该方法包括以下步骤：The present invention is implemented as follows: a LDPC code design method based on a quasi-cyclic semi-random structure is used to improve the reliability of data transmission in a communication system, and the method comprises the following steps:
a.利用循环移位矩阵Pi，通过一个独特的循环参数配置方法，构造LDPC码的校验矩阵H，其中H由多个循环移位矩阵组合而成，以形成指数矩阵E，从而确保LDPC码具有较大的最小环长；a. Using the cyclic shift matrix Pi , a unique cyclic parameter configuration method is used to construct the check matrix H of the LDPC code, where H is composed of multiple cyclic shift matrices to form an exponential matrix E, thereby ensuring that the LDPC code has a larger minimum cycle length;
b.设计子指数矩阵Ei，形成复杂而灵活的校验矩阵结构，其中子指数矩阵Ei包括若干循环参数，用于精确控制LDPC码的特性，使得码具有优异的错误更正能力和稳定的性能表现；b. Designing a sub-index matrix Ei to form a complex and flexible check matrix structure, wherein the sub-index matrix Ei includes several cyclic parameters for precisely controlling the characteristics of the LDPC code, so that the code has excellent error correction capability and stable performance;
c.利用特定的参数选择策略和构造算法，确保LDPC码在大圈长条件下的设计和实现，从而满足通信系统中对高可靠性的需求。c. Use specific parameter selection strategies and construction algorithms to ensure the design and implementation of LDPC codes under large cycle length conditions, thereby meeting the demand for high reliability in communication systems.
该方法进一步包括以下步骤：The method further comprises the following steps:
a.采用基于随机整数的方法确定每个子指数矩阵Ei中循环参数的值，确保各参数间存在充分的随机性和差异性，避免短环的生成，增强LDPC码在不同环境下的适应性和鲁棒性；a. A random integer-based method is used to determine the value of the cyclic parameter in each sub-index matrix Ei to ensure that there is sufficient randomness and difference between the parameters, avoid the generation of short loops, and enhance the adaptability and robustness of LDPC codes in different environments;
b.根据给定的圈长要求，如不小于8或10，采用特定的算法调整矩阵E中的循环参数，确保校验矩阵H中不存在小于预定圈长的环，从而优化LDPC码的性能，减少误差更正过程中的复杂度；b. According to the given circle length requirement, such as not less than 8 or 10, a specific algorithm is used to adjust the cyclic parameters in the matrix E to ensure that there is no circle less than the predetermined circle length in the check matrix H, thereby optimizing the performance of the LDPC code and reducing the complexity of the error correction process;
c.结合现代通信系统的需求，将所设计的LDPC码应用于数据传输过程中，通过其优异的错误更正能力，提高数据传输的准确性和系统的整体可靠性。c. In combination with the needs of modern communication systems, the designed LDPC code is applied to the data transmission process, and its excellent error correction capability can improve the accuracy of data transmission and the overall reliability of the system.
本发明提供了一种大圈长准循环半随机LDPC码设计方法，所述LDPC码有两种构造方法：随机码和结构化码；The present invention provides a large-cycle quasi-cyclic semi-random LDPC code design method, wherein the LDPC code has two construction methods: a random code and a structured code;
所述结构化LDPC码具体如下：The structured LDPC code is specifically as follows:
Pi是一个循环移位矩阵，它将N*N的单位矩阵I向右循环平移i次，其中i是整数，如果i为∞，那么Pi为全零矩阵；由(1)可知，校验矩阵H可以由循环移位矩阵唯一刻画，方便起见，可以采用下面的指数矩阵表示校验矩阵H；Pi is a cyclic shift matrix, which cyclically shifts the N*N identity matrix I to the right i times, where i is an integer. If i is ∞,Pi is an all-zero matrix. From (1), we can see that the check matrix H can be uniquely characterized by the cyclic shift matrix. For convenience, the following exponential matrix can be used to represent the check matrix H:
考虑矩阵E中长度为2l的环W，假设环W上所经过的循环参数为a0,a1,...,a2l-1，那么环W对应的移位参数可以用公式表示。Consider a ring W of length 2l in the matrix E. Assuming that the cycle parameters on the ring W are a0 , a1 , ..., a2l-1 , the shift parameters corresponding to the ring W can be expressed by the formula.
如果pW＝0，那么在矩阵H中将形成一个长度为2l的环；If pW = 0, then a ring of length 2l will be formed in the matrix H;
构建的QC-LDPC码的指数校验矩阵E的结构如下所示：The structure of the exponential check matrix E of the constructed QC-LDPC code is as follows:
Ei为2*L的子指数矩阵，其形式如下：Ei is a 2*L sub-index matrix, which has the following form:
其中S≥L。Where S≥L.
子指数矩阵D＝[D0 D1 … DS-1]有S行，L*S列，同时子指数矩阵D具有如下性质：The sub-index matrix D = [D0 D1 … DS-1 ] has S rows and L*S columns. The sub-index matrix D has the following properties:
1)子矩阵Di列重均为1，行重不大于1；1) The column weight of the submatrix Di is 1, and the row weight is no more than 1;
2)子矩阵D的行重为L，列重均为1。2) The row weight of submatrix D is L, and the column weight is 1.
进一步，圈长不小于8的LDPC码设计方法如下：Furthermore, the design method of LDPC code with a circle length not less than 8 is as follows:
1)N>L；1) N>L;
2)ei(i＝0,…,L-1)是小于N的随机整数，且互不相等；2) ei (i＝0,…,L-1) are random integers less than N and are not equal to each other;
3)D的构造方法如下：3) The construction method of D is as follows:
3-1)构造一个行重和列重均为L的矩阵K，显然此矩阵的行数和列数均为S；3-1) Construct a matrix K with both row weight and column weight L. Obviously, the number of rows and columns of this matrix is S;
3-2)在生成D中的每一个子矩阵Di时，取出矩阵K的第i列，显然这一列中有L个不为0的元素，记录这L个不为0的元素所在的行数到集合Ridx中；3-2) When generating each submatrixDi in D, take out the i-th column of the matrix K. Obviously, there are L non-zero elements in this column. Record the row numbers of these L non-zero elements in the setRidx ;
3-3)Di有L列S行，首先初始化Di，其所有的元素均为∞；3-3)Di has L columns and S rows. First, initializeDi so that all its elements are ∞.
3-4)从第0到第L-1列，每构造一列，首先随机的从Rinx集合中不重复的取出一个行数r，然后在该列的第r行随机生成一个小于N的整数。3-4) From the 0th to the L-1th column, each time a column is constructed, first a row number r is randomly selected from the Rinx set without duplication, and then an integer less than N is randomly generated in the rth row of the column.
经过上述三个步骤，所构造的矩阵满足公式(4)和(5)以及本发明约定的校验矩阵指数矩阵的要求，其对应的校验矩阵H的圈长不小于8。After the above three steps, the constructed matrix meets the requirements of formulas (4) and (5) and the check matrix index matrix stipulated in the present invention, and the circle length of the corresponding check matrix H is not less than 8.
进一步，圈长不小于10的LDPC码设计方法如下：Furthermore, the design method of LDPC code with a cycle length not less than 10 is as follows:
1)ei(i＝0,…,L-1)互不相等，且对于任意的i,j,m和n，ei-ej≠em-en；1) ei (i＝0,…,L-1) are not equal to each other, and for any i, j, m and n, ei -ej ≠ em -en ;
2)N(N>0)满足：2) N (N>0) satisfies:
2-1)对于任意的i和j,满足(ei-ej)mod N≠0；2-1) For any i and j, (ei -ej ) mod N ≠ 0;
2-2)对于任意的i,j,m和n,满足(ei-ej+em-en)mod N≠0；2-2) For any i, j, m and n, (ei -ej +em -en ) mod N ≠ 0;
3)D的构造方法如下：3) The construction method of D is as follows:
3-1)构造一个行重和列重均为L的矩阵K，其圈长为6，显然此矩阵的行数和列数相等，令其为t；3-1) Construct a matrix K with row weight and column weight both being L, and its circle length being 6. Obviously, the number of rows and columns of this matrix is equal, let it be t;
3-2)令S＝t；3-2) Let S = t;
3-3)在生成D中的每一个子矩阵Di时，取出矩阵K的第i列，显然这一列中有L个不为0的元素，记录这L个不为0的元素所在的行数到集合Ridx中；3-3) When generating each submatrixDi in D, take out the i-th column of the matrix K. Obviously, there are L non-zero elements in this column. Record the row numbers of these L non-zero elements in the setRidx ;
3-4)Di有L列S行，首先初始化Di，其所有的元素均为∞；3-4)Di has L columns and S rows. First, initializeDi so that all its elements are ∞.
3-5)从第0到第L-1列，每构造一列，首先随机的从Rinx集合中不重复的取出一个行数r，然后在该列的第r行随机生成一个小于N的整数；3-5) From the 0th to the L-1th column, each time a column is constructed, first randomly select a row number r from the Rinx set without duplication, and then randomly generate an integer less than N in the rth row of the column;
经过上述三个步骤，所构造的矩阵满足公式(4)以及本发明约定的校验矩阵指数矩阵的要求，其对应的校验矩阵H的圈长不小于10。After the above three steps, the constructed matrix meets the formula (4) and the requirements of the check matrix index matrix stipulated in the present invention, and the circle length of the corresponding check matrix H is not less than 10.
本发明提供的一种用于生成大圈长准循环半随机LDPC码的系统，该系统包括：The present invention provides a system for generating a large-cycle-length quasi-cyclic semi-random LDPC code, the system comprising:
用于生成循环移位矩阵Pi的模块，该模块能够处理N*N的单位矩阵I，并对其进行向右平移i次的操作，以产生循环移位矩阵Pi；A module for generating a cyclic shift matrixPi , which can process an N*N identity matrix I and perform an operation of right-shifting it i times to generate a cyclic shift matrixPi ;
一个指数矩阵表示模块，用于将校验矩阵H表示为指数矩阵E，以便于处理和简化LDPC码的构造；An exponential matrix representation module for representing the check matrix H as an exponential matrix E to facilitate processing and simplify the construction of LDPC codes;
一个QC-LDPC码构造模块，用于根据预设的条件生成指数校验矩阵E，且该模块能够处理子指数矩阵Ei和Di的生成和排列，以满足构造大圈长LDPC码的要求。A QC-LDPC code construction module is used to generate an exponential check matrix E according to preset conditions, and the module can process the generation and arrangement of sub-exponential matrices Ei and Di to meet the requirements of constructing large cycle length LDPC codes.
进一步，该系统还包括：Furthermore, the system includes:
一个数字序列及参数配置模块，生成一组满足圈长要求的整数序列ei(i＝0,…,L-1)，特别的，当圈长要求为8时，ei互不相等，当圈长要求为10时，要求ei互不相等，且ei之间的差值满足特定数学条件，并根据序列配置相应的N值；A digital sequence and parameter configuration module generates a set of integer sequences ei (i=0,…,L-1) that meet the circle length requirements. In particular, when the circle length requirement is 8, the ei are not equal to each other. When the circle length requirement is 10, the ei are not equal to each other, and the difference between the ei meets a specific mathematical condition, and configures the corresponding N value according to the sequence;
一个子矩阵D生成模块，用于构造满足特定行重和列重要求的子矩阵D，并通过随机交换操作来增加LDPC码的随机性，以确保校验矩阵H的圈长满足设定的要求。A submatrix D generation module is used to construct a submatrix D that meets specific row weight and column weight requirements, and to increase the randomness of the LDPC code through random exchange operations to ensure that the circle length of the check matrix H meets the set requirements.
进一步，该系统还包括：Furthermore, the system includes:
一个矩阵K构造模块，用于生成一个行重和列重均为L的矩阵K，其中当构造圈长为10的LDPC码时K的圈长要求为6，并确定其尺寸t；a matrixK construction module, for generating a matrix K with both row weight and column weight L, wherein when constructing an LDPC code with a circle length of 10, the circle length of K is required to be 6, and determining its size t;
一个子矩阵Di构造模块，用于从矩阵K中提取信息并生成Di，进而在矩阵D中排列这些子矩阵，以满足指数校验矩阵E的结构要求。A submatrix Di construction module is used to extract information from the matrix K and generate Di , and then arrange these submatrices in the matrix D to meet the structural requirements of the exponential check matrix E.
进一步，该系统还包括：Furthermore, the system includes:
一个优化模块，用于对生成的校验矩阵H进行进一步优化，以提高LDPC码性能，包括但不限于降低误码率和增强解码效率；An optimization module, used for further optimizing the generated check matrix H to improve the performance of the LDPC code, including but not limited to reducing the bit error rate and enhancing the decoding efficiency;
一个用户界面模块，用于接收用户输入的参数设置，并显示生成的LDPC码及其相关属性，如圈长和码率；a user interface module for receiving parameter settings input by a user and displaying the generated LDPC code and its related properties, such as circle length and code rate;
一个存储模块，用于保存生成的LDPC码和相关配置参数，以便于未来的检索和使用；A storage module for saving the generated LDPC codes and related configuration parameters for future retrieval and use;
一个测试模块，用于对生成的LDPC码进行性能测试，包括但不限于误差性能和解码延迟，以验证码的有效性和实用性。A test module is used to perform performance tests on the generated LDPC code, including but not limited to error performance and decoding delay, to verify the effectiveness and practicality of the code.
结合上述的技术方案和解决的技术问题，本发明所要保护的技术方案所具备的优点及积极效果为：In combination with the above technical solutions and the technical problems solved, the advantages and positive effects of the technical solutions to be protected by the present invention are as follows:
第一、本发明结合随机和结构化构造的特点，设计大圈长准循环，同时具有半随机特性的LDPC码，通过仿真验证，本发明所设计的码具有良好的纠错性能。First, the present invention combines the characteristics of random and structured construction to design a large-length quasi-cyclic LDPC code with semi-random characteristics. Through simulation verification, the code designed by the present invention has good error correction performance.
本发明通过设计圈长不小于8和10的LDPC码，增强对噪声和信道干扰的容错能力，从而提高通信系统的可靠性和性能。通过编码，原始数据被转换为编码字，其中包含了冗余信息，这使得接收端能够检测和纠正由信道导致的错误。The present invention enhances the fault tolerance to noise and channel interference by designing LDPC codes with a cycle length of not less than 8 and 10, thereby improving the reliability and performance of the communication system. Through encoding, the original data is converted into a coded word, which contains redundant information, so that the receiving end can detect and correct errors caused by the channel.
本发明有效解决了信道导致的错误，通过设计圈长不小于8和10的LDPC码，增强对噪声和信道干扰的容错能力，从而提高通信系统的可靠性和性能。The present invention effectively solves the errors caused by the channel, and enhances the fault tolerance to noise and channel interference by designing LDPC codes with a cycle length of not less than 8 and 10, thereby improving the reliability and performance of the communication system.
本发明在保证所设计的准循环LDPC码具有较大圈长的基础上，引入部分随机特性，优化了其码重的分布，具体来说就是降低了低重量码字的数量，提高纠错性能；另外不同于目前各标准中规定固定的校验矩阵，本发明可以随机的生成校验矩阵，实现隐秘的信道传输。The present invention introduces partial random characteristics on the basis of ensuring that the designed quasi-cyclic LDPC code has a large cycle length, optimizes the distribution of its code weight, specifically reduces the number of low-weight codewords and improves the error correction performance; in addition, unlike the fixed check matrix specified in the current standards, the present invention can randomly generate a check matrix to achieve covert channel transmission.
第二，本发明提供了一种大圈长准循环半随机LDPC码设计方法，解决了现有技术中LDPC码设计在圈长、随机性和结构化方面的技术问题，并获取了显著的技术进步。Second, the present invention provides a method for designing large-cycle quasi-cyclic semi-random LDPC codes, which solves the technical problems of LDPC code design in the prior art in terms of cycle length, randomness and structure, and achieves significant technical progress.
首先，该设计方法结合了随机码和结构化码的特点，通过特定的构造方法，实现了大圈长、准循环、半随机的LDPC码设计。这种设计方式既保留了随机码的良好性能，又具备了结构化码的易于实现和优化的特点。First, the design method combines the characteristics of random codes and structured codes, and realizes the design of large-cycle, quasi-cyclic, and semi-random LDPC codes through a specific construction method. This design method not only retains the good performance of random codes, but also has the characteristics of easy implementation and optimization of structured codes.
其次，对于圈长不小于8和10的LDPC码设计，该方法提供了详细的构造步骤和条件。这些步骤和条件确保了所构造的LDPC码具有较大的圈长，从而提高了码的纠错性能和解码效率。Secondly, the method provides detailed construction steps and conditions for the design of LDPC codes with a circle length not less than 8 and 10. These steps and conditions ensure that the constructed LDPC code has a larger circle length, thereby improving the error correction performance and decoding efficiency of the code.
最后，通过本发明的设计方法，可以方便地构造出满足特定要求的LDPC码，具有广泛的应用前景。同时，该方法的实施也相对简单，便于在实际通信系统中进行应用和推广。Finally, through the design method of the present invention, an LDPC code that meets specific requirements can be easily constructed, which has a wide range of application prospects. At the same time, the implementation of the method is relatively simple, which is convenient for application and promotion in actual communication systems.
综上所述，本发明在LDPC码设计方面取得了显著的技术进步，为通信系统的性能提升和可靠性保障提供了新的解决方案。In summary, the present invention has achieved significant technical progress in LDPC code design and provided a new solution for improving the performance and ensuring the reliability of communication systems.
附图说明BRIEF DESCRIPTION OF THE DRAWINGS
图1是本发明实施例提供的Ei，Ej和Di，Dj中的环最小是8，8环的结构示意图；FIG1 is a schematic diagram of a structure in which the minimum number of rings in Ei , Ej and Di , Dj is 8, provided by an embodiment of the present invention;
图2是本发明实施例提供的两个圈长为8的LDPC码的性能图；FIG2 is a performance diagram of two LDPC codes with a circle length of 8 provided in an embodiment of the present invention;
图3是本发明实施例提供的两个圈长为10的LDPC码的性能图。FIG3 is a performance diagram of two LDPC codes with a cycle length of 10 provided by an embodiment of the present invention.
具体实施方式Detailed ways
为了使本发明的目的、技术方案及优点更加清楚明白，以下结合实施例，对本发明进行进一步详细说明。应当理解，此处所描述的具体实施例仅仅用以解释本发明，并不用于限定本发明。In order to make the purpose, technical solution and advantages of the present invention more clearly understood, the present invention is further described in detail below in conjunction with the embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not used to limit the present invention.
以下是根据上述大圈长准循环半随机LDPC码设计方法所列举的两个具体的应用实施例：The following are two specific application embodiments listed according to the above large cycle length quasi-cyclic semi-random LDPC code design method:
**实施例一：卫星通信系统****Example 1: Satellite Communication System**
在卫星通信系统中，数据的传输质量往往受到各种因素的影响，如信号衰减、干扰等。因此，采用一种高效的纠错编码技术是提高卫星通信系统性能的关键。In satellite communication systems, the quality of data transmission is often affected by various factors, such as signal attenuation, interference, etc. Therefore, adopting an efficient error correction coding technology is the key to improving the performance of satellite communication systems.
根据前述权利要求，可以设计一种大圈长准循环半随机LDPC码，并将其应用于卫星通信系统中。首先，根据卫星通信系统的要求，确定码长N、行重L和列重等参数。然后，按照所述设计方法构造校验矩阵H。在构造过程中，特别关注圈长的要求，以确保LDPC码具有良好的纠错性能。According to the above claims, a large-circle-length quasi-cyclic semi-random LDPC code can be designed and applied to a satellite communication system. First, according to the requirements of the satellite communication system, parameters such as code length N, row weight L and column weight are determined. Then, the check matrix H is constructed according to the design method. During the construction process, special attention is paid to the requirements of the circle length to ensure that the LDPC code has good error correction performance.
在卫星通信系统的发送端，将待传输的数据进行LDPC编码，形成具有纠错能力的码字。然后，通过卫星链路将编码后的数据发送至接收端。在接收端，利用相同的LDPC码进行解码，以恢复原始数据。由于LDPC码具有强大的纠错能力，即使在信号受到干扰或衰减的情况下，也能有效地恢复数据，从而提高卫星通信系统的传输质量。At the transmitting end of the satellite communication system, the data to be transmitted is LDPC encoded to form a codeword with error correction capability. The encoded data is then sent to the receiving end via a satellite link. At the receiving end, the same LDPC code is used for decoding to restore the original data. Since LDPC codes have powerful error correction capabilities, data can be effectively restored even when the signal is interfered or attenuated, thereby improving the transmission quality of the satellite communication system.
**实施例二：深空探测任务****Example 2: Deep Space Exploration Mission**
在NASA的深空探测任务中，如火星科学实验室等，数据传输的可靠性至关重要。深空环境复杂多变，通信链路极易受到各种干扰和衰减的影响。因此，采用一种高效的纠错编码技术是确保深空探测任务数据传输可靠性的关键。In NASA's deep space exploration missions, such as the Mars Science Laboratory, the reliability of data transmission is crucial. The deep space environment is complex and changeable, and communication links are extremely susceptible to various interferences and attenuation. Therefore, the use of an efficient error correction coding technology is the key to ensuring the reliability of data transmission in deep space exploration missions.
根据前述权利要求，可以设计一种适用于深空探测任务的大圈长准循环半随机LDPC码。在设计过程中，充分考虑深空环境的特殊性，选择合适的码长、行重和列重等参数。同时，特别关注圈长的要求，以确保LDPC码在深空环境下仍具有优异的纠错性能。According to the above claims, a large-circle-length quasi-cyclic semi-random LDPC code suitable for deep space exploration missions can be designed. In the design process, the particularity of the deep space environment is fully considered, and appropriate parameters such as code length, row weight and column weight are selected. At the same time, special attention is paid to the requirements of the circle length to ensure that the LDPC code still has excellent error correction performance in the deep space environment.
在深空探测任务的发送端，将重要的科学数据和其他关键信息进行LDPC编码，形成具有强大纠错能力的码字。然后，通过深空通信链路将编码后的数据发送至地面接收站或其他探测器。在接收端，利用相同的LDPC码进行解码，以恢复原始数据。通过采用这种大圈长准循环半随机LDPC码，可以有效地提高深空探测任务数据传输的可靠性，为科学研究的顺利进行提供有力保障。At the transmitting end of the deep space exploration mission, important scientific data and other key information are LDPC encoded to form codewords with strong error correction capabilities. The encoded data is then sent to ground receiving stations or other detectors via deep space communication links. At the receiving end, the same LDPC code is used for decoding to restore the original data. By adopting this large-cycle quasi-cyclic semi-random LDPC code, the reliability of data transmission in deep space exploration missions can be effectively improved, providing a strong guarantee for the smooth progress of scientific research.
这两个实施例展示了大圈长准循环半随机LDPC码在卫星通信系统和深空探测任务中的具体应用，体现了其在提高数据传输质量和可靠性方面的优势。当然，这只是两个示例，该LDPC码设计方法还可以广泛应用于其他通信和存储系统中，以提高系统的整体性能。These two embodiments demonstrate the specific application of large-cycle quasi-cyclic semi-random LDPC codes in satellite communication systems and deep space exploration missions, reflecting its advantages in improving data transmission quality and reliability. Of course, these are just two examples, and the LDPC code design method can also be widely used in other communication and storage systems to improve the overall performance of the system.
应用实施例1：通信系统中的错误校正Application Example 1: Error Correction in Communication Systems
信道编码器：集成了大圈长准循环半随机LDPC码生成系统，用于生成和编码数据以提高传输过程中的可靠性。Channel encoder: It integrates a large cycle length quasi-cyclic semi-random LDPC code generation system to generate and encode data to improve the reliability during transmission.
发射装置：将编码后的数据通过无线或有线媒介发送。Transmitter: Sends the encoded data via wireless or wired media.
接收装置：接收传输的数据，并使用LDPC码进行解码和错误校正。Receiver: Receives the transmitted data and performs decoding and error correction using LDPC codes.
解码器：集成了专门的算法，用于解码接收到的LDPC码并校正错误。Decoder: Integrates specialized algorithms to decode received LDPC codes and correct errors.
#实施步骤：#Implementation steps:
1.参数配置：用户通过用户界面模块输入通信系统的参数，如码长N和校验矩阵的稀疏度。1. Parameter configuration: The user inputs the parameters of the communication system, such as the code length N and the sparsity of the check matrix, through the user interface module.
2.LDPC码生成：系统根据输入的参数使用子矩阵D生成模块和矩阵K构造模块来生成适合通信系统需求的LDPC码。2. LDPC code generation: The system uses the sub-matrix D generation module and the matrix K construction module to generate LDPC codes suitable for the communication system requirements based on the input parameters.
3.编码数据：信道编码器使用生成的LDPC码对待发送的数据进行编码。3. Encoded data: The channel encoder uses the generated LDPC code to encode the data to be transmitted.
4.数据传输：发射装置通过选择的媒介发送编码数据。4. Data transmission: The transmitting device sends the encoded data through the selected medium.
5.接收与解码：接收装置捕获信号并传递给解码器，后者利用LDPC码的校验矩阵H进行解码和错误修正。5. Receiving and decoding: The receiving device captures the signal and passes it to the decoder, which uses the check matrix H of the LDPC code for decoding and error correction.
6.性能测试：测试模块评估传输过程中的误码率和数据完整性，以确保通信质量。6. Performance test: The test module evaluates the bit error rate and data integrity during transmission to ensure communication quality.
应用实施例2：数据存储系统中的数据完整性保护Application Example 2: Data Integrity Protection in Data Storage System
数据写入模块：在数据存储之前，使用大圈长准循环半随机LDPC码生成系统对数据进行编码。Data writing module: Before data storage, the data is encoded using a large-cycle quasi-cyclic semi-random LDPC code generation system.
存储设备：将编码后的数据存储在硬盘驱动器、固态硬盘或其他存储介质中。Storage device: Stores the encoded data on a hard drive, solid-state drive, or other storage media.
数据读取模块：从存储设备读取数据，并使用LDPC码进行错误检测和纠正。Data reading module: reads data from the storage device and uses LDPC code for error detection and correction.
监控模块：监控存储系统的健康状况，使用LDPC码检测潜在的数据损坏。Monitoring module: monitors the health of the storage system and detects potential data corruption using LDPC codes.
#实施步骤：#Implementation steps:
1.配置存储参数：用户通过用户界面模块设置数据块大小和存储设备的规格。1. Configure storage parameters: Users set the data block size and storage device specifications through the user interface module.
2.生成LDPC码：系统根据存储设备的特性生成适合的LDPC码，以保护数据完整性。2. Generate LDPC code: The system generates a suitable LDPC code based on the characteristics of the storage device to protect data integrity.
3.编码数据块：数据写入模块使用生成的LDPC码对数据块进行编码，然后写入存储设备。3. Encode data block: The data writing module encodes the data block using the generated LDPC code and then writes it to the storage device.
4.数据保护：监控模块定期检查存储数据的完整性，使用LDPC码进行错误检测。4. Data protection: The monitoring module regularly checks the integrity of stored data and uses LDPC codes for error detection.
5.数据恢复：在读取数据时，数据读取模块使用LDPC码进行错误校正，确保从存储设备中恢复的数据是完整的。5. Data recovery: When reading data, the data reading module uses LDPC code for error correction to ensure that the data recovered from the storage device is complete.
6.性能监控：存储系统的性能监控模块记录LDPC码的纠错能力和影响存储性能的相关指标。6. Performance monitoring: The performance monitoring module of the storage system records the error correction capability of the LDPC code and related indicators that affect storage performance.
本发明实施例提供一种大圈长准循环半随机LDPC码设计方法，所述LDPC码有两种构造方法：随机码和结构化码；The embodiment of the present invention provides a large-cycle quasi-cyclic semi-random LDPC code design method, wherein the LDPC code has two construction methods: a random code and a structured code;
所述结构化LDPC码具体如下：The structured LDPC code is specifically as follows:
Pi是一个循环移位矩阵，它将N*N的单位矩阵I向右循环平移i次，其中i是整数，如果i为∞，那么Pi为全零矩阵；由(1)可知，校验矩阵H可以由循环移位指数矩阵唯一刻画，方便起见，可以采用下面的指数矩阵表示校验矩阵H；Pi is a cyclic shift matrix, which cyclically shifts the N*N identity matrix I to the right i times, where i is an integer. If i is ∞, then Piis an all-zero matrix. From (1), we can see that the check matrix H can be uniquely characterized by the cyclic shift exponential matrix. For convenience, the following exponential matrix can be used to represent the check matrix H:
考虑矩阵E中长度为2l的环W，假设环W上所经过的循环参数为a0,a1,...,a2l-1，那么环W对应的移位参数可以用公式表示。Consider a ring W of length 2l in the matrix E. Assuming that the cycle parameters on the ring W are a0 , a1 , ..., a2l-1 , the shift parameters corresponding to the ring W can be expressed by the formula.
如果pW＝0，那么在矩阵H中将形成一个长度为2l的环；If pW = 0, then a ring of length 2l will be formed in the matrix H;
构建的QC-LDPC码的指数校验矩阵E的结构如下所示：The structure of the exponential check matrix E of the constructed QC-LDPC code is as follows:
Ei为2*L的子指数矩阵，其形式如下：Ei is a 2*L sub-index matrix, which has the following form:
其中S≥L。Where S≥L.
子指数矩阵D＝[D0 D1 … DS-1]有S行，L*S列，同时子指数矩阵D具有如下性质：The sub-index matrix D = [D0 D1 … DS-1 ] has S rows and L*S columns. The sub-index matrix D has the following properties:
1)子矩阵Di列重均为1，行重不大于1；1) The column weight of the submatrix Di is 1, and the row weight is no more than 1;
2)子矩阵D的行重为L，列重均为1。2) The row weight of submatrix D is L, and the column weight is 1.
圈长不小于8的LDPC码设计方法如下：The design method of LDPC code with a circle length not less than 8 is as follows:
1)N>L；1) N>L;
2)ei(i＝0,…,L-1)是小于N的随机整数，且互不相等；2) ei (i＝0,…,L-1) are random integers less than N and are not equal to each other;
3)D的构造方法如下：3) The construction method of D is as follows:
3-1)构造一个行重和列重均为L的矩阵K，显然此矩阵的行数和列数均为S；3-1) Construct a matrix K with both row weight and column weight L. Obviously, the number of rows and columns of this matrix is S;
3-2)在生成D中的每一个子矩阵Di时，取出矩阵K的第i列，显然这一列中有L个不为0的元素，记录这L个不为0的元素所在的行数到集合Ridx中；3-2) When generating each submatrixDi in D, take out the i-th column of the matrix K. Obviously, there are L non-zero elements in this column. Record the row numbers of these L non-zero elements in the setRidx ;
3-3)Di有L列S行，首先初始化Di，其所有的元素均为∞；3-3)Di has L columns and S rows. First, initializeDi so that all its elements are ∞.
3-4)从第0到第L-1列，每构造一列，首先随机的从Rinx集合中不重复的取出一个行数r，然后在该列的第r行随机生成一个小于N的整数。3-4) From the 0th to the L-1th column, each time a column is constructed, first a row number r is randomly selected from the Rinx set without duplication, and then an integer less than N is randomly generated in the rth row of the column.
经过上述三个步骤，所构造的矩阵满足公式(4)以及本发明约定的校验矩阵指数矩阵的要求，其对应的校验矩阵H的圈长不小于8。After the above three steps, the constructed matrix meets the formula (4) and the requirements of the check matrix index matrix stipulated in the present invention, and the circle length of the corresponding check matrix H is not less than 8.
证明：Ei的结构决定Ei对应的校验矩阵的圈长只能是4，8和12，在矩阵Ei中的所有4环的循环移位参数pW的值为：Proof: The structure of Ei determines that the circle length of the check matrix corresponding to Ei can only be 4, 8 and 12. The value of the cyclic shift parameter pW of all 4 circles in the matrix Ei is:
pW＝ei-ej mod N (6)pW = ei - ej mod N (6)
因为ei和ej均小于N，且ei互不相等，所以pW≠0，说明Ei对应的校验矩阵没有4环，也就是最小圈长为8。Because ei and ej are both less than N, and ei are not equal to each other, pW ≠ 0, which means that the check matrix corresponding to Ei does not have a 4-ring, that is, the minimum ring length is 8.
由于公式(4)中定义的矩阵结构要求Di的行重和列重均不大于1，因此单个Ei和Di不能构成环，Di和Dj之间也不能构成环。因此环除了存在于Ei中，还存在于Ei，Ej和Di，Dj中，很显然，根据公式(4)所规定的矩阵结构，存在于Ei，Ej和Di，Dj中的环最小是8，8环的结构如图1所示。Since the matrix structure defined in formula (4) requires that the row weight and column weight ofDi are not greater than 1, a singleEi andDi cannot form a ring, andDi andDj cannot form a ring. Therefore, in addition to existing inEi , the ring also exists inEi ,Ej andDi ,Dj . Obviously, according to the matrix structure specified by formula (4), the minimum number of rings existing inEi ,Ej andDi ,Dj is 8. The structure of 8 rings is shown in Figure 1.
圈长不小于10的LDPC码设计方法如下：The design method of LDPC code with a cycle length not less than 10 is as follows:
1)ei(i＝0,…,L-1)互不相等，且对于任意的i,j,m和n，ei-ej≠em-en；1) ei (i＝0,…,L-1) are not equal to each other, and for any i, j, m and n, ei -ej ≠ em -en ;
2)N(N>0)满足：2) N (N>0) satisfies:
2-1)对于任意的i和j,满足(ei-ej)mod N≠0；2-1) For any i and j, (ei -ej ) mod N ≠ 0;
2-2)对于任意的i,j,m和n,满足(ei-ej+em-en)mod N≠0；2-2) For any i, j, m and n, (ei -ej +em -en ) mod N ≠ 0;
3)D的构造方法如下：3) The construction method of D is as follows:
3-1)构造一个行重和列重均为L的矩阵K，其圈长为6，显然此矩阵的行数和列数相等，令其为t；3-1) Construct a matrix K with row weight and column weight both being L, and its circle length being 6. Obviously, the number of rows and columns of this matrix is equal, let it be t;
3-2)令S＝t；3-2) Let S = t;
3-3)在生成D中的每一个子矩阵Di时，取出矩阵K的第i列，显然这一列中有L个不为0的元素，记录这L个不为0的元素所在的行数到集合Ridx中；3-3) When generating each submatrixDi in D, take out the i-th column of the matrix K. Obviously, there are L non-zero elements in this column. Record the row numbers of these L non-zero elements in the setRidx ;
3-4)Di有L列S行，首先初始化Di，其所有的元素均为∞；3-4)Di has L columns and S rows. First, initializeDi so that all its elements are ∞.
3-5)从第0到第L-1列，每构造一列，首先随机的从Rinx集合中不重复的取出一个行数r，然后在该列的第r行随机生成一个小于N的整数；3-5) From the 0th to the L-1th column, each time a column is constructed, first randomly select a row number r from the Rinx set without duplication, and then randomly generate an integer less than N in the rth row of the column;
经过上述三个步骤，所构造的矩阵满足公式(4)以及本发明约定的校验矩阵指数矩阵的要求，其对应的校验矩阵H的圈长不小于10。After the above three steps, the constructed matrix meets the formula (4) and the requirements of the check matrix index matrix stipulated in the present invention, and the circle length of the corresponding check matrix H is not less than 10.
证明：Ei的结构决定Ei对应的校验矩阵的圈长只能是4，8和12，在矩阵Ei中的所有4环的循环移位参数pW的值为：Proof: The structure of Ei determines that the circle length of the check matrix corresponding to Ei can only be 4, 8 and 12. The value of the cyclic shift parameter pW of all 4 circles in the matrix Ei is:
pW＝ei-ej mod N (7)pW = ei - ej mod N (7)
在矩阵Ei中的所有8环的循环移位参数pW的值为：The value of the cyclic shift parameterpW for all 8 rings in the matrixEi is:
pW＝ei-ej+em-en mod N (8)pW = ei - ej + em -e n mod N (8)
根据2-1)和2-2)的定义，很显然pW≠0，说明Ei对应的校验矩阵没有4环和8环，也就是圈长为12。According to the definitions of 2-1) and 2-2), it is obvious that pW ≠ 0, which means that the check matrix corresponding to Ei does not have 4-ring and 8-ring, that is, the ring length is 12.
由于公式(4)中定义的矩阵结构要求Di的行重和列重均不大于1，因此单个Ei和Di不能构成环，Di和Dj之间也不能构成环。因此环除了存在于Ei中，还存在于Ei，Ej和Di，Dj中，很显然，根据公式(4)所规定的矩阵结构，存在于Ei，Ej和Di，Dj中的环最小是8，8环的结构如图1所示。Since the matrix structure defined in formula (4) requires that the row weight and column weight ofDi are not greater than 1, a singleEi andDi cannot form a ring, andDi andDj cannot form a ring. Therefore, in addition to existing inEi , the ring also exists inEi ,Ej andDi ,Dj . Obviously, according to the matrix structure specified by formula (4), the minimum number of rings existing inEi ,Ej andDi ,Dj is 8. The structure of 8 rings is shown in Figure 1.
根据构造的步骤3)，Di和Dj是由矩阵K的第i和第j列扩展得到的，因为矩阵K的圈长为6，因此第i和第j列中最多只有1行有不为0的元素，那么显然在图1中的三种形成8环的情形不存在。According to step 3) of the construction,Di andDj are obtained by expanding the i-th and j-th columns of the matrix K. Since the cycle length of the matrix K is 6, there is at most one row in the i-th and j-th columns with non-zero elements. Obviously, the three situations of forming 8 rings in Figure 1 do not exist.
综合得知，本方法构造的LDPC码的圈长为10。It is concluded that the circle length of the LDPC code constructed by this method is 10.
具体实施例：Specific embodiment:
一、圈长不小于8的LDPC码1. LDPC codes with a cycle length of no less than 8
1)取L＝3，N＝5，S＝4；1) Take L=3, N=5, S=4;
2)随机选择e0，e1和e2，为{0，1，3}；2) Randomly select e0 , e1 and e2 from {0, 1, 3};
3)D的构造方法如下：3) The construction method of D is as follows:
3-1)构造一个行重和列重均为L的矩阵K，K的行数和列数均为4；3-1) Construct a matrix K with row weight and column weight both being L, and the number of rows and columns of K being 4;
3-2)按照步骤生成D中的每一个子矩阵Di，D0～D3分别如下：3-2) Generate each sub-matrix Di in D according to the steps, D0 ~ D3 are as follows:
最终得到的校验矩阵如下所示：The final check matrix is as follows:
经验证，H矩阵行列均为60，行列重均为3，圈长为8，满足设计要求。It has been verified that the number of rows and columns of the H matrix is 60, the weight of the rows and columns is 3, and the circle length is 8, which meets the design requirements.
二、圈长不小于10的LDPC码2. LDPC codes with a circle length of no less than 10
1)L＝3，选择e0，e1和e2为{0，1，3}；1) L = 3, select e0 , e1 and e2 as {0, 1, 3};
2)选择N＝7；2) Select N=7;
3)D的构造方法如下：3) The construction method of D is as follows:
3-1)构造一个行重和列重均为L的矩阵K，其圈长为6，K的行数和列数相等，t＝7；3-1) Construct a matrix K with row weight and column weight both being L, with a circle length of 6, and the number of rows and columns of K being equal, t=7;
3-2)令S＝7；3-2) Let S = 7;
3-3)按照步骤生成D中的每一个子矩阵Di，D0～D6分别如下：3-3) Generate each sub-matrix Di in D according to the steps, D0 ~ D6 are as follows:
最终得到的校验矩阵如下所示：The final check matrix is as follows:
经验证，H矩阵行列均为147，行列重均为3，实际圈长为12，满足设计要求。It has been verified that the number of rows and columns of the H matrix is 147, the weight of the rows and columns is 3, and the actual circle length is 12, which meets the design requirements.
应当注意，本发明的实施方式可以通过硬件、软件或者软件和硬件的结合来实现。硬件部分可以利用专用逻辑来实现；软件部分可以存储在存储器中，由适当的指令执行系统，例如微处理器或者专用设计硬件来执行。本领域的普通技术人员可以理解上述的设备和方法可以使用计算机可执行指令和/或包含在处理器控制代码中来实现，例如在诸如磁盘、CD或DVD-ROM的载体介质、诸如只读存储器(固件)的可编程的存储器或者诸如光学或电子信号载体的数据载体上提供了这样的代码。本发明的设备及其模块可以由诸如超大规模集成电路或门阵列、诸如逻辑芯片、晶体管等的半导体、或者诸如现场可编程门阵列、可编程逻辑设备等的可编程硬件设备的硬件电路实现，也可以用由各种类型的处理器执行的软件实现，也可以由上述硬件电路和软件的结合例如固件来实现。It should be noted that the embodiments of the present invention can be implemented by hardware, software, or a combination of software and hardware. The hardware part can be implemented using dedicated logic; the software part can be stored in a memory and executed by an appropriate instruction execution system, such as a microprocessor or dedicated design hardware. It can be understood by a person of ordinary skill in the art that the above-mentioned devices and methods can be implemented using computer executable instructions and/or contained in a processor control code, such as a carrier medium such as a disk, CD or DVD-ROM, a programmable memory such as a read-only memory (firmware), or a data carrier such as an optical or electronic signal carrier. Such code is provided on the carrier medium. The device and its modules of the present invention can be implemented by hardware circuits such as very large-scale integrated circuits or gate arrays, semiconductors such as logic chips, transistors, etc., or programmable hardware devices such as field programmable gate arrays, programmable logic devices, etc., can also be implemented by software executed by various types of processors, and can also be implemented by a combination of the above-mentioned hardware circuits and software, such as firmware.
采用上述方法，构造了两个圈长为8的LDPC码，一个行重和列重分别是3和4，长度为80，一个行重和列重分别是3和5，长度为175，对所生成的两个码在加性高斯白噪声信道上仿真，采用标准的BP算法进行译码，最大迭代次数为100，其性能图2所示。Using the above method, two LDPC codes with a cycle length of 8 are constructed, one with a row weight and a column weight of 3 and 4 respectively, and a length of 80, and the other with a row weight and a column weight of 3 and 5 respectively, and a length of 175. The two generated codes are simulated on an additive white Gaussian noise channel and decoded using the standard BP algorithm with a maximum number of iterations of 100. The performance is shown in Figure 2.
采用上述方法，构造了两个圈长为10的LDPC码，一个行重和列重分别是3和4，长度为1200，一个行重和列重分别是3和5，长度为2205，对所生成的两个码在加性高斯白噪声信道上仿真，采用标准的BP算法进行译码，最大迭代次数为100，其性能图3所示。从仿真结果可以看出，所构造的码具有良好的纠错性能。Using the above method, two LDPC codes with a cycle length of 10 are constructed, one with a row weight and a column weight of 3 and 4, and a length of 1200, and one with a row weight and a column weight of 3 and 5, and a length of 2205. The two codes generated are simulated on an additive white Gaussian noise channel and decoded using a standard BP algorithm with a maximum number of iterations of 100. The performance is shown in Figure 3. From the simulation results, it can be seen that the constructed code has good error correction performance.
以上所述，仅为本发明的具体实施方式，但本发明的保护范围并不局限于此，任何熟悉本技术领域的技术人员在本发明揭露的技术范围内，凡在本发明的精神和原则之内所作的任何修改、等同替换和改进等，都应涵盖在本发明的保护范围之内。The above description is only a specific implementation mode of the present invention, but the protection scope of the present invention is not limited thereto. Any modifications, equivalent substitutions and improvements made by any technician familiar with the technical field within the technical scope disclosed by the present invention and within the spirit and principle of the present invention should be covered by the protection scope of the present invention.
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