CN111900997A - Space coupling LDPC code sliding window decoding optimization algorithm and system - Google Patents

Space coupling LDPC code sliding window decoding optimization algorithm and system Download PDF

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CN111900997A
CN111900997A CN202010781291.8A CN202010781291A CN111900997A CN 111900997 A CN111900997 A CN 111900997A CN 202010781291 A CN202010781291 A CN 202010781291A CN 111900997 A CN111900997 A CN 111900997A
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周林
张娅妹
陈辰
陈启望
傅玉青
贺玉成
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Huaqiao University
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    • H03—ELECTRONIC CIRCUITRY
    • H03M—CODING; DECODING; CODE CONVERSION IN GENERAL
    • H03M13/00—Coding, decoding or code conversion, for error detection or error correction; Coding theory basic assumptions; Coding bounds; Error probability evaluation methods; Channel models; Simulation or testing of codes
    • H03M13/03—Error detection or forward error correction by redundancy in data representation, i.e. code words containing more digits than the source words
    • H03M13/05—Error detection or forward error correction by redundancy in data representation, i.e. code words containing more digits than the source words using block codes, i.e. a predetermined number of check bits joined to a predetermined number of information bits
    • H03M13/11—Error detection or forward error correction by redundancy in data representation, i.e. code words containing more digits than the source words using block codes, i.e. a predetermined number of check bits joined to a predetermined number of information bits using multiple parity bits
    • H03M13/1102—Codes on graphs and decoding on graphs, e.g. low-density parity check [LDPC] codes
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Abstract

The invention discloses a sliding window decoding optimization algorithm and a system of a space coupling LDPC code. The method comprises the following steps: s1: determining the size of a window according to the degree distribution, the coupling width w, the coupling length L and the expansion factor M of the SC-LDPC code; s2: determining the number of variable nodes and check nodes contained in the window; s3: defining the leftmost original model graph in the window as a target symbol, and executing a belief propagation decoding algorithm on the target symbol in the window; s4: carrying out iterative decoding on the target symbol in the window according to the maximum iterative decoding times, and expanding the size of the window according to the average received signal-to-noise ratio of the current window; s5: and after the iterative decoding of the current target symbol is finished, sliding the current window to the next position, decoding the next target symbol, recovering the window size to the initial size, and repeating the steps until the decoding of all the target symbols is finished. The invention can improve the decoding performance of the SC-LDPC code WD in the Rayleigh fading channel.

Description

Space coupling LDPC code sliding window decoding optimization algorithm and system
Technical Field
The invention relates to the technical field of communication, in particular to a sliding window decoding optimization algorithm and a system of a space coupling LDPC code.
Background
When the SC-LDPC code is decoded by adopting belief-propagation (BP) decoding algorithm, decoding can be started only after the whole code word is received. Therefore, in practical cases, BP decoding may cause higher delay when the code length of the SC-LDPC code is large. To solve this problem, an iterative decoding scheme of a sliding window structure is proposed. The SC-LDPC code is a kind of convolutional LDPC code (LDPC-CC). Therefore, the parity check matrix of the LDPC convolutional code is similar to the parity check matrix structure of the LDPC convolutional code and presents a diagonal band structure with non-zero terms. This structure makes it possible to run BP decoding within a window of W dimension, and an iterative decoding scheme of this sliding window structure is called sliding Window Decoding (WD). WD performs BP decoding within a window using a partial Tanner graph of the codeword after receiving a portion of the entire codeword. The decoding window is slid along diagonal bands of the parity check matrix to estimate codewords group by group with a lower decoding delay. The new method keeps the advantages of the BP decoding algorithm in performance, and effectively reduces the decoding delay, the decoding complexity and the requirement on a memory. Fig. 5 shows that the decoding window of WD slides along the diagonal band of the parity check matrix, and fig. 6 shows that the decoding window of WD slides along the original pattern of the spatially coupled LDPC code.
WD limits BP decoding to a window in the W dimension, and while WD reduces its decoding latency and decoding complexity, it loses its decoding performance.
Disclosure of Invention
The invention aims to provide a space coupling LDPC code sliding window decoding optimization algorithm and a system, which can reduce the decoding performance loss in the SC-LDPC code WD decoding algorithm in a Rayleigh fading channel and improve the decoding performance of the SC-LDPC code WD in the Rayleigh fading channel.
In order to achieve the purpose, the invention provides the following scheme:
a sliding window decoding optimization algorithm of a spatial coupling LDPC code comprises the following steps:
s1: determining the size of a window according to the degree distribution, the coupling width, the coupling length and the expansion factor of the SC-LDPC code;
s2: determining the number of variable nodes and check nodes contained in the window;
s3: defining a leftmost original model graph in the window as a target symbol, and executing a belief propagation decoding algorithm on the target symbol in the window;
s4: carrying out iterative decoding on the target symbol in the window according to the maximum iterative decoding times, and expanding the size of the window according to the average received signal-to-noise ratio of the current window;
s5: and after the iterative decoding of the current target symbol is finished, sliding the current window to the next position, decoding the next target symbol, recovering the window size to the initial size, and repeating the steps S3-S5 until the decoding of all the target symbols is finished.
Optionally, the SC-LDPC code is constructed based on an original graph, and the (J, K, L) SC-LDPC codes are obtained by coupling the regular LDPC codes distributed by L degrees as (J, K) by using an "edge spreading" method on the basis of the original graph of the regular LDPC code.
Optionally, the coupling width w represents that the variable node of the original model graph is connected with the check nodes of w adjacent original model graphs; the coupling length L represents that the SC-LDPC code is generated by constructing L regular LDPC code protographs, and the expansion factor is that one node of the M regular LDPC code protograph corresponds to a set of M nodes in the Tanner graph.
Optionally, the step S2 specifically includes:
let a be gcd (J, K), a represents the greatest common divisor of J and K, and if positive integers J 'and K' respectively satisfy J being aJ ', K being aK', and gcd (J ', K') being 1, then there are K 'W variable nodes and J' W check nodes in the window W.
Optionally, the step S4 specifically includes:
step S41: iteratively decoding a target symbol within the window;
step S42: judging whether the iterative decoding times are equal to the maximum iterative decoding times or not, if so, entering the step S43; if not, go to step S41;
step S43: calculating the average received signal-to-noise ratio of the target symbol in the window, judging whether the average received signal-to-noise ratio is smaller than a threshold value, if so, adding 1 to the size of the window, and entering a step S3; if not, the process proceeds to step S5.
Optionally, the calculation formula of the threshold θ is as follows:
Figure BDA0002620318300000031
Figure BDA0002620318300000032
wherein, WfIndicates the initial size of the window, WincIndicates the size of the current window, WmaxRepresents the maximum value of the window, Winc＝Wmax-Wf；wsRepresenting a variable window size;
Figure BDA0002620318300000033
indicating that the t-th window has a window size wsAverage received signal-to-noise ratio of time, ajRepresents the fading coefficient of the jth information bit in the current window, Es＝S/B，EsRepresenting signal power, S is the fixed transmit power of the transmitting end, B is the channel bandwidth, N0And/2 is the power spectral density of Gaussian white noise.
The invention also provides a space coupling LDPC code sliding window decoding optimization system, which comprises:
the window size determining module is used for determining the size of a window according to the degree distribution, the coupling width w, the coupling length L and the expansion factor M of the SC-LDPC code;
the node number determining module is used for determining the number of variable nodes and check nodes contained in the window;
the execution module is used for defining the leftmost original model graph in the window as a target symbol and executing a belief propagation decoding algorithm on the target symbol in the window;
the iterative decoding module is used for carrying out iterative decoding on the target symbol in the window according to the maximum iterative decoding times and expanding the size of the window according to the average receiving signal-to-noise ratio of the current window;
and the sliding module is used for sliding the current window to the next position after the iterative decoding of the current target symbol is finished, and decoding the next target symbol.
According to the specific embodiment provided by the invention, the invention discloses the following technical effects:
by setting the window, performing iterative belief propagation decoding on the target symbol in the window, and expanding the size of the window according to the threshold and the average received signal-to-noise ratio, decoding does not need to be started after a complete code word is received, so that the decoding performance loss in the SC-LDPC code WD decoding algorithm in the Rayleigh fading channel is reduced, and the decoding performance of the SC-LDPC code WD in the Rayleigh fading channel is improved.
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In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings needed to be used in the embodiments will be briefly described below, and it is obvious that the drawings in the following description are only some embodiments of the present invention, and it is obvious for those skilled in the art to obtain other drawings without inventive exercise.
FIG. 1 is a flowchart of a sliding window decoding optimization algorithm of a space coupling LDPC code according to an embodiment of the present invention;
FIG. 2 is a process for constructing a spatially coupled LDPC code according to an embodiment of the present invention;
FIG. 3 is a diagram illustrating a window size expansion according to an embodiment of the present invention;
FIG. 4 is a simulation of the present invention and conventional sliding window decoding;
FIG. 5 is a diagram of conventional sliding window decoding sliding along diagonal bands of a parity check matrix;
FIG. 6 is a schematic diagram of a decoding window sliding along an original pattern of a spatially coupled LDPC code in a conventional sliding window decoding;
FIG. 7 is a block diagram of a sliding window decoding optimization system of a spatially-coupled LDPC code according to an embodiment of the present invention.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
The invention aims to provide a space coupling LDPC code sliding window decoding optimization algorithm and a system, which can reduce the decoding performance loss in the SC-LDPC code WD decoding algorithm in a Rayleigh fading channel and improve the decoding performance of the SC-LDPC code WD in the Rayleigh fading channel.
In order to make the aforementioned objects, features and advantages of the present invention comprehensible, embodiments accompanied with figures are described in further detail below.
As shown in fig. 1, a sliding window decoding optimization algorithm for spatially coupled LDPC codes includes:
s1: and determining the window size according to the degree distribution, the coupling width w, the coupling length L and the expansion factor M of the SC-LDPC code.
As shown in fig. 2, the SC-LDPC code is constructed based on an original graph, and the (J, K, L) SC-LDPC code is obtained by coupling the regular LDPC codes with L degree distributions (J, K) by using an "edge spreading" method on the basis of the original graph of the regular LDPC code.
The coupling width w represents that the variable nodes of the original model graphs are connected with the check nodes of the adjacent w original model graphs; the coupling length L represents that the SC-LDPC code is generated by constructing L regular LDPC code protographs, and the expansion factor is that one node of the M regular LDPC code protograph corresponds to a set of M nodes in the Tanner graph.
S2: and determining the number of variable nodes and check nodes contained in the window.
Let a be gcd (J, K), a represents the greatest common divisor of J and K, and if positive integers J 'and K' respectively satisfy J being aJ ', K being aK', and gcd (J ', K') being 1, then there are K 'W variable nodes and J' W check nodes in the window W.
S3: defining a leftmost master pattern within the window as a target symbol, and performing a belief propagation coding algorithm on the target symbol within the window.
S4: and carrying out iterative decoding on the target symbol in the window according to the maximum iterative decoding times, and expanding the size of the window according to the average received signal-to-noise ratio of the current window. As shown in fig. 3.
The method specifically comprises the following steps:
step S41: iteratively decoding a target symbol within the window;
step S42: judging whether the iterative decoding times are equal to the maximum iterative decoding times or not, if so, entering the step S43; if not, go to step S41;
step S43: calculating the average received signal-to-noise ratio of the target symbol in the window, judging whether the average received signal-to-noise ratio is smaller than a threshold value, if so, adding 1 to the size of the window, and entering a step S3; if not, the process proceeds to step S5.
The calculation formula of the threshold value theta is as follows:
Figure BDA0002620318300000061
Figure BDA0002620318300000062
wherein, WfIndicates the initial size of the window, WincIndicates the size of the current window, WmaxRepresents the maximum value of the window, Winc＝Wmax-Wf；wsRepresenting a variable window size, having a value of Wf,Wf+1,...,Wmax；
Figure BDA0002620318300000063
Indicating that the t-th window has a window size wsAverage received signal-to-noise ratio of time, ajRepresents the fading coefficient of the jth information bit in the current window, Es＝S/B，EsRepresenting signal power, S is the fixed transmit power of the transmitting end, B is the channel bandwidth, N0And/2 is the power spectral density of Gaussian white noise.
S5: after the iterative decoding of the current target symbol is completed, the current window is slid to the next position (as shown in fig. 6), and the decoding of the next target symbol is performed until the decoding of all target symbols is completed.
The specific embodiment is as follows:
step 1, decoding an SC-LDPC code having a codeword selection degree distribution of (3,6), where the coupling width w is 2, the coupling length L is 10, and the known degree distribution is (3,6), then a is gcd (3,6) is 3, where J 'satisfying the condition is 1, and K' satisfying the condition is 2.
Step 2, determining the initial size of the window according to the condition (W is more than or equal to 3 and less than or equal to 10) required by the size of the window, and selecting the initial size W of the window in the decodingf＝3。
Step 3, knowing the number of variable nodes and check nodes contained in the window after determining the initial size of the window, wherein the number of the variable nodes and the number of the check nodes are respectively K' Wf、J′Wf. When an iterative process is executed in a window, the window expansion scheme provided by the invention is adopted to sequentially expand the size of the window, and the specific window expansion mode is as follows:
3.1, executing an iteration process in the current window size until the current target symbol meets the decoding condition or reaches the maximum iteration times;
3.2, calculating the average received signal-to-noise ratio of the current window according to the formula (1), if the average received signal-to-noise ratio is smaller than a preset threshold value theta, adding 1 to the size of the window, and returning to the step 3.1 to restart iteration. The preset threshold θ may be represented by equation (2)
Figure BDA0002620318300000071
Figure BDA0002620318300000072
Equation (2) represents that all windows of codewords are scaled from the initial size at a certain signal-to-noise ratioAnd calculating the average received signal-to-noise ratio of the corresponding window to the maximum value, accumulating and averaging. Wherein, WfIndicates the initial size of the window, WincIndicates the size of the current window, WmaxRepresents the maximum value of the window, Winc＝Wmax-Wf；wsRepresenting a variable window size, having a value of Wf,Wf+1,...,Wmax；
Figure BDA0002620318300000073
Indicating that the t-th window has a window size wsAverage received signal-to-noise ratio of time, ajRepresents the fading coefficient of the jth information bit in the current window, Es＝S/B，EsRepresenting signal power, S is the fixed transmit power of the transmitting end, B is the channel bandwidth, N0And/2 is the power spectral density of Gaussian white noise.
3.3, repeating the process until the average received signal-to-noise ratio of the window is larger than a preset threshold value theta or the window size reaches a preset maximum value Wmax。
And 4, carrying out iterative decoding on the target symbol under the new window size. After decoding is completed, the window slides to the next position, and the next target symbol is decoded.
The effects of the present invention can be further illustrated by the following simulations:
under the Rayleigh fading channel, the simulation result of the WD decoding performance of the invention and the traditional WD decoding performance of SC-LDPC codes is shown in FIG. 4, and the window initial size W isfWhen the code length is equal to 5, the invention is superior to the traditional WD in the aspect of decoding performance under different code lengths, and the simulation result proves the effectiveness of reducing the decoding performance loss of the SC-LDPC code WD in the Rayleigh fading channel.
As shown in fig. 7, a sliding window decoding optimization system for spatially-coupled LDPC codes includes:
a window size determining module 701, configured to determine a window size according to the degree distribution of the SC-LDPC code, the coupling width w, the coupling length L, and the extension factor M.
A node number determining module 702, configured to determine the number of variable nodes and check nodes included in the window.
An executing module 703 is configured to define the leftmost original model map in the window as a target symbol, and execute a belief propagation decoding algorithm on the target symbol in the window.
An iterative decoding module 704, configured to perform iterative decoding on the target symbol within the window according to the maximum iterative decoding times, and expand the window size according to the average received signal-to-noise ratio of the current window.
The sliding module 705 is configured to slide the current window to the next position after the iterative decoding of the current target symbol is completed, and perform decoding of the next target symbol.
The embodiments in the present description are described in a progressive manner, each embodiment focuses on differences from other embodiments, and the same and similar parts among the embodiments are referred to each other. For the system disclosed by the embodiment, the description is relatively simple because the system corresponds to the method disclosed by the embodiment, and the relevant points can be referred to the method part for description.
The principles and embodiments of the present invention have been described herein using specific examples, which are provided only to help understand the method and the core concept of the present invention; meanwhile, for a person skilled in the art, according to the idea of the present invention, the specific embodiments and the application range may be changed. In view of the above, the present disclosure should not be construed as limiting the invention.

Claims (7)

1. A sliding window decoding optimization algorithm of a spatial coupling LDPC code is characterized by comprising the following steps:
s1: determining the size of a window according to the degree distribution, the coupling width w, the coupling length L and the expansion factor M of the SC-LDPC code;
s2: determining the number of variable nodes and check nodes contained in the window;
s3: defining a leftmost original model graph in the window as a target symbol, and executing a belief propagation decoding algorithm on the target symbol in the window;
s4: carrying out iterative decoding on the target symbol in the window according to the maximum iterative decoding times, and expanding the size of the window according to the average received signal-to-noise ratio of the current window;
s5: and after the iterative decoding of the current target symbol is finished, sliding the current window to the next position, decoding the next target symbol, recovering the window size to the initial size, and repeating the steps S3-S5 until the decoding of all the target symbols is finished.
2. The sliding window decoding optimization algorithm for the spatially-coupled LDPC code according to claim 1, wherein the SC-LDPC code is constructed based on an original graph, and the (J, K, L) SC-LDPC code is obtained by coupling the regular LDPC codes with L degree distributions of (J, K) by using an "edge spreading" method on the basis of the original graph of the regular LDPC code.
3. The sliding window decoding optimization algorithm for the spatially-coupled LDPC code according to claim 2, wherein the coupling width w represents a connection between a variable node of a prototype graph and check nodes of w adjacent prototype graphs; the coupling length L represents that the SC-LDPC code is generated by constructing L regular LDPC code protographs, and the expansion factor is that one node of the M regular LDPC code protograph corresponds to a set of M nodes in the Tanner graph.
4. The sliding window decoding optimization algorithm for the spatially-coupled LDPC code according to claim 3, wherein the step S2 specifically comprises:
let a be gcd (J, K), a represents the greatest common divisor of J and K, and if positive integers J 'and K' respectively satisfy J being aJ ', K being aK', and gcd (J ', K') being 1, then there are K 'W variable nodes and J' W check nodes in the window W.
5. The sliding window decoding optimization algorithm for the spatially-coupled LDPC code according to claim 1, wherein the step S4 specifically comprises:
step S41: iteratively decoding a target symbol within the window;
step S42: judging whether the iterative decoding times are equal to the maximum iterative decoding times or not, if so, entering the step S43; if not, go to step S41;
step S43: calculating the average received signal-to-noise ratio of the target symbol in the window, judging whether the average received signal-to-noise ratio is smaller than a threshold value, if so, adding 1 to the size of the window, and entering a step S3; if not, the process proceeds to step S5.
6. The sliding window decoding optimization algorithm for the spatially-coupled LDPC code according to claim 4, wherein the threshold θ is calculated as follows:
Figure FDA0002620318290000021
Figure FDA0002620318290000022
wherein, WfIndicates the initial size of the window, WincIndicates the size of the current window, WmaxRepresents the maximum value of the window, Winc＝Wmax-Wf；wsRepresenting a variable window size;
Figure FDA0002620318290000023
indicating that the t-th window has a window size wsAverage received signal-to-noise ratio of time, ajRepresents the fading coefficient of the jth information bit in the current window, Es＝S/B，EsRepresenting signal power, S is the fixed transmit power of the transmitting end, B is the channel bandwidth, N0And/2 is the power spectral density of Gaussian white noise.
7. A sliding window decoding optimization system for spatially coupled LDPC codes, comprising:
the window size determining module is used for determining the size of a window according to the degree distribution, the coupling width w, the coupling length L and the expansion factor M of the SC-LDPC code;
the node number determining module is used for determining the number of variable nodes and check nodes contained in the window;
the execution module is used for defining the leftmost original model graph in the window as a target symbol and executing a belief propagation decoding algorithm on the target symbol in the window;
the iterative decoding module is used for carrying out iterative decoding on the target symbol in the window according to the maximum iterative decoding times and expanding the size of the window according to the average receiving signal-to-noise ratio of the current window;
and the sliding module is used for sliding the current window to the next position after the iterative decoding of the current target symbol is finished, and decoding the next target symbol.
CN202010781291.8A 2020-08-06 2020-08-06 Space coupling LDPC code sliding window decoding optimization algorithm and system Pending CN111900997A (en)

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