CN110830048B - Error correction method for constructing full-diversity LDPC code based on parity check matrix decomposition - Google Patents

Error correction method for constructing full-diversity LDPC code based on parity check matrix decomposition Download PDF

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CN110830048B
CN110830048B CN201911115240.5A CN201911115240A CN110830048B CN 110830048 B CN110830048 B CN 110830048B CN 201911115240 A CN201911115240 A CN 201911115240A CN 110830048 B CN110830048 B CN 110830048B
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陈为刚
黄刚
韩昌彩
彭昱
杨晋生
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Tianjin University
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    • H—ELECTRICITY
    • 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
    • H03M13/1148—Structural properties of the code parity-check or generator matrix
    • H03M13/1151—Algebraically constructed LDPC codes, e.g. LDPC codes derived from Euclidean geometries [EG-LDPC codes]

Abstract

The invention discloses an error correction method for constructing a full diversity LDPC code based on parity check matrix decomposition, which comprises the following steps: performing column exchange on a check matrix of the LDPC code, and decomposing the check matrix into a first sub-matrix corresponding to information bits and a second sub-matrix corresponding to check bits; extracting a unit interleaving matrix from the first sub-matrix, namely a third sub-matrix corresponding to the information bits after the unit interleaving matrix is decomposed and a fourth sub-matrix corresponding to the check bits; and (3) the third sub-matrix corresponding to the information bit, the fourth sub-matrix corresponding to the check bit and 2 unit interleaving matrixes are combined in a cross mode to generate an LDPC code check matrix with full diversity characteristics: optimizing a unit interleaving matrix in the LDPC check matrix to generate a full diversity LDPC code check matrix; the full diversity LDPC code check matrix is applied to a wireless communication multi-antenna system to correct code word errors caused by block fading. The full diversity LDPC code constructed by the method has the full diversity characteristic and is low in construction complexity.

Description

Error correction method for constructing full-diversity LDPC code based on parity check matrix decomposition
Technical Field
The invention belongs to the technical field of error correction coding in communication or storage, and particularly relates to an error correction method for constructing a full-diversity LDPC code based on parity check matrix decomposition.
Background
In a conventional random Noise channel, such as an Additive White Gaussian Noise (AWGN) channel, an error correction code is a main technical means for ensuring reliable information transmission or storage. The coding gain is a main index for measuring the performance of the error correcting code. The Low-Density Parity-Check (LDPC) code proposed by the teaching of the scholars Gallager has very strong error correction capability in the AWGN channel, and has successively entered many communication and storage systems to ensure the reliability of data transmission or storage.
However, in some application scenarios, for example: a multi-antenna transmission system, a retransmission mechanism, cooperative communication, a storage channel with Block deletion, etc., may use a Block Fading (BF) channel or a Block Erasure (BE) channel as its model. Under this model, the diversity order plays a crucial role in improving code performance, while traditional LDPC codes for random error channels (e.g., AWGN channels) cannot achieve full diversity under BF/BE channels.
With the progress of research, a full diversity error correction code capable of obtaining full diversity has been proposed for the characteristics of BF/BE channels. The full diversity LDPC code constructed by the density evolution algorithm and the iterative splitting technology is utilized, all variable nodes and check nodes of the full diversity LDPC code obtain full diversity after a plurality of iterative decoding processes, the proportion of full diversity parity check bits is increased, external information is transmitted to information nodes in the iterative decoding process through the check bits, certain coding gain is obtained, and the error correction performance is improved.
The regular full diversity LDPC code and the regular quasi-cyclic full diversity LDPC code construction method based on the Progressive Edge-Growth (PEG) algorithm can improve the coding gain and enable the performance to be more excellent. The quasi-cyclic algorithm is used for reconstructing the root-LDPC code without influencing the connection of root nodes so as to ensure the full diversity characteristic of the code.
Although the methods all realize the full diversity of the LDPC codes, the methods all need to specially design the structure of the LDPC codes, and cannot well utilize the optimization results obtained in the current LDPC code structure, so that the complexity of system design is increased in some application scenarios, such as the framework of cooperative communication.
Disclosure of Invention
The invention provides an error correction method for constructing a full diversity LDPC code based on parity check matrix decomposition aiming at a block fading channel or a block deleting channel scene in communication or storage, the full diversity LDPC code constructed by the method has full diversity characteristic and low construction complexity, fully utilizes the results in LDPC code research, and can obtain excellent performance in certain application scenes, and the detailed description is as follows:
an error correction method for constructing a full diversity LDPC code based on parity check matrix decomposition, the method comprising:
performing column exchange on a check matrix of the LDPC code, and decomposing the check matrix into a first sub-matrix corresponding to information bits and a second sub-matrix corresponding to check bits;
extracting a unit interleaving matrix from the first sub-matrix, namely a third sub-matrix corresponding to the information bits after the unit interleaving matrix is decomposed and a fourth sub-matrix corresponding to the check bits;
and (3) the third sub-matrix corresponding to the information bit, the fourth sub-matrix corresponding to the check bit and 2 unit interleaving matrixes are combined in a cross mode to generate an LDPC code check matrix with full diversity characteristics:
optimizing a unit interleaving matrix in the LDPC check matrix to generate a full diversity LDPC code check matrix;
the full diversity LDPC code check matrix is applied to a wireless communication multi-antenna system to correct code word errors caused by block fading.
The decomposing of the information bits into the first sub-matrix corresponding to the information bits and the second sub-matrix corresponding to the check bits is specifically:
calculating variable nodes s of check matrixjWeight value omega ofsjSorting the columns in the check matrix from large to small according to the weight;
sequentially putting the columns with smaller weights in the check matrix into a second sub-matrix corresponding to the check bits;
and judging whether the second sub-matrix corresponding to the check bit is a full-rank matrix, and if so, putting the rest columns into the first sub-matrix corresponding to the information bits.
Further, the extracting the unit interleaving matrix from the first sub-matrix specifically includes:
marking all '1' elements in the first sub-matrix corresponding to the information bits as selectable elements;
calculating the ring length, namely the local girth, of the minimum ring of each variable node in the current first sub-matrix, and calculating the average value of the local girths of the variable nodes as the average local girth of the check matrix;
sequentially selecting current variable nodes sjCalculating the average local girth and the increment thereof after the elements are removed according to the selectable elements in the corresponding matrix array;
and extracting the element with the largest increment of the average local girth, and marking other optional elements in the row as the non-optional elements.
Further, the optimizing a unit interleaving matrix in the LDPC check matrix to generate the full diversity LDPC code check matrix specifically includes:
(5.1) marking all '1' elements in the unit interleaving matrix as non-swapped elements;
(5.2) calculating the average local girth of the current check matrix;
(5.3) sequentially selecting the non-exchanged elements in the current check matrix, and calculating the average local girth increment of the check matrix after the elements are removed;
(5.4) taking the element with the largest average local girth increment as an element to be exchanged;
(5.5) sequentially calculating the average local girth increment of the exchanged residual unexchanged elements and the elements to be exchanged;
(5.6) judging whether the average local girth increment of each element which is not exchanged has an element which is not exchanged and is larger than 0, if so, selecting the element with the maximum average local girth increment to be exchanged with the element to be exchanged, marking the element which is not exchanged at present as an exchanged element, and executing the step (5.7);
(5.7) marking the element to be exchanged as an exchanged element, judging whether an unaltered element exists in the current check matrix, and if so, executing the step (5.2).
The technical scheme provided by the invention has the beneficial effects that:
(1) lower design complexity: compared with an error correction method for generating the full-diversity LDPC code based on the PEG algorithm, the method does not need to design the check matrix of the full-diversity LDPC code again according to the optimization algorithm, can obtain the full-diversity LDPC code suitable for the BF channel only by carrying out matrix decomposition on the traditional LDPC code, and has lower design complexity;
(2) superior error correction capability: the full diversity LDPC code constructed through the optimization of the ring can obtain full diversity performance under both BF channels and AWGN channels, has excellent error correction capability, and does not have obvious error floor phenomenon under high signal-to-noise ratio.
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FIG. 1 is a flow chart of an error correction method for constructing a full diversity LDPC code based on parity check matrix decomposition in accordance with the present invention;
FIG. 2 is a flow chart of matrix splitting according to the present invention;
FIG. 3 is a flow chart of the unit interleaving matrix decomposition of the present invention;
FIG. 4 is a flow chart of optimizing a unity interleaving matrix according to the present invention;
FIG. 5 is a comparison of the performance of the regular LDPC code constructed in the present invention in BF channels with other methods;
FIG. 6 is a comparison of the performance of the irregular LDPC code constructed by the present invention in BF channels with other methods;
FIG. 7 is a comparison of the performance of the regular LDPC code constructed in accordance with the present invention in an AWGN channel with other methods.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, embodiments of the present invention are described in further detail below.
In order to solve the problems, the invention provides an error correction method for obtaining the LDPC code with full diversity characteristic by decomposing and constructing the check matrix of the general LDPC code based on the existing LDPC code with excellent performance. The full diversity LDPC code constructed in the method can realize full diversity under the condition of block fading or block deletion channel, has excellent error correction capability and can also obtain excellent error correction performance under the condition of AWGN channel.
In the invention, the check matrix of the full diversity LDPC code is constructed by simply processing the LDPC code aiming at the conventional random error channel (such as an AWGN channel or a BSC channel), the design method has low complexity, and the method is suitable for being applied to scenes such as cooperative communication and the like.
An error correction method for constructing a full diversity code based on parity check matrix decomposition, referring to fig. 1-4, the method comprising the steps of:
(1) construction or selection of a check matrix H for a generic LDPC codem×n；
(2) Matrix splitting by checking matrix H of LDPC codem×nColumn switching is performed to decompose it into a first sub-matrix of corresponding information bits
Figure BDA0002273855870000041
And a second sub-matrix corresponding to the check bits
Figure BDA0002273855870000042
(3) SheetBit interleaved matrix decomposition from a first sub-matrix corresponding to information bits
Figure BDA0002273855870000043
Middle extraction unit interweaving matrix pim×mI.e. the third sub-matrix of corresponding information bits after the unit interleaving matrix decomposition
Figure BDA0002273855870000044
Fourth sub-matrix corresponding to check bit
Figure BDA0002273855870000045
(4) Constructing or selecting 2 unit interleaving matrices (pi)1)m×mAnd (pi)2)m×mA third sub-matrix corresponding to the information bits
Figure BDA0002273855870000046
And a fourth sub-matrix of check bits
Figure BDA0002273855870000047
And 2 unit interleaving matrixes are combined in a cross mode to generate an LDPC code check matrix with full diversity characteristics:
Figure BDA0002273855870000048
(5) optimizing a unity-interlace matrix (pi) in a check matrix1)m×mAnd (pi)2)m×mGenerating a full diversity LDPC code check matrix with good ring length characteristic;
(6) the constructed full diversity LDPC code is applied to a wireless communication multi-antenna system to correct code word errors caused by block fading.
Wherein, the step (2) is specifically as follows:
(2.1) calculating variable nodes s of check matrixjWeight value omega ofsjSorting the columns in the check matrix from large to small according to the weight;
(2.2) sequentially comparing the check matrix (H)LDPC)m×nThe row with the smaller medium weight value is put into a second sub-matrix corresponding to the check bit
Figure BDA0002273855870000049
Performing the following steps;
(2.3) judging the second sub-matrix corresponding to the check bit
Figure BDA00022738558700000410
If the matrix is a full rank matrix, if so, putting the rest columns into a first sub-matrix corresponding to the information bits
Figure BDA0002273855870000051
In the middle, the flow is ended; otherwise, returning to the step (2.2).
Wherein, the step (3) is specifically as follows:
(3.1) first sub-matrix corresponding to information bits
Figure BDA0002273855870000052
All "1" elements in (1) are labeled as optional elements;
(3.2) calculating the ring length, namely the local girth, of the minimum ring of each variable node in the current first sub-matrix, and calculating the average value of the local girths of the variable nodes as the average local girth g of the check matrixaveg；
(3.3) sequentially selecting current variable nodes sjSelectable elements in corresponding matrix columns
Figure BDA0002273855870000053
Calculating the average local girth after the element is removed
Figure BDA0002273855870000054
And average local girth increment
Figure BDA0002273855870000055
(3.4) extracting the element with the largest increment of the average local girth, and marking other optional elements in the row as the non-optional elements;
(3.5) judging whether all variable nodes are processed or not, if unprocessed variable nodes exist, selecting the next variable node sj+1And returning to execute the step (3.2); otherwise, the flow ends.
Wherein, the step (5) is specifically as follows:
(5.1) marking all '1' elements in the unit interleaving matrix as non-swapped elements;
(5.2) calculating the average local girth g of the current check matrixaveg；
(5.3) sequentially selecting the non-exchanged elements in the current check matrix, and calculating the average local girth increment of the check matrix after the elements are removed;
(5.4) the element with the largest increment of the average local girth is taken as the element to be exchanged
Figure BDA0002273855870000056
(5.5) sequentially calculating the average local girth increment of the exchanged residual unexchanged elements and the elements to be exchanged;
(5.6) judging whether the average local girth increment of each unaltered element has an unaltered element larger than 0, if so, selecting the element with the maximum average local girth increment
Figure BDA0002273855870000057
With elements to be exchanged
Figure BDA0002273855870000058
Exchanging and marking the current element which is not exchanged as the exchanged element, executing the step (5.7), if not, executing the step (5.7);
(5.7) marking the element to be exchanged as an exchanged element, judging whether the current check matrix has an element which is not exchanged, and if so, returning to execute the step (5.2); otherwise, outputting the optimized unit interleaving matrix, and ending the process.
The feasibility of the method for constructing a full-diversity LDPC code based on parity check matrix decomposition according to the present invention is described below with reference to specific embodiments.
Example 1
In this embodiment, the regular LDPC code with code length 504 and code rate 1/2 constructed by the PEG algorithm is first split, and is decomposed into the first sub-matrix corresponding to the information bits through column exchange
Figure BDA0002273855870000061
And a second sub-matrix corresponding to the check bits
Figure BDA0002273855870000062
Secondly, from the first sub-matrix
Figure BDA0002273855870000063
Middle extraction unit interweaving matrix pi252×252At this time, the third sub-matrix
Figure BDA0002273855870000064
Fourth sub-matrix
Figure BDA0002273855870000065
Then, 2 unit interleaving matrices (pi) are constructed or selected1)252×252And (pi)2)252×252Sub-matrices to be associated with information bits
Figure BDA0002273855870000066
Sub-matrix of sum check bits
Figure BDA0002273855870000067
And 2 unit interleaving matrixes are combined in a cross mode to generate an LDPC code check matrix with full diversity characteristics; finally, optimizing unit interleaving matrix (pi) in check matrix1)252×252And (pi)2)252×252And generating a full diversity LDPC code check matrix with good ring length characteristic.
The embodiment respectively simulates the full diversity LDPC constructed by the method provided by the invention and the full diversity LDPC code and the non-full diversity LDPC code constructed based on the PEG algorithm. The non-full diversity code is an LDPC code with a code length of 1008 bits and a code rate of 1/2 constructed by the PEG algorithm. The above 3 kinds of regular codes were simulated in BF channel.
FIG. 5 shows the performance comparison of 3 regular LDPC codes with 1008 bits in code length under BF channel, from which it can be seen that the full diversity LDPC code constructed by the method can realize full diversity; although there is no obvious performance difference between the full diversity LDPC code generated by matrix decomposition and the full diversity LDPC code generated based on the PEG algorithm, the algorithm complexity of the method for constructing the full diversity LDPC code is lower than that of the method for constructing the full diversity LDPC code by the PEG algorithm.
Example 2
In this embodiment, the irregular LDPC code with code length 504 and code rate 1/2 constructed by the PEG algorithm is first split, and decomposed into the first sub-matrix of corresponding information bits through column exchange
Figure BDA0002273855870000068
And a second sub-matrix corresponding to the check bits
Figure BDA0002273855870000069
Secondly, from the first sub-matrix
Figure 2
Middle-extracting unit interweaving array pi252×252At this time, the third sub-matrix
Figure BDA00022738558700000611
Fourth sub-matrix
Figure BDA00022738558700000612
Then, 2 unit interleaving matrices (pi) are constructed or selected1)252×252And (pi)2)252×252Sub-matrices to be associated with information bits
Figure BDA00022738558700000613
Sub-matrix of sum check bits
Figure BDA00022738558700000614
And 2 unit interleaving matrixes are combined in a crossing way to generate a matrix with full divisionAn LDPC code check matrix with characteristics; finally, optimizing unit interleaving matrix (pi) in check matrix1)252×252And (pi)2)252×252And generating a full diversity LDPC code check matrix with good ring length characteristic.
The embodiment respectively simulates the full diversity LDPC constructed by the method provided by the invention and the full diversity LDPC code and the non-full diversity LDPC code constructed based on the PEG algorithm. The non-full diversity code is an LDPC code with a code length of 1008 bits and a code rate of 1/2 constructed by the PEG algorithm. The above 3 irregular codes were simulated under BF channel.
Fig. 6 shows the performance comparison of the 3 irregular LDPC codes with the code length of 1008 bits in the BF channel, from which it can be seen that the full-diversity LDPC code constructed by the method can implement full diversity, and reduce the complexity of constructing the full-diversity LDPC code while having similar performance to the full-diversity LDPC code generated based on the PEG algorithm.
Example 3
In this embodiment, the irregular LDPC code with code length 504 and code rate 1/2 constructed by the PEG algorithm is first split, and decomposed into the first sub-matrix of corresponding information bits through column exchange
Figure BDA0002273855870000071
And a second sub-matrix corresponding to the check bits; secondly, from the first sub-matrix
Figure BDA0002273855870000072
Middle-extracting unit interweaving array pi252×252，
Now the third sub-matrix
Figure BDA0002273855870000073
Fourth sub-matrix
Figure BDA0002273855870000074
Then, 2 unit interleaving matrices (pi) are constructed or selected1)252×252And (pi)2)252×252Sub-matrices to be associated with information bits
Figure BDA0002273855870000075
Sub-matrix of sum check bits
Figure BDA0002273855870000076
And 2 unit interleaving matrixes are combined in a cross mode to generate an LDPC code check matrix with full diversity characteristics; finally, optimizing unit interleaving matrix (pi) in check matrix1)252×252And (pi)2)252×252And generating a full diversity LDPC code check matrix with good ring length characteristic.
The embodiment respectively simulates the full diversity LDPC constructed by the method provided by the invention and the full diversity LDPC code and the non-full diversity LDPC code constructed based on the PEG algorithm. The non-full diversity code is an LDPC code with a code length of 1008 bits and a code rate of 1/2 constructed by the PEG algorithm. The above 3 regular codes were simulated under AWGN channel.
Fig. 7 shows the performance comparison of the 3 irregular LDPC codes with the code length of 1008 bits in the AWGN channel, and it can be seen that, in the AWGN channel, the full-diversity LDPC code constructed by the method has a certain performance improvement compared with the full-diversity LDPC code generated based on the PEG algorithm.
In the embodiment of the present invention, except for the specific description of the model of each device, the model of other devices is not limited, as long as the device can perform the above functions.
Those skilled in the art will appreciate that the drawings are only schematic illustrations of preferred embodiments, and the above-described embodiments of the present invention are merely provided for description and do not represent the merits of the embodiments.
The above description is only for the purpose of illustrating the preferred embodiments of the present invention and is not to be construed as limiting the invention, and any modifications, equivalents, improvements and the like that fall within the spirit and principle of the present invention are intended to be included therein.

Claims (1)

1. An error correction method for constructing a full diversity LDPC code based on parity check matrix decomposition, the method comprising:
performing column exchange on a check matrix of the LDPC code, and decomposing the check matrix into a first sub-matrix corresponding to information bits and a second sub-matrix corresponding to check bits;
extracting a unit interleaving matrix from the first sub-matrix, namely a third sub-matrix corresponding to the information bits after the unit interleaving matrix is decomposed and a fourth sub-matrix corresponding to the check bits;
and (3) the third sub-matrix corresponding to the information bit, the fourth sub-matrix corresponding to the check bit and 2 unit interleaving matrixes are combined in a cross mode to generate an LDPC code check matrix with full diversity characteristics:
optimizing a unit interleaving matrix in the LDPC check matrix to generate a full diversity LDPC code check matrix;
applying the full diversity LDPC code check matrix to a wireless communication multi-antenna system to correct code word errors caused by block fading;
the decomposing of the information bits into the first sub-matrix corresponding to the information bits and the second sub-matrix corresponding to the check bits is specifically:
calculating variable nodes s of check matrixjWeight of (2)
Figure FDA0003129999100000011
Sorting the columns in the check matrix from large to small according to the weight;
sequentially putting the columns with smaller weights in the check matrix into a second sub-matrix corresponding to the check bits;
judging whether a second sub-matrix corresponding to the check bit is a full-rank matrix, if so, putting the rest columns into a first sub-matrix corresponding to the information bits;
the extracting the unit interleaving matrix from the first sub-matrix specifically includes:
marking all '1' elements in the first sub-matrix corresponding to the information bits as selectable elements;
calculating the ring length, namely the local girth, of the minimum ring of each variable node in the current first sub-matrix, and calculating the average value of the local girths of the variable nodes as the average local girth of the check matrix;
sequentially selecting current variable nodes sjSelectable in corresponding matrix columnCalculating the average local girth and increment thereof after the element is removed;
extracting the element with the largest increment of the average local girth, and marking other optional elements in the row as the non-optional elements;
wherein the content of the first and second substances,
the optimizing a unit interleaving matrix in the LDPC check matrix and generating the full diversity LDPC code check matrix specifically comprise:
(5.1) marking all '1' elements in the unit interleaving matrix as non-swapped elements;
(5.2) calculating the average local girth of the current check matrix;
(5.3) sequentially selecting the non-exchanged elements in the current check matrix, and calculating the average local girth increment of the check matrix after the elements are removed;
(5.4) taking the element with the largest average local girth increment as an element to be exchanged;
(5.5) sequentially calculating the average local girth increment of the exchanged residual unexchanged elements and the elements to be exchanged;
(5.6) judging whether the average local girth increment of each element which is not exchanged has an element which is not exchanged and is larger than 0, if so, selecting the element with the maximum average local girth increment to be exchanged with the element to be exchanged, marking the element which is not exchanged at present as an exchanged element, and executing the step (5.7);
(5.7) marking the element to be exchanged as an exchanged element, judging whether an unaltered element exists in the current check matrix, and if so, executing the step (5.2).
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