CN106992842B - Multi-element domain data recovery method based on network coding and compressed sensing - Google Patents

Multi-element domain data recovery method based on network coding and compressed sensing Download PDF

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CN106992842B
CN106992842B CN201710250624.2A CN201710250624A CN106992842B CN 106992842 B CN106992842 B CN 106992842B CN 201710250624 A CN201710250624 A CN 201710250624A CN 106992842 B CN106992842 B CN 106992842B
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刘星成
曹凯
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National Sun Yat Sen University
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Abstract

The invention relates to a multi-domain Data Recovery method (NBDR-NC) Based on Network Coding and Compressed Sensing, which utilizes the sparsity of sensor node Data in a wireless sensor Network and the broadcast characteristic of wireless communication, and saves the energy required by Data transmission by compressing a source Data packet through compressing sparse Data; the probability of communication failure caused by the problem of a single wireless link is reduced by a mode of transmitting a data packet by a plurality of relay nodes, namely, one-transmission and multi-reception, and the transmission reliability of the data packet is improved; at a destination node (data fusion end), an iterative decoding algorithm of joint compressed sensing and network coding under a finite field is adopted for receiving a network compressed data packet, and source sparse data can be reconstructed with low complexity.

Description

Multi-element domain data recovery method based on network coding and compressed sensing
Technical Field
The invention relates to the field of wireless sensor networks, in particular to a multi-element domain data recovery method based on network coding and compressed sensing.
Background
Wireless Sensor Networks (WSNs) are crossed and integrated with high and new technologies such as embedded systems, Wireless communication technologies and computer Network technologies, and the application prospect is wide. In recent years, communication and protocol design of a wireless sensor network have been widely researched and are often applied to many hot research fields with great international attention, such as national defense and military, environmental monitoring, traffic management and the like, however, the wireless sensor network also has the characteristic that resources, such as node storage capacity, node energy and the like, are limited, and therefore, how to reduce the acquired data amount, thereby reducing the energy consumption of each node, increasing the communication capacity and data transmission reliability of the network and improving the service life of the network is a hot point of research.
The theory of network coding was proposed by Ahlswede and Cai et al in 2000, and it has profound influence on the research and practical application of the related theory of the network. Network coding is a special network data processing technology, which utilizes the characteristics of a broadcast communication channel to improve the throughput of a network and introduces diversity and redundancy to resist the dynamic change of a topological structure. In addition to transmitting and receiving data, the nodes of the network are allowed to encode a plurality of received data packets and then transmit the encoded data packets onto the communication links, supported by the wireless network coding technology. Wireless network coding may improve the throughput and robustness of the network. Li et al demonstrate: in a limited domain, multicast transmission can be made to maximum traffic by appropriate linear network coding, as long as the domain is large enough. Ho.t et al propose a random network coding method, i.e. an intermediate node randomly selects a set of elements as coefficients in a limited domain to code the received information, and prove that: the failure rate of this approach can be low as long as the finite field is large enough.
The compressive sensing theory is a new theory that the signal data can be properly compressed while sampling aiming at sparse or compressible signals, so that the compressive sensing theory has outstanding advantages and wide application prospect in the field of signal processing. In data acquisition and signal processing, the compressive sensing theory breaks through the limitation of the traditional Shannon theorem, and further development and innovation of the traditional theory are realized by changing the data acquisition mode; by utilizing the correlation among the data, the transmission and the storage of the data in the network are greatly reduced; and by combining with a proper routing protocol, the problems of communication capacity, delay, network life and the like of the whole network are improved.
The main task of a wireless sensor network is to collect the measurement data of the nodes and then transmit them to a sink node at a remote end. Sensor nodes are often deployed in unsupervised or even harsh environments, and due to obstacle interference, broken links or node faults and the like, the topological structure of the WSN network is often changed. In addition, most sensor data need to be transmitted in a multi-hop manner to reach the sink node, so when a transmission strategy of the wireless sensor network is designed, the main problem is that the broadcasting characteristic of the wireless sensor network can be fully utilized while the dynamic characteristic of the network is overcome, so that the high-efficiency transmission of the data is realized.
In 2005, Baron and Wakin et al developed a distributed compressed sensing framework and SOMP reconstruction algorithm for sensor data compression that takes advantage of both temporal and spatial correlation of signals to reduce sensor workload, but did not take into account transmission issues. Rabbat et al proposes a random projection compression scheme applied to a multi-level wireless sensor network, where the transmission scheme uses a simple Gossip routing algorithm, so that all random projections can fill the entire network, and the scheme has a certain adaptability to time-varying network topology and transmission link failures, but the process of aggregating information is time-consuming without applying a network coding technique. The view of combining network coding with compressed sensing has been previously proposed by sachinn katti and Shintre, but no implementation is given. Nguyen et al discloses a network compression coding (netcompression) scheme that utilizes random linear network coding techniques at neighboring source and intermediate nodes and employs a minimum-perceptive compression reconstruction method, however, the design of packet headers and the description of the mechanism for packet deletion are not clear. Li yun crane et al proposed a CNC scheme that designed the format of the data packets and the choice of encoding vectors, but did not propose an efficient algorithm in terms of decoding. In summary, in order to fully utilize the broadcast characteristics and data correlation of network coding and compressed sensing to the wireless sensor network, further improve the network throughput of the WSN, reduce the energy consumption required for data transmission, and reconstruct source data with high probability, it is necessary to design a practical and energy-efficient coding and joint iterative decoding algorithm for the wireless sensor network data transmission scenario.
Disclosure of Invention
In order to solve the defects of the prior art, the invention provides a Network Coding and compressed sensing-Based multi-domain Data Recovery method (NBDR-NC), which can save energy consumption required in the Data transmission process and improve energy efficiency in a wireless sensor Network.
In order to solve the technical problem, the patent comprises the following steps: the multi-element domain data recovery method based on network coding and compressed sensing mainly comprises the following three processing stages:
s1, source node sparse data encoding stage:
under the condition that the data packet meets sparsity, the source node performs compression coding on the data packet by adopting a compression sensing method under a finite field and sends a network coding measurement data packet after compression coding to the relay node;
s2, relay node recoding and forwarding stage:
the relay node processes all received network coding measurement data packets in a network recoding process, and then transmits the network coding measurement data packets to a target node (also called a data fusion end) through a multi-hop cooperative data transmission scheme;
s3, a destination node mixed iterative decoding stage:
and the target node reconstructs the data packet in the source node by adopting a hybrid network coding and compressed sensing iterative decoding method for the successfully received network coding measurement data packet.
Compared with the prior art, the method has the advantages that in the stage of source node sparse data coding, the energy required by the data packet to be transmitted at each relay node is saved and the energy consumption is reduced by performing compression coding on sparse data, namely, performing compression coding on the data packet; the data packet is received by the plurality of relay nodes and finally transmitted to the destination node of the destination cluster, and even if one or more transmission lines have problems, the data packet can be transmitted to the destination node through other lines, so that the reliability is good; in the stage of hybrid iterative decoding of the target node, the target node only needs to perform network decoding on the received data packet and then call a compressed sensing reconstruction algorithm under a finite field to reconstruct the source sparse data packet, so that the source sparse data can be reconstructed at low complexity, and the energy efficiency in the wireless sensor network is improved.
Further, the specific implementation steps of step S1 are as follows:
s11, compressed sensing of the source node: the sparse data x is set as an n-dimensional vector comprising k non-zero elements and n-k zero elements, and k<<n, each element belonging to the range of the finite field gf (q); measurement matrix phi of source node passing through m rows and n columnsm×nPerforming compression sampling on sparse data x to obtain a m × 1-dimensional measurement vector y, namely, y ═ Φm×nx, wherein m <n; each time the source node generates g measurement data packets, i.e. g measurement vectors Y, it is grouped into a measurement vector set Ym×g＝{y1,y2,...,ygG measurement data packets in the measurement vector set are used as data of one Generation to be grouped, the source node carries out network coding transmission according to the data group of each Generation, the Generation IDs of the data packets of the same Generation are distinguished by using the Generation IDs in the measurement data packet format, and the Generation IDs of the data packets of the same Generation are the same;
s12, source node network coding: randomly selecting g elements on GF (q) domain by a source node to form a g x 1-dimensional network coding column vector v ═ { v ═ v }1,v2,…,vg}TIs a reaction of Ym×gMultiplying v in GF (q) domain to obtain m x 1 dimensional network coding measurement vector C, namely Cm×1×Ym×g＝vg×1＝(y1,y2,…,yg)(v1,v2,…,vg)T＝(c1,c2,…,cm)T；
And S13, the source node packs v and C into a network coding measurement data packet and sends the network coding measurement data packet to the relay node in the source cluster.
Further, the specific implementation steps of step S2 are as follows:
s21, after successfully receiving the network coding measurement data packet, the relay node in the source cluster collaboratively distributes the network coding measurement data packet to the relay nodes in the middle clusters, a time slice is distributed to the relay node in each cluster, and the relay node in each middle cluster collaboratively transmits the network coding measurement data packet to the relay node in the next middle cluster according to a Time Division Multiple Access (TDMA) mode;
and S22, when the time slice of the previous-hop intermediate cluster is used up, the relay node of the current intermediate cluster carries out re-network coding on the received network coding measurement data packet, and sends the re-network coded network coding measurement data packet to the relay node in the target cluster.
Further, the implementation steps of the re-network coding in step S22 are as follows:
let each intermediate cluster have N relaysThe node combines g' network coding measurement data packets received by the relay node into a network coding measurement data set PR＝(PR1,PR2,...,PRg') Wherein g'<N, to PRPerforming a network recoding process: randomly selecting g' number { u } from GF (q) domain1,u2,…,ug’Forming a re-network coded column vector u ═ u1,u2,…,ug’}TFor all network coding measurement data packets P received by the relay nodeRiV in (1)RiAnd CRiPerforming linear combination over GF (q) -based domain, where i ═ 1,2, …, g', constitutes a new uTAnd CTThe concrete method is
Figure GDA0002251784120000061
And
Figure GDA0002251784120000062
and then packaging the data into a new network coding measurement data packet for sending.
Further, the step S3 is divided into a data receiving and collecting stage, a destination node network decoding stage, and a destination node compressed sensing data reconstruction stage, and the three stages are specifically implemented as follows:
s31, data receiving and gathering stage:
the relay nodes in the destination cluster transmit the received network coding measurement data packets to the destination node, a subscript symbol SR (SinkReceived) is used for representing the processing process of the destination node on the received data packet set, and when the destination node receives gSRA data packet, which is formed into a network coding measurement data set
Figure GDA0002251784120000063
And storing the data in a decoding buffer area;
s32, destination node network decoding stage:
separately fetch the sets PSRIn each network coding measurement data packet Pi(i＝1,2,…,gSR) G x 1 dimensional network coded column vector v in (1)i＝(vi1,vi2,…,vig)TAnd its corresponding m x 1 dimensional network coding measurement vector Ci＝(ci1,ci2,…,cim)TWherein i is 1,2, …, gSRForming the extracted network coding column vector into a network coding set USR(g×gSR)＝{v1,v2,...,vgSRAnd combining network coding measurement vectors in the data packets corresponding to the network coding column vectors into a measurement data set
Figure GDA0002251784120000071
Then U isSR、CSRAnd Y in step S1m×gHas the relationship of Ym×g·USR＝CSRExpressed as:
Figure GDA0002251784120000072
if set
Figure GDA0002251784120000073
Corresponding network coding matrix USR(g×gSR) If the matrix is a full rank matrix, the measured data vector set is obtained by decoding and recovering the network by a Gaussian elimination method
Figure GDA0002251784120000074
If the rank is not full, the data packet in the network coding measurement data set is lost, and the decoding stage exits;
s33, a target node compressed sensing data reconstruction stage:
to pair
Figure GDA0002251784120000075
Each set of measurement vectors y iniI is 1,2, …, g, sparse data reconstruction is performed, and the same sparse signal as the sparse data x in step S11 is obtained
Figure GDA0002251784120000076
And (5) vector quantity.
Further, the specific steps of sparse data reconstruction in step S33 are as follows:
using channel prior probability information
Figure GDA0002251784120000077
Initializing the constraint nodes, i.e.
Figure GDA0002251784120000078
Probability information corresponding by sparsity
Figure GDA0002251784120000079
Initializing variable nodes, i.e.
Figure GDA00022517841200000710
After all the variable nodes and the constraint nodes acquire information and complete information initialization, iterative update transfer of the information is started, and the update steps in each iteration are as follows:
s34, updating the variable nodes by using the constraint nodes, selecting the variable node number as n, updating all the edge messages from the constraint nodes M (n) adjacent to the variable node n C2V, and expressing as
Figure GDA0002251784120000081
S35, updating the constraint node by using the variable node, selecting the constraint node with the number m, and updating all the edge messages from the variable node N (m) adjacent to the constraint node m to the V2C of the constraint node m, namely
Figure GDA0002251784120000082
S36, making hard decision for the information of the current iteration, namely
Figure GDA0002251784120000083
Then to the judged
Figure GDA0002251784120000084
Checking when the signal is sparse
Figure GDA0002251784120000085
The vectors satisfy the constraint relation
Figure GDA0002251784120000086
And is
Figure GDA0002251784120000087
Successfully decoding, successfully reconstructing sparse data x, and exiting the decoding stage; when the constraint condition is not met and the current iteration number does not reach the maximum iteration number, continuing to perform iteration updating according to the steps; when the constraint condition is not met and the current iteration number reaches the maximum iteration number, the iterative decoding is quitted and the decoding fails;
wherein M (n) is the set of all constraint equations in which the variable node n participates;
n (m) \\ n represents a set of all variable nodes corresponding to the constraint equation corresponding to the constraint node m except the variable node n;
γmnis a normalization operation, i.e. guarantees
Figure GDA0002251784120000088
M (n) \ m represents the set of all constraint equations in which the variable node n participates, except for the constraint equation in which the constraint node m participates;
Figure GDA0002251784120000089
the mth measurement symbol of the measurement vector y takes the probability value of a, a belongs to GF (q), and a q-element Symmetric Channel (q-SC) is adopted for a transmission noise Channel, namely z is y + e, e represents noise and obeys pmDistribution of the mathematical formula
Figure GDA0002251784120000091
Wherein z ism,ymE.g. GF (q), e represents the channel transition probability of a q-element symmetric channel, with probability 1-e to successfully transmit a measurement symbol ymTransition to z with probability εm≠ym,zmE.g. GF (q) and z is related by the probability e/(q-1)mTransmit, at this time satisfy
Figure GDA0002251784120000092
Figure GDA0002251784120000093
As a sparse signal vector
Figure GDA0002251784120000094
The nth information symbol is taken as the probability value of a, a belongs to GF (q), and the probability value of the nonzero information symbol is related to the sparsity s of the sparse signal and is specifically expressed as
Figure GDA0002251784120000095
Wherein a belongs to GF (q) \\ 0 indicates that the element a is a nonzero element in GF (q), and the sparsity s is the ratio of the number k of the nonzero element of the n-dimensional sparse signal vector x to the dimension n;
Figure GDA0002251784120000096
in the ith iteration, the information transmitted to the variable node n by the constraint node m represents the probability that the constraint relation of the constraint node m is established on the premise that the value of the variable node n is known to be a and the information of other variable nodes is known;
Figure GDA0002251784120000097
in the ith iteration, a variable node n transmits information of a constraint node m and represents the probability that the variable node n is judged as a symbol a on the premise that constraint messages sent by other constraint nodes connected with the variable node n are known;
each element of the measurement vector y is called a constraint node and corresponds to a constraint equation, and m constraint equations are total1＝Φ1×x,y2＝Φ2×x,...,ym＝ΦmX, wherein, phiiRepresenting the measurement matrix phim×nI-1, 2, …, m, sparse signal
Figure GDA0002251784120000098
The vector is n-dimensional and comprises k non-zero elements and n-k zero elements, k<<n, where each element is called a variable node and belongs to gf (q).
The invention has the beneficial effects that:
1. the source data packets are compressed by compressing the sparse data, so that energy required by data transmission is saved;
2. the data packet is transmitted from the source node in the source cluster to the plurality of relay nodes and finally reaches the destination node, the probability of communication failure caused by the problem of a single wireless link is reduced by a one-transmission and multiple-reception mode, and the transmission reliability of the data packet is improved;
3. in a destination node, an iterative decoding algorithm of joint compressed sensing and network coding under a finite field is adopted for receiving a network compressed data packet, namely, source sparse data is reconstructed with low complexity, and the energy efficiency in a wireless sensor network is improved.
Drawings
FIG. 1 is a flow chart of the method of the present invention;
FIG. 2 is a block diagram of wireless sensor network data transmission;
FIG. 3 is a diagram of a network coded packet format;
FIG. 4 is a relay node (intermediate cluster) re-encoding block diagram;
FIG. 5 is a flow chart of a hybrid decoding phase of a destination node;
FIG. 6 is a flow chart of iterative update of a sparse signal x vector;
FIG. 7 is a graph of noiseless network coded compressed packet performance;
figure 8 is a graph of noisy network coded compressed packet performance.
Detailed Description
The following detailed description of the present patent refers to the accompanying drawings and the accompanying examples.
Interpretation of the symbols appearing in the examples:
wherein M (n) is the set of all constraint equations in which the variable node n participates;
n (m) \\ n represents a set of all variable nodes corresponding to the constraint equation corresponding to the constraint node m except the variable node n;
Figure GDA0002251784120000111
in the ith iteration, the information transmitted to the variable node n by the constraint node m represents the probability that the constraint relation of the constraint node m is established on the premise that the value of the variable node n is known to be a and the information of other variable nodes is known;
Figure GDA0002251784120000112
in the ith iteration, the variable node n transmits the information of the constraint node m and represents the probability that the variable node n is judged as the symbol a on the premise that constraint messages sent by other constraint nodes connected with the variable node n are known;
Figure GDA0002251784120000113
the mth measurement symbol of the measurement vector y takes the probability value of a, a belongs to GF (q), and a q-element symmetric channel (q-SC) is adopted for a transmission noise channel, namely z is y + e, e represents noise and obeys pmDistribution of the mathematical formula
Figure GDA0002251784120000114
Wherein z ism,ymE.g. GF (q), e represents the channel transition probability of a q-element symmetric channel, with probability 1-e to successfully transmit a measurement symbol ymTransition to z with probability εm≠ym,zmE.g. GF (q) and z is related by the probability e/(q-1)mTransmit, at this time satisfy
Figure GDA0002251784120000115
Figure GDA0002251784120000116
The value of the probability value of an nth information symbol of a sparse signal vector x is aGF (q) and the probability value of the non-zero information symbol is related to the sparsity s of the sparse signal, expressed in particular as
Figure GDA0002251784120000117
Wherein a belongs to GF (q) \\ 0 indicates that the element a is a nonzero element in GF (q), and the sparsity s is the ratio of the number k of the nonzero element of the n-dimensional sparse signal vector x to the dimension n;
γmnis a normalization operation, i.e. guarantees
Figure GDA0002251784120000118
M (n) \ m represents the set of all constraint equations in which the variable node n participates, except for the constraint equation in which the constraint node m participates;
as shown in fig. 1 and 2, in a Network Coding and Compressed Sensing-Based multi-domain data Recovery method (NBDR-NC) as shown in fig. 1 and 2, a data processing process mainly includes the following three processing stages:
s1, source node sparse data encoding stage:
under the condition that the data packet meets sparsity, the source node performs compression coding on the data packet by adopting a compression sensing method under a finite field, and transmits a network coding measurement data packet after compression coding to the relay node through the wireless transmitting module;
s2, relay node recoding and forwarding stage:
the relay node processes all received network coding measurement data packets in a network recoding process, and then transmits the network coding measurement data packets to a target node (also called a data fusion end) through a multi-hop cooperative data transmission scheme;
s3, a destination node mixed iterative decoding stage:
and the target node reconstructs the data packet in the source node by adopting a hybrid network coding and compressed sensing iterative decoding method for the successfully received network coding measurement data packet.
In the stage of encoding the sparse data of the source node, the compressed encoding of the sparse data, namely the compressed encoding of the data packet, is carried out, so that the energy required by the data packet for transmission at each relay node is saved, and the energy consumption is reduced; the data packet is received by the plurality of relay nodes and finally transmitted to the destination node of the destination cluster, and even if one or more transmission lines have problems, the data packet can be transmitted to the destination node through other lines, so that the reliability is good; in the stage of hybrid iterative decoding of the target node, the target node only needs to perform network decoding on the received data packet and then call a compressed sensing reconstruction algorithm under a finite field to reconstruct the source sparse data packet, so that the source sparse data can be reconstructed at low complexity, and the energy efficiency in the wireless sensor network is improved.
In the scheme of the invention, the specific steps of data processing in each stage are described as follows:
s1, source node sparse data encoding stage:
s11, compressed sensing of the source node: the sparse data x is set as an n-dimensional vector comprising k non-zero elements and n-k zero elements, and k<<n, each element belonging to the range of the finite field gf (q); measurement matrix phi of source node passing through m rows and n columnsm×nPerforming compression sampling on sparse data x to obtain a m × 1-dimensional measurement vector y, namely, y ═ Φm×nx, wherein m < n; each time the source node generates g measurement data packets, i.e. g measurement vectors Y, it is grouped into a measurement vector set Ym×g＝{y1,y2,...,ygG measurement packets in the measurement vector set are grouped as data of one Generation, as shown in fig. 3, the source node performs network coding transmission according to the data packet of each Generation, distinguishes different generations by using the Generation ID in the measurement packet format, and the Generation IDs of the packets of the same Generation are the same;
s12, source node network coding: randomly selecting g element groups on GF (q) field by source node
Network coding column vector v ═ { v ═ v of dimension g × 11,v2,…,vg}TIs a reaction of Ym×gMultiplying v in GF (q) domain to obtain m x 1 dimensional network coding measurement vector C, namely Cm×1×Ym×g＝vg×1＝(y1,y2,…,yg)(v1,v2,…,vg)T＝(c1,c2,…,cm)T；
S13, the source node packs the network coding column vector v and the network coding measurement vector C into a network coding measurement data packet and broadcasts the network coding measurement data packet to the relay node in the source cluster;
s2, relay node recoding and forwarding stage:
s21, after successfully receiving the network coding measurement data packet, the relay node in the source cluster collaboratively distributes the network coding measurement data packet to the relay nodes in the middle clusters, a time slice is distributed to the relay node in each cluster, and the relay node in each middle cluster collaboratively transmits the network coding measurement data packet to the relay node in the next middle cluster according to a Time Division Multiple Access (TDMA) mode;
s22, when the time slice of the previous-hop intermediate cluster is used up, the relay node of the current intermediate cluster performs re-network coding on the received network coding measurement packet, and sends the re-network coded network coding measurement packet to the relay node in the destination cluster, as shown in fig. 4, where the specific steps of re-network coding are as follows:
setting N relay nodes in each intermediate cluster, and forming a network coding measurement data set P by g' network coding measurement data packets received by the relay nodesR＝(PR1,PR2,...,PRg') Wherein g'<N, to PRPerforming a network recoding process: randomly selecting g' number { u } from GF (q) domain1,u2,…,ug' } forming a re-network coded column vector u ═ u1,u2,…,ug’H, measuring data packet P for all network codes received by the relay nodeRiV in (1)RiAnd CRiPerforming linear combination over GF (q) -based domain, where i ═ 1,2, …, g', constitutes a new uTAnd CTThe concrete method is
Figure GDA0002251784120000141
And
Figure GDA0002251784120000142
and then packaging the data into a new network coding measurement data packet for sending.
As shown in fig. 5, step S3 is divided into a data receiving and collecting stage, a destination node network decoding stage, and a destination node compressed sensing data reconstruction stage, and the three stages are specifically implemented as follows:
s31, data receiving and gathering stage:
the relay nodes in the destination cluster all forward the received network coding measurement data packet to the destination node, and when the destination node receives gSRA data packet, which is formed into a network coding measurement data set
Figure GDA0002251784120000143
And storing the data packet into a decoding buffer area, wherein a subscript symbol SR (SinkReceived) represents the processing process of a destination node for receiving a data packet set so as to distinguish the mentioned data packet set;
s32, destination node network decoding stage:
separately fetch the sets PSRIn each network coding measurement data packet Pi(i＝1,2,…,gSR) G x 1 dimensional network coded column vector v in (1)i＝(vi1,vi2,…,vig)TAnd its corresponding m x 1 dimensional network coding measurement vector Ci＝(ci1,ci2,…,cim)TWherein i is 1,2, …, gSRForming the extracted network coding column vector into a network coding set
Figure GDA0002251784120000151
And combining the network coding measurement vectors in the data packet corresponding to the network coding column vector into a measurement data set
Figure GDA0002251784120000152
Then U isSR、CSRAnd Y in step S1m×gHas the relationship of Ym×g·USR＝CSRExpressed as:
Figure GDA0002251784120000153
if set
Figure GDA0002251784120000154
Corresponding network coding matrix USR(g×gSR) If the matrix is a full rank matrix, the measured data vector set is obtained by decoding and recovering the network by a Gaussian elimination method
Figure GDA0002251784120000155
If the rank is not full, the data packet in the network coding measurement data set is lost, and the decoding stage exits;
s33, a target node compressed sensing data reconstruction stage:
as shown in fig. 6, for
Figure GDA0002251784120000156
Each set of measurement vectors y ini I 1,2, …, g, performing sparse data reconstruction: using channel prior probability information
Figure GDA0002251784120000157
The constraint nodes (square nodes in FIG. 6) are initialized, i.e.
Figure GDA0002251784120000158
Probability information corresponding by sparsity
Figure GDA0002251784120000159
Initializing variable nodes (circle nodes in FIG. 6), i.e.
Figure GDA00022517841200001510
After all the variable nodes and the constraint nodes acquire information and complete information initialization, iterative update transfer of the information is started, and the update steps in each iteration are as follows:
s34, updating the variable nodes by using the constraint nodes, and selecting the variable node number to be recorded asn, updating all the constraint nodes M (n) adjacent to the variable node n to the edge message of C2V of the variable node n, as shown in FIG. 5 when the message is passed in the arrow downward direction, which is shown as
Figure GDA0002251784120000161
S35, updating the constraint node by using the variable node, selecting the constraint node with the number m, and updating all the edge messages from the variable node N (m) adjacent to the constraint node m to the V2C of the constraint node m, namely
Figure GDA0002251784120000162
S36, making hard decision for the information of the current iteration, namely
Figure GDA0002251784120000163
Then to the judged
Figure GDA0002251784120000164
Checking when the sparse signal vector satisfies the constraint relation
Figure GDA0002251784120000165
Successfully decoding, successfully reconstructing sparse data x, and exiting the decoding stage; when the constraint condition is not met and the current iteration number does not reach the maximum iteration number MaxIter, continuing to perform iteration updating according to the steps; and when the constraint condition is not met and the current iteration number reaches the maximum iteration number, the iterative decoding is quitted and the decoding fails.
To sum up, the transmission scheme of the present invention adopts a data transmission scheme based on a multi-hop cooperative cluster, and after a source node completes network coding and data packing, a data packet is transmitted from the source node to a destination node, that is, to a data fusion terminal, as shown in fig. 2, it is assumed that node forwarding of each cluster is allocated to obtain its own forwarding Time slot in a Time Division Multiple Access (TDMA) manner, and the number of relay nodes of each cluster is the same and is N. Firstly, a source node broadcasts a data packet to a relay node of a source cluster, then the relay node in the source cluster forwards an encoded data packet to a relay node of an intermediate cluster in a forwarding time slot of the relay node, the relay node in the intermediate cluster carries out network recoding on the data packet after receiving the data packet of the previous cluster, and then the relay node in the intermediate cluster continuously forwards the encoded data packet until the data packet is forwarded to the relay node in a target cluster. And finally, after the destination node in the destination cluster collects the data packet forwarded by the relay node in the cluster, the destination node reconstructs the source data of the successfully received data packet by adopting a hybrid network coding and compressed sensing iterative decoding method.
In fig. 2, a transmission scheme connected by a solid line describes a Store-and-Forward (SF) mode of Compressed Sensing (SFCS) scheme, and a combination of a solid line and a dotted line describes the inventive scheme NBDR-NC. For convenience, hereinafter, SF and SFCS are referred to as direct-propagation and direct-propagation compressed sensing, respectively.
In the multi-hop cooperation (hop count hp is 3, and number of cooperative nodes N is 3) transmission process, sparse signal vector is 512 symbols in 16-ary system, and sparse signal is recovered by using a measurement matrix with compression rate 1/2, i.e. row number m is 256 and column number N is 512 and a measurement vector with length 256, here, the scheme NBDR-NC is mainly compared with the conventional direct transmission scheme SFCS. As shown in fig. 7, the decoding performance of the noise-free measurement vector at the recovery percentage vs sparsity level is improved in NBDR-NC compared to the conventional direct transfer scheme SFCS when the same number of noise-free measurement vectors are received. As shown in fig. 8, the decoding performance of the noise-carrying measurement vector at the recovery percentage vs sparsity level is better than that of the conventional direct transmission scheme SFCS 5% -15% in the NBDR-NC performance when the same number of noise-carrying (i.e., the channel transition probability epsilon of q-ary symmetric channel is 0.1) measurement vectors are received. In other words, the NBDR-NC consumes less energy than the FWCS scheme, satisfying the same reliability condition in a noisy environment, and thus the energy efficiency of the scheme is superior to that of the direct transfer scheme SFCS.

Claims (5)

1. The method for recovering the multi-element domain data based on network coding and compressed sensing is characterized in that the data processing process comprises the following steps:
s1, source node sparse data encoding stage:
under the condition that the data packet meets sparsity, the source node performs compression coding on the data packet by adopting a compression sensing method under a finite field and sends a network coding measurement data packet after compression coding to the relay node;
s11, compressed sensing of the source node: the sparse data x is set as n-dimensional vector containing k nonzero elements and n-k zero elements, and k < n, each element belonging to the range of finite field GF (q); measurement matrix phi of source node passing through m rows and n columnsm×nPerforming compression sampling on sparse data x to obtain a m × 1-dimensional measurement vector y, namely, y ═ Φm×nx, wherein m < n; each time the source node generates g measurement data packets, i.e. g measurement vectors Y, it is grouped into a measurement vector set Ym×g＝{y1，y2，...，ygG measurement data packets in the measurement vector set are used as data of one generation to be grouped, and the source node carries out network coding transmission according to the data groups of each generation;
s12, source node network coding: randomly selecting g elements on GF (q) domain by a source node to form a g x 1-dimensional network coding column vector v ═ { v ═ v }1，v2，...，vg}TIs a reaction of Ym×gMultiplying v in GF (q) domain to obtain m x 1 dimensional network coding measurement vector C, i.e.
Cm×1＝Ym×g×vg×1＝(y1，y2，...，yg)(v1，v2，...，vg)T＝(c1，c2，...，cm)T；
S13, the source node packs v and C into a network coding measurement data packet and sends the network coding measurement data packet to the relay node in the source cluster;
s2, relay node recoding and forwarding stage:
the relay node processes all received network coding measurement data packets in a network recoding process, and then transmits the network coding measurement data packets to a target node through a multi-hop cooperative data transmission scheme;
s3, a destination node mixed iterative decoding stage:
and the target node reconstructs the data packet in the source node by adopting a hybrid network coding and compressed sensing iterative decoding method for the successfully received network coding measurement data packet.
2. The method for recovering multi-element domain data based on network coding and compressed sensing according to claim 1, wherein the step S2 is implemented as follows:
s21, after successfully receiving the network coding measurement data packet, the relay node in the source cluster collaboratively distributes the network coding measurement data packet to the relay nodes in the middle clusters, a time slice is distributed to the relay node in each cluster, and the relay node in each middle cluster collaboratively transmits the network coding measurement data packet to the relay node in the next middle cluster in a time division multiple access mode;
and S22, when the time slice of the previous-hop intermediate cluster is used up, the relay node of the current intermediate cluster carries out re-network coding on the received network coding measurement data packet, and sends the re-network coded network coding measurement data packet to the relay node in the target cluster.
3. The method for recovering network-coding and compressed sensing-based multi-element domain data according to claim 2, wherein the step S22 of implementing the re-network coding comprises the following steps:
setting N relay nodes in each intermediate cluster, and forming a network coding measurement data set P by g' network coding measurement data packets received by the relay nodesR＝(PR1,PR2,...,PRg') Wherein g'<N, to PRPerforming a network recoding process: randomly selecting g' number { u } from GF (q) domain1,u2,…,ug’Forming a re-network coded column vector u ═ u1,u2,…,ug’}TFor all network coding measurement data packets P received by the relay nodeRiV in (1)RiAnd CRiPerforming linear combination over GF (q) -based domain, where i ═ 1,2, …, g', constitutes a new uTAnd CTThe concrete method is
Figure FDA0002281338060000031
And
Figure FDA0002281338060000032
and then packaging the data into a new network coding measurement data packet for sending.
4. The method for recovering data in multiple domains based on network coding and compressive sensing as claimed in claim 3, wherein the step S3 is divided into a data receiving and collecting stage, a destination node network decoding stage, and a destination node compressive sensing data reconstruction stage, and the three stages are implemented as follows:
s31, data receiving and gathering stage:
the relay nodes in the destination cluster all forward the received network coding measurement data packet to the destination node, and when the destination node receives gSREach network coding measurement data packet is formed into a network coding measurement data set
Figure FDA0002281338060000033
And storing the data in a decoding buffer area;
s32, destination node network decoding stage:
separately fetch the sets PSRIn each network coding measurement data packet Pi(i＝1,2,…,gSR) G x 1 dimensional network coded column vector v in (1)i＝(vi1,vi2,…,vig)TAnd its corresponding m x 1 dimensional network coding measurement vector Ci＝(ci1,ci2,…,cim)TWherein i is 1,2, …, gSRForming the extracted network coding column vector into a network coding set
Figure FDA0002281338060000034
And combining the network coding measurement vectors in the data packet corresponding to the network coding column vector into a measurement data set
Figure FDA0002281338060000035
Then U isSR、CSRAnd Y in step S11m×gHas the relationship of Ym×g·USR＝CSRExpressed as:
Figure FDA0002281338060000041
if set
Figure FDA0002281338060000042
Corresponding network coding matrix USR(g×gSR) If the matrix is a full rank matrix, the measured data vector set is obtained by decoding and recovering the network by a Gaussian elimination method
Figure FDA0002281338060000043
If not, quitting the decoding stage;
s33, a target node compressed sensing data reconstruction stage:
to pair
Figure FDA0002281338060000044
Each set of measurement vectors y iniI is 1,2, …, g, sparse data reconstruction is performed, and the same sparse signal as the sparse data x in step S11 is obtained
Figure FDA0002281338060000045
And (5) vector quantity.
5. The method for recovering network coding and compressed sensing-based multi-element domain data according to claim 4, wherein the specific steps of sparse data reconstruction in the step S33 are as follows:
using channel prior probability information
Figure FDA0002281338060000046
Initializing the constraint nodes, i.e.
Figure FDA0002281338060000047
Probability information corresponding by sparsity
Figure FDA0002281338060000048
Initializing variable nodes, i.e.
Figure FDA0002281338060000049
After all the variable nodes and the constraint nodes acquire information and complete information initialization, iterative update transfer of the information is started, and the update steps in each iteration are as follows:
s34, updating the variable nodes by using the constraint nodes, selecting the variable node number as n, updating all the edge messages from the constraint nodes M (n) adjacent to the variable node n C2V, and expressing as
Figure FDA00022813380600000410
S35, updating the constraint node by using the variable node, selecting the constraint node with the number m, and updating all the edge messages from the variable node N (m) adjacent to the constraint node m to the V2C of the constraint node m, namely
Figure FDA0002281338060000051
S36, making hard decision for the information of the current iteration, namely
Figure FDA0002281338060000052
Then to the judged
Figure FDA0002281338060000053
Checking when the signal is sparse
Figure FDA0002281338060000054
The vectors satisfy the constraint relation
Figure FDA0002281338060000055
And is
Figure FDA0002281338060000056
Successfully decoding, successfully reconstructing sparse data x, and exiting the decoding stage; when the constraint condition is not met and the current iteration number does not reach the maximum iteration number, continuing to perform iteration updating according to the steps; when the constraint condition is not met and the current iteration number reaches the maximum iteration number, the iterative decoding is quitted and the decoding fails;
wherein M (n) is the set of all constraint equations in which the variable node n participates;
n (m) \\ n represents a set of all variable nodes corresponding to the constraint equation corresponding to the constraint node m except the variable node n;
γmnis a normalization operation, i.e. guarantees
Figure FDA0002281338060000057
M (n) \ m represents the set of all constraint equations in which the variable node n participates, except for the constraint equation in which the constraint node m participates;
Figure FDA0002281338060000058
the mth measurement symbol of the measurement vector y takes the probability value of a, a belongs to GF (q), and the transmission noise channel adopts a q-element symmetric channel, namely z is y + e, e represents noise and obeys pmDistribution of the mathematical formula
Figure FDA0002281338060000059
Wherein z ism,ymE.g. GF (q), e represents the channel transition probability of a q-element symmetric channel, with probability 1-e to successfully transmit a measurement symbol ymTransition to z with probability εm≠ym,zmE.g. GF (q) and z is related by the probability e/(q-1)mTransmit, at this time satisfy
Figure FDA0002281338060000061
Figure FDA0002281338060000062
As a sparse signal vector
Figure FDA0002281338060000063
The nth information symbol is taken as the probability value of a, a belongs to GF (q), and the probability value of the nonzero information symbol is related to the sparsity s of the sparse signal and is specifically expressed as
Figure FDA0002281338060000064
Wherein a belongs to GF (q) \\ 0 indicates that the element a is a nonzero element in GF (q), and the sparsity s is the ratio of the number k of the nonzero element of the n-dimensional sparse signal vector x to the dimension n;
Figure FDA0002281338060000065
in the ith iteration, the information transmitted to the variable node n by the constraint node m represents the probability that the constraint relation of the constraint node m is established on the premise that the value of the variable node n is known to be a and the information of other variable nodes is known;
Figure FDA0002281338060000066
in the ith iteration, a variable node n transmits information of a constraint node m and represents the probability that the variable node n is judged as a symbol a on the premise that constraint messages sent by other constraint nodes connected with the variable node n are known;
each element of the measurement vector y is called a constraint node and corresponds to a constraint equation, and m constraint equations are total1＝Φ1×x,y2＝Φ2×x,...,ym＝ΦmX, wherein, phiiRepresenting the measurement matrix phim×nI-1, 2, …, m, sparse signal
Figure FDA0002281338060000067
The vector is n-dimensional and comprises k non-zero elements and n-k zero elements, k<<n, where each element is called a variable node and belongs to gf (q).
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