CN111510160A - Truncation convolutional coding optimization construction method - Google Patents

Truncation convolutional coding optimization construction method Download PDF

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CN111510160A
CN111510160A CN202010400367.8A CN202010400367A CN111510160A CN 111510160 A CN111510160 A CN 111510160A CN 202010400367 A CN202010400367 A CN 202010400367A CN 111510160 A CN111510160 A CN 111510160A
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dpc
spreading
truncated
code
matrix
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王平
高原
王景
郭洋
阮启明
贾天伟
曹江
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Research Institute of War of PLA Academy of Military Science
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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
    • H03M13/116—Quasi-cyclic LDPC [QC-LDPC] codes, i.e. the parity-check matrix being composed of permutation or circulant sub-matrices
    • H03M13/1165—QC-LDPC codes as defined for the digital video broadcasting [DVB] specifications, e.g. DVB-Satellite [DVB-S2]
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L1/00—Arrangements for detecting or preventing errors in the information received
    • H04L1/004—Arrangements for detecting or preventing errors in the information received by using forward error control
    • H04L1/0045—Arrangements at the receiver end
    • H04L1/0047—Decoding adapted to other signal detection operation
    • H04L1/005—Iterative decoding, including iteration between signal detection and decoding operation
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L1/00—Arrangements for detecting or preventing errors in the information received
    • H04L1/004—Arrangements for detecting or preventing errors in the information received by using forward error control
    • H04L1/0056—Systems characterized by the type of code used
    • H04L1/0057—Block codes
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L1/00—Arrangements for detecting or preventing errors in the information received
    • H04L1/004—Arrangements for detecting or preventing errors in the information received by using forward error control
    • H04L1/0056—Systems characterized by the type of code used
    • H04L1/0059—Convolutional codes
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L1/00—Arrangements for detecting or preventing errors in the information received
    • H04L1/004—Arrangements for detecting or preventing errors in the information received by using forward error control
    • H04L1/0056—Systems characterized by the type of code used
    • H04L1/0061—Error detection codes

Abstract

The invention discloses an optimized construction method of truncated convolution coding, which comprises the following steps of constructing a master pattern and a base matrix of a truncated convolution L DPC spreading code set, obtaining a decoding threshold of the truncated convolution L DPC spreading code set through iterative calculation, optimizing and reducing the decoding time delay of the truncated convolution L DPC spreading code set through iterative search, and constructing a check matrix of a truncated convolution L DPC spreading code.

Description

Truncation convolutional coding optimization construction method
Technical Field
The invention relates to a communication channel coding technology, in particular to a truncation convolutional coding optimization construction method.
Background
For the vision and requirements of the ubiquitous connection of future 5G and 6G mobile communications, the network elements of different layers, such as macro-cell, micro-cell, device-to-device (D2D) connection, bluetooth and the like, can realize deep fusion to form a heterogeneous network system with multiple layers, ultra-dense and overlapping coverage. In the above heterogeneous network, a large amount of inter-channel interference having an impulse characteristic is frequently generated along with a communication process. For example, unscheduled deployment, random access femtocells will result in non-gaussian impulse noise in the macro and other femtocell networks; in the dynamic spectrum sharing process of the network, the inter-channel interference can be generated when the spectrum access is collided due to misjudgment of the cognitive radio, and the collision interference has obvious pulse characteristics. Domestic and foreign research shows that noise interference in future heterogeneous mobile cellular networks no longer follows the ideal gaussian noise assumption, but should be modeled as a superposition of thermal noise and impulse noise. The impulse noise interference will seriously affect the efficient and reliable information transmission of the communication link, and restrict the overall performance of the heterogeneous mobile cellular network.
The error correction capability of low-density parity-check codes (L DPC) adopted in the 5G standard is difficult to deal with a large number of burst errors and bit deletion errors on a pulse channel, and the problem of difficult optimization design of low-code-rate L DPC codes exists. L DPC spreading codes replace single parity check constraints in check nodes with linear block code constraints with stronger error correction capability and have the advantage of easily constructing low-code-rate code words.
Disclosure of Invention
According to the embodiment of the invention, the invention provides a truncation convolutional coding optimization construction method, which comprises the following steps:
constructing a protograph and a base matrix of a truncated convolutional L DPC spreading code set;
obtaining a decoding threshold of a truncated convolution L DPC spreading code set through iterative calculation;
optimizing and reducing the decoding time delay of the truncated convolution L DPC spreading code set through iterative search;
a check matrix is constructed that truncates the convolutional L DPC spreading codes.
Further, constructing the protograph and the base matrix of the truncated convolutional L DPC spreading code set comprises the following sub-steps:
grouping truncated convolutional L DPC spreading code sets to obtain (J, K, m) grouped L DPC spreading codes, wherein J represents column weight, K represents row weight, and m represents check sequence length of L DPC spreading codes;
copying and edge-spreading the protographs of the (J, K, m) grouped L DPC spreading codes to obtain protographs of truncated convolutional L DPC spreading code sets;
the base matrix of the (J, K, m) grouped L DPC spreading codes is split and matrix-diagonal rearranged, obtaining a base matrix of a truncated convolutional L DPC spreading code set.
Further, in the master pattern diagram of the DPC spreading codes of the (J, K, m) packet L is set, there is nJVariable node with J number of degrees and nKA base matrix B of K degree spread check nodes, (J, K, m) grouped L DPC spreading codes has dimension nJ×nKEach spreading check node satisfies m parity check constraints in the spreading code.
Further, copying and edge spreading the master pattern of the (J, K, m) packet L DPC spreading codes comprises the sub-steps of:
copy L copies of the master pattern of (J, K, m) grouped L DPC spreading codes;
adding ω position spaces in the (J, K, m) grouped L DPC spreading codes;
coupling and connecting variable nodes of the current grouping L DPC codes with extended check nodes on the position space of the rear omega to obtain a coupling chain, wherein L represents a coupling length, and omega represents a memory length;
a raw pattern of (J, K, m, L, ω) truncated convolutional L DPC spreading codes is obtained.
Further, in the newly added ω position spaces, each position space contains nKAnd the extension check nodes do not contain variable nodes.
Further, the splitting and matrix diagonal rearrangement of the base matrix of the (J, K, m) grouped L DPC spreading codes comprises the sub-steps of:
splitting the base matrix of (J, K, m) grouped L DPC spreading codes into ω +1 sub-matrices B0,B1,…,BωThe dimension of the sub-matrix is the same as the base matrix of the (J, K, m) grouped L DPC spreading codes and satisfies the constraint
Figure BDA0002489159730000031
Arranging omega +1 sub-matrixes into the form of diagonal matrixes according to the connection relation of nodes in a master graph of L DPC spreading codes grouped by (J, K, m), and obtaining a base matrix of the (J, K, m, L, omega) truncated convolution L DPC spreading codes
Figure BDA0002489159730000032
Further, obtaining a decoding threshold for the truncated convolutional L DPC spreading code set comprises the following sub-steps:
setting the number of variable nodes and the number of spread check nodes of the current truncated convolution L DPC spreading code set to be N respectivelyLAnd MLSetting each variable node to viSetting each extended check node to cjWherein i is 0,1, …, NL-1，j＝0,1,…,ML-1；
Let Ψ (i) represent the node v with the variableiConnected extended check node cjThe set of (a) and (b),
Figure BDA0002489159730000033
representing the mutual information transmitted to the extended check node by the variable node in the first iteration calculation, if the extended check node cj∈ Ψ (i), then variable node viTo extended check node cjCan be expressed as
Figure BDA0002489159730000034
Wherein, IchMutual information for communication channels;
order to
Figure BDA0002489159730000035
Representing and extending check nodes cjConnected variable nodes viThe set of (a) and (b),
Figure BDA0002489159730000036
indicating an extended check node c in the ith iterationjTo variable node viMutual information of
Figure BDA0002489159730000037
Updating according to the following formula:
Figure BDA0002489159730000038
wherein, n and n-1Representing random displacement interleaving and inverse interleaving, Ψ (-) representing a multi-dimensional input-output information transfer function,
Figure BDA0002489159730000039
djindicating an extended check node cjThe degree of (d);
for each variable node viOutputting extrinsic information in the first iteration
Figure BDA00024891597300000310
Updating according to the following formula:
Figure BDA00024891597300000311
wherein S represents the finite state space number of the communication channel, πsRepresenting the stationary distribution of the finite state Markov chain of the communication channel, A representing the impulse exponent, г representing the mean power ratio of Gaussian noise to impulse noise, σGRepresenting the total noise variance. J (-) and J-1(. represents the input-output information conversion of the repeated codeA shift function and an inverse function;
for each variable node viThe decoding information for soft decision in the first iteration is calculated according to the following formula
Figure BDA0002489159730000041
Figure BDA0002489159730000042
When all variable nodes viSatisfy the requirement of
Figure BDA0002489159730000043
The iteration is terminated and the decoding threshold under the current communication channel parameters is obtained.
Further, optimizing and reducing the decoding delay of the truncated convolutional L DPC spreading code set comprises the following sub-steps:
setting the initial memory length omega0Is 1;
starting iterative search, in the k-th iterative search, at the current coupling width omegakSelecting a group of edge expansion patterns as initial input, and searching the optimal edge expansion pattern of the communication channel parameter closest to the channel capacity limit under the current constraint width;
if the shannon limit reachable rate corresponding to the current edge expansion style is larger than 98%, terminating the search, and obtaining the relation between the minimum coupling width and the column weight as omegaminJ-1; otherwise, let ω bek+1＝ωk+1, and returning to the above steps to continue the iterative search until the search is terminated.
Further, constructing the check matrix of truncated convolutional L DPC spreading codes comprises the following sub-steps:
setting the map spreading factor to M, truncating (J, K, M, L, omega) the base matrix of the convolutional L DPC spreading code
Figure BDA0002489159730000044
Each non-zero element in the array is replaced by a permutation matrix with M × M dimension, each zero element is replaced by an all-zero matrix, and the dimension of M (L + omega) n is obtainedk×MLnJTruncated convolutional L DPC codeThe check matrix of (2);
and expanding the row and column of the check matrix row by row, wherein 1 in each row is replaced by 1 column in the check matrix, and 0 in each row is replaced by an M × 1-dimensional all-zero column vector.
Further, a shortening code of the spreading code is adopted when the row and the column of the check matrix corresponding to the spreading check nodes at the two ends of the coupling chain are spread.
According to the truncation convolution coding optimization construction method provided by the embodiment of the invention, a truncation convolution L DPC spreading code suitable for 5G and 6G heterogeneous cellular network pulse channels is constructed, so that the transmission reliability of data on the pulse channels can be effectively improved, and the transmission delay is reduced.
It is to be understood that both the foregoing general description and the following detailed description are exemplary and are intended to provide further explanation of the claimed technology.
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FIG. 1 is a flow chart of a method for truncating a convolutional code optimized construction method according to an embodiment of the present invention;
FIG. 2 is a diagram of a prototype of truncated convolutional L DPC spreading codes of a truncated convolutional code optimization construction method according to an embodiment of the present invention;
FIG. 3 is a schematic diagram of the convergence of decoding truncated convolutional L DPC spreading codes according to the embodiment of the present invention.
Detailed Description
The present invention will be further explained by describing preferred embodiments of the present invention in detail with reference to the accompanying drawings.
First, the truncated convolutional coding optimization construction method according to the embodiment of the present invention will be described with reference to fig. 1 to 3, which is used to improve the decoding performance of the truncated convolutional L DPC spreading code of the 5G and 6G heterogeneous cellular network impulse channel, and has a wide application range.
As shown in fig. 1, the truncated convolutional coding optimization construction method according to the embodiment of the present invention includes the following steps:
specifically, as shown in fig. 1 and 2, in S1, a protograph and a base matrix of a truncated convolutional L DPC spreading code set are constructed;
further, in S11, a group of truncated L DPC spreading code sets is grouped to obtain a (J, K, m) group L DPC spreading code, wherein J denotes a column weight, K denotes a row weight, and m denotes a check sequence length of L DPC spreading code, and in the present embodiment, n is set in a prototype diagram constructing the (J, K, m) group L DPC spreading codeJVariable node with J number of degrees and nKA base matrix B of K degree spread check nodes, (J, K, m) grouped L DPC spreading codes has dimension nJ×nKEach spreading check node satisfies m parity check constraints in the spreading code.
Further, in S12, the protogram of the (J, K, m) group L DPC spreading code is copied and edge-spread to obtain a protogram of a truncated convolution L DPC spreading code set;
in S121, the master pattern of the (J, K, m) grouped L DPC spreading codes is copied L times;
in S122, omega position spaces are added to the (J, K, m) grouped L DPC spreading codes, and in the present embodiment, each position space contains n in the newly added omega position spacesKAnd the extension check nodes do not contain variable nodes.
In S123, coupling and connecting the variable node of the current grouping L DPC code with the extended check node on the following ω position space to obtain a coupling chain, where L denotes a coupling length, and ω denotes a memory length;
at S124, as shown in FIG. 2, a protogram of (J, K, m, L, ω) truncated convolutional L DPC spreading codes is obtained, setting NLRepresenting the number of variable nodes on the truncated convolutional L DPC spreading code protograph, N isL＝LnJ(ii) a Let MLM represents the number of spread check nodes on the truncated convolution L DPC spreading code prototype graphL＝(L+ω)nK。
Further, in S13, the base matrix of the (J, K, m) grouped L DPC spreading codes is split and matrix-diagonal rearranged, obtaining a base matrix of a truncated convolutional L DPC spreading code set.
In S131, the basis matrix of (J, K, m) grouped L DPC spreading codes is split into ω +1 sub-matrices B0,B1,…,BωDimension of submatrix and (J, K, m) groupingL DPC spreading codes have the same base matrix and satisfy the constraint
Figure BDA0002489159730000061
In S132, the omega +1 sub-matrixes are grouped L connection relations of nodes in the original pattern diagram of the DPC spreading codes according to the (J, K, m) into a diagonal matrix form, and the base matrix of the (J, K, m, L, omega) truncated convolution L DPC spreading codes is obtained
Figure BDA0002489159730000062
Specifically, as shown in fig. 1, in S2, a decoding threshold of the truncated convolutional L DPC spreading code set is obtained through iterative computation;
in S21, each variable node is set to viSetting each extended check node to cjWherein i is 0,1, …, NL-1，j＝0,1,…,ML-1；
In S22, let Ψ (i) represent the AND variable node viConnected extended check node cjThe set of (a) and (b),
Figure BDA0002489159730000063
representing the mutual information transmitted to the extended check node by the variable node in the first iteration calculation, if the extended check node cj∈ Ψ (i), then variable node viTo extended check node cjCan be expressed as
Figure BDA0002489159730000064
Wherein, IchMutual information for communication channels;
in S23, let
Figure BDA0002489159730000065
Representing and extending check nodes cjConnected variable nodes viThe set of (a) and (b),
Figure BDA0002489159730000066
indicating an extended check node c in the ith iterationjTo variable node viMutual information of
Figure BDA0002489159730000067
Updating according to the following formula:
Figure BDA0002489159730000068
wherein, n and n-1Representing random displacement interleaving and inverse interleaving, Ψ (-) representing a multi-dimensional input-output information transfer function,
Figure BDA0002489159730000071
djindicating an extended check node cjThe degree of (d);
in S24, node v is assigned to each variableiOutputting extrinsic information in the first iteration
Figure BDA0002489159730000072
Updating according to the following formula:
Figure BDA0002489159730000073
wherein S represents the finite state space number of the communication channel, πsRepresenting the stationary distribution of the finite state Markov chain of the communication channel, A representing the impulse exponent, г representing the mean power ratio of Gaussian noise to impulse noise, σGRepresenting the total noise variance. J (-) and J-1() represents the transfer function and the inverse function of the input and output information of the repeated code;
in S25, node v is assigned to each variableiThe decoding information for soft decision in the first iteration is calculated according to the following formula
Figure BDA0002489159730000074
Figure BDA0002489159730000075
When all variable nodes viSatisfy the requirement of
Figure BDA0002489159730000076
The iteration is terminated and the decoding threshold under the current communication channel parameters is obtained.
Specifically, as shown in fig. 1, in S3, the decoding delay of the truncated convolutional L DPC spreading code set is optimized and reduced by iterative search;
in S31, an initial memory length ω is set0Is 1;
in S32, an iterative search is started, and in the kth iterative search, at the current coupling width ωkSelecting a group of edge expansion patterns as initial input, and searching the optimal edge expansion pattern of the communication channel parameter closest to the channel capacity limit under the current constraint width;
in S33, if the shannon limit reachable rate corresponding to the current edge expansion pattern is greater than 98%, terminating the search, and obtaining a relation ω between the minimum coupling width and the column weightminJ-1; otherwise, let ω bek+1＝ωk+1, and returning to the above steps to continue the iterative search until the search is terminated.
Specifically, as shown in fig. 1, in S4, a check matrix is constructed that truncates the convolutional L DPC spreading codes.
At S41, the map spreading factor is set to M, and the base matrix of the convolved L DPC spreading code is truncated by (J, K, M, L, ω)
Figure BDA0002489159730000077
Each non-zero element in the array is replaced by a permutation matrix with M × M dimension, each zero element is replaced by an all-zero matrix, and the dimension of M (L + omega) n is obtainedk×MLnJThe check matrix of the truncated convolutional L DPC code of (1);
in S42, the check matrix is row-by-row spread in rows and columns, with 1 in each row being replaced by 1 column in the check matrix and 0 in each row being replaced by an M × 1-dimensional all-zero column vector.
According to the truncated convolutional coding optimization construction method of the above embodiment, an example of the transmission application of the truncated convolutional L PDC spreading code under the Class-a burst channel is as follows, and the Class-a burst channel can be used for modeling a communication channel with burst characteristics in a heterogeneous cellular network, an internet of vehicles and the like.
Three groups of L DPC spreading codes are constructed, the column weight is 2,3 and 4 respectively, the row weight is 36 respectively, the spreading codes adopt (36,30) linear block codes obtained by shortening (63,57) BCH codes, three groups of truncated convolution L PDC spreading codes with the minimum memory length are obtained through simulation, the minimum constraint length omega of the three groups of code words are (2,36,6, L, 1), (3,36,6, L, 2) and (4,36,6, L, 3) respectivelymin1,2 and 3 respectively. Three minimum constraint lengths omegaminComplying with a constraint with the column weight J, i.e. ωminJ-1. Simulation shows that under the condition that the Shannon limit reachable rate is more than 98%, more than one edge is unfolded. Edge-expanded pattern B0＝B1＝[11…1]1×36iFor example, the decoding convergence thresholds of three code sets are analyzed and explained, where i is 1,2, and 3.
Fig. 3 shows the decoding convergence of the optimally designed three truncated convolutional 8 DPC spreading codes on the Class-a burst channel, where the burst index a of the channel parameter is 0.1, the average power ratio г of gaussian noise to impulse noise is 0.1, the decoding threshold of the grouped г DPC spreading code corresponding to the truncated convolutional г DPC spreading code is also shown in fig. 3, the г 2DPC spreading code decoding threshold of 2 is 0.6661, which has very close to the channel capacity limit, (2,36,6, г,1) the decoding convergence threshold of the truncated convolutional г 4DPC spreading code is 0.6858, which is further increased from the corresponding decoding threshold of г DPC, the increase ratio is 3%. the decoding threshold of the grouped г DPC 6DPC spreading code with column weight 3 is 0.7447, which is further away from the channel capacity limit than the grouped г with column weight 2, which decoding performance starts to be further away from the channel capacity limit, which means that the decoding performance starts to deteriorate, (3, 6, 5, 582) the decoding threshold of the group 466 DPC spreading code L is further away from the channel capacity limit, which is greater than the corresponding decoding threshold of the truncated convolutional linear weight of the group 463, which is further than the column weight limit of the decoding threshold of the truncated 120, which is equal to the group of the truncated convolutional linear expansion code, which is further than the corresponding decoding threshold of the group of the truncated 120, which is equal to the group of the truncated 120, which is further than the group of the decode threshold of the truncated 120, which is equal to the group of the truncated 120.
In the above, with reference to fig. 1 to 3, the truncated convolutional coding optimization construction method according to the embodiment of the present invention is described, and a truncated convolutional L DPC spreading code suitable for a 5G and 6G heterogeneous cellular network burst channel is constructed, so that the transmission reliability of data on the burst channel can be effectively improved, and the transmission delay can be reduced.
It should be noted that, in the present specification, the terms "comprises," "comprising," or any other variation thereof, are intended to cover a non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements does not include only those elements but may include other elements not expressly listed or inherent to such process, method, article, or apparatus. Without further limitation, an element defined by the phrase "comprising … …" does not exclude the presence of other identical elements in a process, method, article, or apparatus that comprises the element.
While the present invention has been described in detail with reference to the preferred embodiments, it should be understood that the above description should not be taken as limiting the invention. Various modifications and alterations to this invention will become apparent to those skilled in the art upon reading the foregoing description. Accordingly, the scope of the invention should be determined from the following claims.

Claims (10)

1. A truncated convolutional code optimization construction method is characterized by comprising the following steps:
constructing a protograph and a base matrix of a truncated convolutional L DPC spreading code set;
obtaining a decoding threshold of the truncated convolution L DPC spreading code set through iterative calculation;
optimizing and reducing the decoding time delay of the truncated convolution L DPC spreading code set through iterative search;
constructing a check matrix of the truncated convolutional L DPC spreading codes.
2. The truncated convolutional code optimal construction method of claim 1, wherein constructing the protograph and the base matrix of the truncated convolutional L DPC spreading code set comprises the sub-steps of:
grouping the truncated convolutional L DPC spreading code sets to obtain (J, K, m) grouped L DPC spreading codes, wherein J represents column weight, K represents row weight, and m represents check sequence length of the L DPC spreading codes;
copying and edge-spreading the protographs of the (J, K, m) grouped L DPC spreading codes to obtain protographs of the truncated convolutional L DPC spreading code sets;
splitting and matrix diagonal rearranging the base matrix of the (J, K, m) grouped L DPC spreading codes to obtain the base matrix of the truncated convolutional L DPC spreading code set.
3. The method of claim 2, wherein there is n in the protographs set for constructing (J, K, m) grouped L DPC spreading codesJVariable node with J number of degrees and nKA plurality of K-degree spread check nodes, the dimension of the base matrix B of the (J, K, m) grouped L DPC spread codes is nJ×nKEach of the spread check nodes satisfies m parity check constraints in the spreading code.
4. The truncated convolutional code optimal construction method as claimed in claim 3, wherein the copying and edge-spreading of the original pattern of the (J, K, m) block L DPC spreading codes comprises the sub-steps of:
copying L times a master pattern of the (J, K, m) grouped L DPC spreading codes;
adding ω position spaces in the (J, K, m) grouped L DPC spreading codes;
coupling and connecting the variable node of the current grouped L DPC code with the extended check nodes on the next omega position spaces to obtain a coupling chain, wherein L represents a coupling length, and omega represents a memory length;
a raw pattern of (J, K, m, L, ω) truncated convolutional L DPC spreading codes is obtained.
5. The truncated convolutional code optimizing construction method of claim 4 wherein each of said position spaces contains n of newly added ω position spacesKAnd the extension check nodes do not contain the variable nodes.
6. The truncated convolutional code optimal construction method as claimed in claim 4 or 5, wherein the splitting and matrix diagonal rearrangement of the base matrix of the (J, K, m) grouped L DPC spreading codes comprises the sub-steps of:
splitting a base matrix of the (J, K, m) grouped L DPC spreading codes into omega +1 sub-matrices B0,B1,…,BωThe dimension of the sub-matrix is the same as the base matrix of the (J, K, m) grouped L DPC spreading codes and satisfies the constraint
Figure FDA0002489159720000021
Arranging omega +1 sub-matrixes into the form of diagonal matrixes according to the connection relation of nodes in the original pattern graph of the (J, K, m) grouped L DPC spreading codes, and obtaining a base matrix of the (J, K, m, L, omega) truncated convolution L DPC spreading codes
Figure FDA0002489159720000022
7. The truncated convolutional code optimal construction method of claim 6, wherein obtaining a decoding threshold for said truncated convolutional L DPC spreading code set comprises the sub-steps of:
setting the number of variable nodes and the number of spread check nodes of the current truncated convolution L DPC spreading code set to be N respectivelyLAnd MLSetting each of the variable nodes to viSetting each extended check node to cjWherein i is 0,1, …, NL-1，j＝0,1,…,ML-1；
Let Ψ (i) represent the variable node viThe connected extended check node cjThe set of (a) and (b),
Figure FDA0002489159720000023
representing the mutual information transmitted to the extended check node by the variable node in the ith iterative computation, if the extended check node cj∈ Ψ (i), the variable node viTo said extended check node cjCan be expressed as
Figure FDA0002489159720000024
Wherein, IchMutual information for communication channels;
order to
Figure FDA0002489159720000025
Representation and said extended check node cjConnected variable nodes viThe set of (a) and (b),
Figure FDA0002489159720000026
represents the extended check node c in the l-th iterationjTo the variable node viMutual information of
Figure FDA0002489159720000027
Updating according to the following formula:
Figure FDA0002489159720000028
wherein, n and n-1Representing random displacement interleaving and inverse interleaving, Ψ (-) representing a multi-dimensional input-output information transfer function,
Figure FDA0002489159720000031
djrepresenting said extended check node cjThe degree of (d);
for each of the variable nodes viOutputting extrinsic information in the first iteration
Figure FDA0002489159720000032
Updating according to the following formula:
Figure FDA0002489159720000033
wherein S represents the finite state space number of the communication channel, πsRepresenting the stationary distribution of the finite state Markov chain of the communication channel, A representing the impulse exponent, г representing the mean power ratio of Gaussian noise to impulse noise, σGRepresenting the total noise variance. J (-) and J-1() represents the transfer function and the inverse function of the input and output information of the repeated code;
for each of the variable nodes viThe decoding information for soft decision in the first iteration is calculated according to the following formula
Figure FDA0002489159720000034
Figure FDA0002489159720000035
When all the variable nodes viSatisfy the requirement of
Figure FDA0002489159720000036
The iteration is terminated and the decoding threshold under the current communication channel parameters is obtained.
8. The truncated convolutional code optimal construction method as claimed in claim 6, wherein optimizing and reducing the decoding delay of said truncated convolutional L DPC spreading code set comprises the sub-steps of:
setting the initial memory length omega0Is 1;
starting iterative search, in the k-th iterative search, at the current coupling width omegakSelecting a group of edge expansion patterns as initial input, and searching the optimal edge expansion pattern of the communication channel parameter closest to the channel capacity limit under the current constraint width;
if the shannon limit reachable rate corresponding to the current edge expansion style is larger than 98%, terminating the search, and obtaining the relation between the minimum coupling width and the column weight as omegaminJ-1; otherwise, let ω bek+1＝ωk+1, and returning to the above steps to continue the iterative search until the search is terminated.
9. The truncated convolutional code optimal construction method of claim 6, wherein constructing the check matrix of the truncated convolutional L DPC spreading code comprises the sub-steps of:
setting the graph spreading factor to M, truncating the (J, K, M, L, omega) to the base matrix of the L DPC spreading code
Figure FDA0002489159720000037
Each non-zero element in the array is replaced by a permutation matrix with M × M dimension, each zero element is replaced by an all-zero matrix, and the dimension of M (L + omega) n is obtainedk×MLnJThe check matrix of the truncated convolutional L DPC code of (1);
and expanding the row and column of the check matrix row by row, wherein 1 in each row is replaced by 1 column in the check matrix, and 0 in each row is replaced by an M × 1-dimensional all-zero column vector.
10. The truncated convolutional code optimal construction method as claimed in claim 9, wherein a shortened code of said spreading code is used for row column spreading corresponding to said spread check nodes located at both ends of said coupling chain in said check matrix.
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