CN111464191A - RC-L DPC code construction method based on matrix expansion and Fibonacci sequence - Google Patents
RC-L DPC code construction method based on matrix expansion and Fibonacci sequence Download PDFInfo
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Abstract
The invention relates to a RC-L DPC code construction method based on matrix expansion and Fibonacci number sequence, which obtains a group of RC-L DPC codes with the same information bit length and different code rates by expanding check bits on the basis of a mother code matrix, wherein a shifting matrix of the mother code matrix and an expanding matrix is constructed by utilizing the Fibonacci number sequence with special properties, and a final check matrix is obtained after the shifting matrix is combined with a sparse matrix‑6Compared with other L DPC code patterns with the same code length code rate, the net coding gain of the constructed F-RC-L DPC code is improved to a certain extent, so that the scheme has practical application value in a communication system.
Description
Technical Field
The invention belongs to the field of signal processing, and relates to a construction method of L DPC code in channel coding, which mainly carries out low computation complexity RC-L DPC code construction based on matrix expansion and Fibonacci Sequence (FS).
Background
The design of a communication system aims to ensure that information can be transmitted effectively and reliably, but noise and other interference exist in the transmission process, a channel coding technology improves the error correction and detection capability of a code word by adding redundant information, and is a crucial ring in the communication system, a low-Density Parity-Check (L ow-Density Parity-Parity Check, L DPC) code is a channel coding technology, is a linear block code with a sparse Check matrix, is easy to carry out theoretical analysis and research, has flexible structure, very close performance to Shannon limit, is simple to decode, is suitable for hardware realization, and is considered as the code with the best error correction performance so far.
L DPC code construction method is roughly divided into random construction and structured construction, although L DPC code of random construction has good error correction performance and code length code rate can be flexibly selected, because its check matrix and generating matrix have no definite form, the encoding and decoding complexity is extremely high, the hardware is difficult to realize, it is not suitable for the communication system of practical application, especially the satellite communication system with limited hardware resources.
The invention provides a low-computation-complexity RC-L DPC code construction scheme based on matrix expansion and a Fibonacci sequence0And an extended square matrix HextThe cyclic shift coefficient matrix is circularly expanded to obtain two check matrixes, and finally the check matrixes are combined with a sparse matrix H formed by combining an identity matrix and a zero matrixsAnd combining the zero bits to obtain a final check matrix. The scheme isThe simulation result shows that the error correction performance of the F-RC-L DPC constructed by the scheme is superior to that of a PEG-L DPC (3510,2340) code and a document [1 ] which are constructed by a same code length and code rate and utilize a Progressive Edge Growth (PEG) algorithm]'Yuan Jian Guo, Zheng De Chong and Tao hong' a method for constructing multi-code rate original model diagram QC-L DPC code by using large derivation sequence [ J]P-DY-QC-L DPC (3510,2340) code of 2018,197(3), 88-92 ″, and document [2 ]]' Huangsheng, Pangxiao, Jia Xue Ting, etc. Lucas number series-based large girth QC-L DPC code construction method [ J]Code L S-QC-L DPC (4680,2340) in the university of electronic technology, 2016,45(2):174-]“Zhang Y,Yang F F.The performance analysis of QC-LDPCcodes constructed by Dayan sequence for coded cooperative relay[C]DY-QC-L DPC (4680,2340) code in I EEE computers, Communications and IT Applications Conf,2014:84-88.
Disclosure of Invention
In view of the above, the present invention provides a low complexity RC-L DPC code construction method based on matrix expansion and fibonacci number sequence (FS) by which a mother code matrix and a shift matrix of an expanded square matrix are designed to obtain two module matrices0And PextThe middle cyclic shift coefficient is described by a simple algebraic expression, and 4 loops can be completely eliminated without computer search, so that the algorithm complexity is reduced. The scheme not only has simple structure, but also can adjust the code length and the code rate of the code word by setting corresponding parameters. Therefore, the scheme can meet the requirements of the communication system on good error correction performance and low computational complexity.
In order to achieve the purpose, the invention provides the following technical scheme:
the RC-L DPC code check matrix structure based on matrix expansion is divided into four parts:
the upper left corner is a high code rate matrix Hi-1，H0Is M0×N0The matrix of the mother code of (a),the upper right corner is filled with zero bits to maintain the characteristics of the mother code, and the lower left corner is a sparse matrix HsThe lower right corner is an M × M expanded square matrix Hext. The configurable code rate is Ri＝(N0-M0)/(N0+ i × M) where i ═ 0,1,2,3, …, H0And HextUsing a Fibonacci series construction, HsThe method is obtained by combining an identity matrix and a zero matrix.
1. Constructing a mother code matrix H0And an extended square matrix HextConstructing its shift matrix P from a Fibonacci sequence0And PextConstructing a mother code matrix H using a Fibonacci sequence F (n)0And an extended square matrix HextOf the shift matrix, matrix P0The first row element is 0, the remaining ith row and jth column elements can be represented as F (2i + j) + j, and the matrix PextThe elements in row i and column j can be denoted as F (i +2j), so that the matrix constructed is incremental in each row and column element, ensuring that no 4-loops are present. The matrix H can be obtained by replacing corresponding elements with a zero matrix, an identity matrix and a cyclic permutation matrix0And Hext。
2. Constructing a sparse matrix Hs。HsHas a fixed structure and is obtained by transversely combining two unit matrixes with the number of rows M and a zero matrix, wherein when the unit matrixes are expanded for the first time, the two unit matrixes are arranged at the head side by side, and when the unit matrixes are expanded for the second time and later, the interval N between the two unit matrixes is0The 3M presents a diagonal arrangement, the remaining positions being supplemented with a zero matrix.
3. Is constructed well H0、HextAnd HsAnd then, combining according to formats of upper left, lower right and lower left, filling zero bits at the upper right, and finally obtaining the check matrix of the RC-L DPC.
Finally, under the same simulation environment, the code pattern construction scheme provided by the patent is compared and analyzed with other code pattern construction schemes in a simulation mode.
The invention has the beneficial effects that a low-computation-complexity RC-L DPC code construction scheme based on matrix expansion and Fibonacci sequence is provided, the RC-L DPC code check matrix structure is divided into four parts, and a mother code matrix H0Extended matrix HextSparse matrix HsAnd zero bits, in the method, a Fibonacci sequence with special properties is fully utilized to construct a cyclic shift coefficient matrix, the formation of 4 rings is successfully avoided, and H with the girth of 6 is constructed0And HextAnd constructing a sparse matrix H by combining the identity matrix and the zero matrixsAnd the sparse matrix is in dislocation arrangement and has a fixed structure skillfully avoiding four rings, and finally the sparse matrix is combined to obtain an RC-L DPC code check matrix with the girth of 60And an extended square matrix HextIn terms of error correction performance, the final constructed RC-L DPC has a girth of 6 by skillfully designing a shift matrix and arranging the identity matrixes, can quickly converge during decoding and shows good error correction performance, and under the same simulation environment, the error correction performance of the F-RC-L DPC constructed based on matrix expansion and a Fibona series is superior to that of a PEG-L DPC (3510,2340) constructed by a progressive edge growth algorithm with the same code length code rate, a multi-code rate P-DY-QC-L (3510,2340) constructed by a large derivative series and a primitive modulus graph, a DY-QC-L (QC 734) constructed by directly utilizing the large derivative series, and a DPC-829-QC-734 (QC 734) constructed by directly utilizing the large derivative series, and a DPC-QC-464 (DPC-QC-XC-483) code constructed by utilizing a DPC series and a DPC-MCK series have the advantages of being better than that the other DPC-L DPC-QC-L (QC-ZC) code constructed by matrix expansion and DPC-465, and DPC series, and the DPC-XC-387 series can provide the advantages of the same simple linear code structure and the invention which have the advantages of the storage system and the storage system of the storage system and the storage of the simple linear code structure, and the invention, and.
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In order to make the object, technical scheme and beneficial effect of the invention more clear, the invention provides the following drawings for explanation:
FIG. 1 is a technical roadmap for the process of the invention;
FIG. 2 is a check matrix diagram
FIG. 3 is a simulation analysis diagram of F-RC-L DPC codes with code rate set {2/3,3/5,6/11,1/2,6/13} constructed based on the present invention.
FIG. 4 is a graph showing the comparison of the performance simulation of the F-RC-L DPC (3510,2340) code with the code rate of 0.67 constructed based on the present invention and other codes.
FIG. 5 is a graph showing the comparison of the performance simulation of the F-RC-L DPC (4680,2340) code with the code rate of 0.5 constructed based on the present invention and other codes.
Detailed Description
Preferred embodiments of the present invention will be described in detail below with reference to the accompanying drawings.
1. Referring to the description of the attached FIG. 1, the RC-L DPC code check matrix structure form H based on matrix expansioniCan be expressed as:
the RC-L DPC code is divided into four parts, H on the right side of the equationi-1Check matrix obtained for last expansion, H0Then represents the mother code matrix with size M0×N0In order to maintain the characteristics of the mother code, the upper right part of the matrix is zero, the length of the information bit is kept unchanged, M rows and M columns are added to the mother code every time the mother code is expanded, and H is usedsIs a sparse matrix added in each expansion, in which at least one check information is ensured in each row so as to establish the dependency relationship between the mother code and the new check bit, HextIs an extended square matrix with the size of M × M.
2. With reference to the attached figure 1, H is given according to formula (1)0And HextThe construction method of (2):
a fibonacci number sequence is a sequence of integers, each number being defined as the sum of the first two terms, the first two fibonacci numbers being F (0) ═ 1 and F (1) ═ 1. So the fibonacci number series can be expressed as follows:
constructing a shift matrix P using a Fibonacci sequence F (n)0And PextThe constructed matrix is expressed by formula (3) and formula (4).
Wherein, the matrix P0Is 0, and the remaining elements in the ith row and jth column can be represented as F (2i + j) + j, matrix PextThe element at row i and column j can be represented as F (i +2j), thus constructed P0And PextEach row and column element in (a) is an incremental sequence. After obtaining the shift matrix, it is extended, p0And pextFor expanding the factor, in order to ensure that no 4-ring exists in the expanded check matrix, p needs to be set0≥F(2i+j)+j，pext≧ F (i +2j), and then the shift matrix P0Wherein the zero element is p0×p0Replacement of the identity matrix of (1), non-zero elements with p0×p0The identity matrix of (A) is circularly shifted to the right by a cyclic permutation matrix of the corresponding number of bits, and P is similarly shiftedextWherein the zero element is pext×pextReplacement of the identity matrix of (1), non-zero elements with pext×pextThe identity matrix of (a) is circularly shifted to the right by a cyclic permutation matrix replacement of the corresponding number of bits.
3. Constructing a sparse matrix H is described with reference to FIG. 2s。HsThe method is characterized in that M rows exist, two M × M unit matrixes are specially arranged, the rest positions are supplemented by zero elements, the two unit matrixes are arranged side by side during first expansion, the two unit matrixes in the second and later stages have the same interval and are arranged in an oblique diagonal line mode, except that the two parallel unit matrixes in the first expansion may generate four rings together with a mother code, the rest arrangement mode can skillfully avoid the generation of four rings, and the mother code matrix is designed to eliminate all four rings.
Combining the constructed mother code matrix, the expanded square matrix, the sparse matrix and the zero bit according to a mode of a formula (1) to obtain a final RC-L DPC code check matrix, wherein a high code rate part is nested in a low code rate part, and after the ith expansion, the code rate R of a code wordiCan be expressed as follows:
4. with reference to fig. 3, fig. 4, and fig. 5, in order to verify that the RC-L DPC code construction scheme proposed by the present patent has excellent error correction performance, Matlab simulation analysis is performed, where the simulation environment is an Additive White Gaussian Noise (AWGN) channel, Binary Phase Shift Keying (BPSK) modulation and Belief Propagation (BP) decoding algorithm are used, and the maximum number of iterations is 50.
Example 1: constructing (3,9) a shift matrix P according to the proposed construction method0As shown in formula (6):
get p0And (2) replacing zero elements by using a unit matrix of 390 × 390, replacing non-zero elements by using a cyclic permutation matrix of 390 × 390 with right-shifted corresponding bit number to obtain a mother code with the information bit length of 2340, the code length of 3510 and the code rate of 2/3, then performing matrix expansion, and taking M as 390 to obtain the F-RC-L DPC with the code rate set of {2/3,3/5,6/11,1/2 and 6/13 }.
In order to verify the code word performance of a single code rate of the F-RC-L DPC, the F-RC-L DPC with the code rate of 0.67 and the same code length and the same code rate are constructed by utilizing a progressive edge growth algorithm under the same condition to obtain a PEG-L DPC (3510,2340) code and documents [1 ] 1]Middle utilizing large derivative array and original pattern structureCompared with the multi-code-rate P-DY-QC-L DPC (3510,2340) code in a simulation mode, the F-RC-L DPC code constructed in the method has better waterfall area performance, and when the error rate is 10-6Compared with PEG-L DPC (3510,2340) code constructed by random construction method, net coding gain is improved by about 0.03dB, compared with multi-code rate P-DY-QC-L DPC (3510,2340) code constructed by large derivative array and original pattern diagram, net coding gain is improved by about 0.29dB, F-RC-L DPC code with code rate of 0.5 and document [2 ] with same code length and same code rate under same condition]Large girth L S-QC-L DPC (4680,2340) code constructed by using Lucas number series and document [3]In the method, DY-QC-L DPC (4680,2340) codes with a large derivative sequence structure are directly utilized for simulation comparison, and the error rate is 10-6Compared with a large girth L S-QC-L DPC (4680,2340) code constructed by using the Lucas number sequence, the net coding gain is improved by about 1.73dB, and compared with a DY-QC-L DPC (4680,2340) code constructed by directly using the large derivative sequence, the net coding gain is improved by about 0.29 dB.
Finally, it is noted that the above-mentioned preferred embodiments illustrate rather than limit the invention, and that, although the invention has been described in detail with reference to the above-mentioned preferred embodiments, it will be understood by those skilled in the art that various changes in form and detail may be made therein without departing from the scope of the invention as defined by the appended claims.
Claims (3)
1. The invention relates to an RC-L DPC code construction method based on matrix expansion and Fibonacci number sequence, which is characterized in that aiming at the problems that the RC-L DPC code constructed by adopting a random construction method has high coding and decoding complexity and difficult hardware realization, a class of RC-L DPC codes with quasi-cyclic characteristic are constructed by matrix expansion, the same number of rows and columns are added in each expansion, a code word structure is divided into an upper part, a lower part, a left part and a right part, and the upper left part is a mother code matrix H0Zero bit at the top right and sparse matrix H at the bottom leftsThe lower right is an extended square matrix Hext. Designing a shift matrix P based on a Fibonacci sequence0And PextEnsuring no four rings, and obtaining a matrix H after expansion0And HextUsing two identity matrices of equal number of rows andand combining the three constructed matrixes and the zero elements according to an upper, lower, left and right format to finally obtain the check matrix of the RC-L DPC code.
2. The method for constructing the RC-L DPC code based on the matrix expansion and the Fibonacci sequence according to claim 1, wherein the matrix size of the mother code is not fixed, and H can be flexibly selected0The matrix expansion can obtain a series of L DPC codes from high code rate to low code rate, and the expansion square matrix HextM × M, the value of M determining the code rate interval of RC-L DPC code, constructing a mother code matrix H using a fibonacci number sequence f (n)0And an extended square matrix HextIs shifted matrix P0And PextThe matrix P0The first row element is 0, the remaining ith row and jth column elements can be represented as F (2i + j) + j, and the matrix PextThe elements in the ith row and the jth column can be expressed as F (i +2j), so that the elements in each row and each column of the constructed matrix are increased progressively to ensure that 4 loops do not appear, the sparse matrix is composed of an identity matrix and a zero matrix, and the check matrix obtained by carefully designing the mother code matrix and combining the three does not have 4 loops.
3. The method of claim 2, wherein H is H, and the method is characterized in that the RC-L DPC code construction method is based on matrix expansion and Fibonacci number sequence0And HextAll are obtained by designing a shift matrix by utilizing a Fibonacci sequence and expanding by using a zero matrix, an identity matrix and a cyclic permutation matrix, and a sparse matrix HsThe check matrix is obtained by combining the zero matrix and the unit matrix, and the finally obtained check matrix has quasi-cyclic characteristics and extremely low encoding and decoding complexity.
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