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A non-binary ldpc code optimization method based on progressive string edge growth
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An LDPC code, non-binary technology, applied in the field of digital communication coding, can solve the problem of high algorithm complexity and achieve the effect of low complexity
Active Publication Date: 2021-08-13
TIANJIN UNIV
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However, this method needs to continuously expand the tree to determine the local girth and calculate the upper limit of the minimum distance, and the algorithm complexity is very high
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[0054] The embodiment of the present invention provides a method of optimizing a non-two-input LDPC code. figure 1 For the present invention, the present invention is based on the overall schematic of a non-binary LDPC code for the progressive string, which is considered to increase a string e-in-one in the Hami ring. jJ = 1, 2, ..., K form the process of the Hamilton ring. For each additional string e j , the submaps after j = 1, 2, ..., k, search with a tree-based method, including new string e j , J = 1, 2, ..., K ring, and get a ring collection A j , J = 1, 2, ..., K; further, from binary map binary image with a good minimum distance of non-zero elements, randomly select the non-zero element of the Hamilton ring, and set A according to the ring collection j , the full rank conditions of the ring in J = 1, 2, ..., and K, determine the non-zero element of each new string in a manner that grows in progressive string.
[0055] figure 2 The integral flow of the non-binary LDPC cod...
specific Embodiment
[0079]The embodiment of the present invention is as an example of a Hamiltonia, which is composed of 26 vertices, 26 strings, and the configuration is defined at the GF (64) to be 312 bits, and the code rate is 1 / 2 non-binary LDPC code. The selected base map is 12, and the maximum ring length is 16, considering the maximum number of candidate configurations corresponding to each string. max Unconstrained and T max = 24 two cases, the number of candidate configurations corresponding to each string is not bound, that is, "PCEG", will constrain T max = 24 The situation is recorded as a simplified version of PCEG, "S-PCEG", the following combination Figure 5 to 8 Detailed description.
[0080] First, search for the rings corresponding to each string of the progressive string, resulting in the corresponding ring collection. Add J, J = 1, 2, ..., 26 strings to the Hamilton ring to get the sub-map G j , J = 1, 2, ..., 26. The root node corresponding to the top of the row, use the tree-ba...
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Abstract
The invention discloses a non-binary LDPC code optimization method based on progressive chord edge growth, including: according to the obtained ring set A related to each chord edge j , and the nonzero elements on the determined Hamiltonian ring, all chord edges e j Added to the Hamiltonian ring in turn, and the chord edge e is determined based on the full rank condition of the ring j After determining the non-zero elements of all chord edges, one is randomly selected from all non-zero element configurations that meet the conditions, and the optimized non-binary LDPC code is obtained by using the mapping relationship between the Hamiltonian graph and the parity check matrix check matrix. The invention constructs the non-binary LDPC code with low error floor in the way of progressive chord growth, and has lower complexity.
Description
Technical field [0001] The present invention relates to the field of digital communication coding, and more particularly to a non-two-binary LDPC code optimization method based on the growth of progressive string. Background technique [0002] The Low-Density Parity-Check, LDPC code is a performance-effective error correction code for the Low-Density Parity-Check (LDPC) code proposed by Gallager. When the code length is approaching infinity, the performance of the LDPC code is close to the limits of incense. M. C. Davey and D. Mackay introduce non-binary LDPC code, replacing the "1" element in the two-way LDPC code to the non-zero element in a limited domain, thereby expanding the binary LDPC code to a limited domain. The work of Davey and Mackay also proves that the performance of non-binary LDPC code is superior to binary LDPC code in some cases. In addition, non-binary LDPC can seamlessly bind to high-order modulation techniques, and have potential to be used in multi-input mu...
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