CN107294540A - Coding method and device, interpretation method and device - Google Patents
Coding method and device, interpretation method and device Download PDFInfo
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- CN107294540A CN107294540A CN201610221921.XA CN201610221921A CN107294540A CN 107294540 A CN107294540 A CN 107294540A CN 201610221921 A CN201610221921 A CN 201610221921A CN 107294540 A CN107294540 A CN 107294540A
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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
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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
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- Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
- Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
- Y02D—CLIMATE CHANGE MITIGATION TECHNOLOGIES IN INFORMATION AND COMMUNICATION TECHNOLOGIES [ICT], I.E. INFORMATION AND COMMUNICATION TECHNOLOGIES AIMING AT THE REDUCTION OF THEIR OWN ENERGY USE
- Y02D30/00—Reducing energy consumption in communication networks
- Y02D30/70—Reducing energy consumption in communication networks in wireless communication networks
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Abstract
The invention provides a kind of coding method and device, interpretation method and device, wherein, the coding method includes：Message to be sent is obtained, wherein, the message to be sent includes：The true messages of k bits, the random message of (l k) bit, wherein l, k are natural number；The message to be sent is encoded according to check matrix H, code word r is obtainedn+k, wherein, the n is the code word size of the true messages, and the check matrix H meets following condition：rn+kHT=0；Send code word rn+k.Using above-mentioned technical proposal, the problem of implication in information theory is safe can not be reached by solving coding techniques, realize safe coding decoding.
Description
Technical field
The present invention relates to the communications field, in particular to a kind of coding method and device, interpretation method and device.
Background technology
In the related art, although just defining the performance of channel coding early in Shannon's theorems in 1984, but until
Before turbine Turbo code occurs within 1993, most of channel coding algorithms are all far away from shannon limit.So, the birth of Turbo code
Mean beginning of the channel coding close to shannon limit in additive white Gaussian noise channel.After the two years, mikey Mackay and
Neil Neal is rediscovered by the inspiration of Turbo code, the loe-density parity-check code (Low ignored since some time by people
Density Parity Check code, referred to as LDPC), there is the performance closer to shannon limit.LDPC code is 1962
What year was proposed by Gallager, this code that he is proposed is a kind of linear block codes based on sparse check matrix.
Gallager illustrates the building method of LDPC code, iteration probability decoding algorithm and its theoretical description.But because its
Coding and decoding need higher hsrdware requirements, and at that time BCH code, Reed-Solomon codes and concatenated code show it is simple
And efficient performance, except a small number of researchers, such as outside Pinsker and Margulis, researchers and less
LDPC code is paid close attention to, is even almost forgotten.
In eighties of last century the nineties, MacKay et al. is had found again to low density parity check code, and is proved
When being communicated with the arbitrary bit rate less than shannon limit, based on maximum posteriori decoding (Maximum A
Posteriori, referred to as MAP) algorithm LDPC code decoding error probability as little as 10-7, it is in close proximity to 0.
Regrettably, the optimal decoding algorithm of LDPC code is (a Non-deterministic Polynomial, abbreviation
For NP) complete problem (difficult problem of nonpolynomial time).MacKay also demonstrates Gallager decoding algorithms simultaneously to be had
Outstanding experience performance.Luby et al. have studied discovery after erasure channel (Erasure Channel), LDPC code can compared with
The decoding of low complex degree is issued to channel capacity, and proposes a kind of simple linear time decoding calculation in erasure channel
Method.The Major research field of current LDPC code concentrates on four different aspects, and they are respectively：The construction of check matrix, translate
Code algorithm optimization, the application of the analysis of performance and LDPC code in systems in practice.
The security of communication system is analyzed from the angle of information theory will trace back to 1949, and Shannon has delivered one in the year
A piece is entitled《The communication theory of secrecy system》Important article, gone with information theory to analyze communication system security so as to establish
Basis.After this, Wyner and its partner propose two class tapping channel models：First kind tapping channel (wiretap
Channel I) and Equations of The Second Kind tapping channel (wiretap channel of type II).
In first kind tapping channel model, sender wants to pass confidential information by the main channel of a discrete memoryless
Give legitimate receiver.At the same time, a listener-in attempts to eavesdrop by the tapping channel of another discrete memoryless
The output of main channel.Wyner with conditional entropy H (W | ZN) represent that (W is sends out to listener-in here to the doubt degree of confidential information
The confidential information sent, ZNFor the output of tapping channel), i.e. safety is weighed in this doubt degree first kind tapping channel model
The important parameter of property.Wyner is featured by all reachable efficiency of transmission-doubt degree to the region constituted, and we are generally this
It is all reachable that individual region, which is called points all in capacity-doubt degree region, i.e. this region, and point all outside region is all
It is inaccessible.On this basis, Wyner is defined and is featured safe capacity this concept, that is, is ensureing the doubt degree of listener-in
The maximum of efficiency of transmission in the case of maximum.In Wyner systematic analyses communication system between efficiency of transmission and security
Trade-off relation (i.e. the security of communication system and maximize transmission can not be guaranteed simultaneously), this has been established is gone point with information theory
Analyse the basis of relation between communication system security and efficiency of transmission.In the existence proof in capacity-doubt degree region,
Wyner proposes the coding techniques of random vanning (random binning).In the channel model for considering safety, the technology is
Through as a kind of most common coding techniques.Random vanning refers to the message sent and a code book (collection for a pile code word composition
Close) correspond.When sender sends a specific message, the code book corresponding with this message, Ran Housui are found out first
Choose a code word in this code book to send, the output of the code word just as encoder machine.
After Wyner proposes first kind tapping channel model soon, he and Ozarow have also been proposed one and simplified
Tapping channel model, i.e. Equations of The Second Kind tapping channel model.In Equations of The Second Kind tapping channel model, main channel is without making an uproar, together
When the code word of N length that can be exported from main channel of listener-in in arbitrarily choose μ and carry out nothings and make an uproar eavesdropping, namely listener-in can be with
Obtain arbitrary μ in the code word of N length.Wyner and Ozarow give capacity-doubt degree area of Equations of The Second Kind tapping channel model
Domain.
After first and second class tapping channel model is proposed, the actual code word that can approach implication in information theory safety of construction is just
Become one new research direction of coding field.In the research of Equations of The Second Kind tapping channel model, by specifically calculating eavesdropping
The doubt degree of person, V.K.Wei and Forney propose the concept of Generalized Hamming Weight.The proposition of Generalized Hamming Weight is second
Reach that the construction of the actual coding scheme of implication in information theory safety specifies direction in class tapping channel model.When tapping channel is
Gaussian noise, is that any one holds up to tapping channel using coset encoding scheme and subcode in the case of main channel is muting
During the dual code of the good code of amount, the safety on implication in information theory can be reached.In first kind tapping channel model based coding scheme
In research, Thangaraj points out that the code for meeting specific structure can make system reach the safety on implication in information theory.
The problem of implication in information theory is safe can not be reached for the coding techniques in correlation technique, there is presently no effectively
Solution.
The content of the invention
The invention provides a kind of coding method and device, interpretation method and device, at least to solve to compile in correlation technique
Code technology can not reach the problem of implication in information theory is safe.
According to an aspect of the invention, there is provided a kind of coding method, including：
Message to be sent is obtained, wherein, the message to be sent includes：The true messages of k bits, (l-k) bit with
Machine message, wherein l, k are natural number；
The message to be sent is encoded according to check matrix H, code word r is obtainedn+k, wherein, the n is described true
The code word size of real message, the check matrix H meets following condition：rn+kHT=0；
Send the code word rn+k。
Further,
The check matrix H is that code word size is n+k bits, and message-length is the low-density checksum of l bits
The check matrix of code LDPC code, wherein, k<l<n+k.
Further, the random message of (l-k) bit described in determining in the following manner：
Randomly generate the random message of (l-k) bit；
Generator matrix generation and the random message pair of the random message of (l-k) bit by linear block codes by described in
The code word answered.
Further, the code word r is sentn+kBefore, methods described also includes one below：
The code word rn+kIt is divided into 2kIndividual subcode, the message of each one k bit length of the subcode correspondence；
A code word transmission is randomly selected from the subcode corresponding to the k bits true messages；
Determine the code word rn+kActual transfer rate be less than main channel channel capacity, and the subcode reality
Transmission rate is equal to the channel capacity of tapping channel.
Further, the code word r is determined in the following mannern+kActual transfer rate be less than main channel channel hold
Amount, and the subcode actual transfer rate be equal to tapping channel channel capacity：
Wherein, the actual transfer rate of the subcode isThe code word rn+kActual transfer rate be
It is the noise variance of main channel Gaussian noise,It is the noise variance of tapping channel noise, P is the code word rn+kTransmission work(
Rate, the channel capacity maxI (X of main channel；Y) it isChannel capacity maxI (the X of tapping channel；Z) it is
Further, the code word r is solvedn+kMode include：
By rn+kHT=0 draws (cn+k-l, sk,dl-k)HT=0, solve cn+k-l, wherein, the skFor the true messages to
Amount, the dl-kFor random message vector, the cn+k-lThe check bit of n+k-l bits after presentation code；
According to an aspect of the invention, there is provided a kind of interpretation method, including：
Receive code word rn+k, wherein, the code word rn+kFor the code word obtained in the following manner：According to check matrix H pair
Message to be sent is encoded, and obtains code word rn+k, wherein, the message to be sent includes：The true messages of k bits, (l-k)
The random message of bit, wherein l, k are natural number, and the n is the code word size of the true messages, the check matrix H
Meet following condition：rn+kHT=0；
Parse the code word rn+k。
According to another aspect of the present invention there is provided a kind of code device, including：
First acquisition module, for obtaining message to be sent, wherein, the message to be sent includes：The true of k bits disappears
Breath, the random message of (l-k) bit, wherein l, k is natural number；
Second acquisition module, for being encoded according to check matrix H to the message to be sent, obtains code word rn+k, its
In, the n is the code word size of the true messages, and the check matrix H meets following condition：rn+kHT=0；
Sending module, for sending the code word rn+k。
Further, the code word r is solvedn+kMode include：
By rn+kHT=0 draws (cn+k-l, sk,dl-k)HT=0, solve cn+k-l, wherein, the skFor the true messages to
Amount, the dl-kFor random message vector, the cn+k-lThe check bit of n+k-l bits after presentation code；
According to another aspect of the present invention there is provided a kind of code translator, including：
Receiving module, for receiving code word rn+k, wherein, the code word rn+kFor the code word obtained in the following manner：According to
Message to be sent is encoded according to check matrix H, code word r is obtainedn+k, wherein, the message to be sent includes：K bits it is true
Real message, the random message of (l-k) bit, wherein l, k is natural number, and the n is the code word size of the true messages, institute
State check matrix H and meet following condition：rn+kHT=0；
Parsing module, for parsing the code word rn+k。
By the present invention, message to be sent is obtained, wherein, the message to be sent includes：The true messages of k bits, (l-k)
The random message of bit, wherein l, k are natural number；The message to be sent is encoded according to check matrix H, code word is obtained
rn+k, wherein, the n is the code word size of the true messages, and the check matrix H meets following condition：rn+kHT=0；Send the code
Word rn+k.The problem of implication in information theory is safe can not be reached by solving coding techniques, realize safe coding decoding.
Brief description of the drawings
Accompanying drawing described herein is used for providing a further understanding of the present invention, constitutes the part of the application, this hair
Bright schematic description and description is used to explain the present invention, does not constitute inappropriate limitation of the present invention.In the accompanying drawings：
Fig. 1 is a kind of flow chart of coding method according to embodiments of the present invention；
Fig. 2 is a kind of flow chart of interpretation method according to embodiments of the present invention；
Fig. 3 is a kind of structured flowchart of code device according to embodiments of the present invention；
Fig. 4 is a kind of structured flowchart of code translator according to embodiments of the present invention；
Fig. 5 is applicable channel model schematic diagram according to the preferred embodiment of the invention；
Fig. 6 is the encoder building method schematic diagram designed according to the preferred embodiment of the present invention；
Fig. 7 is curve map according to the preferred embodiment of the invention.
Embodiment
Describe the present invention in detail below with reference to accompanying drawing and in conjunction with the embodiments.It should be noted that not conflicting
In the case of, the feature in embodiment and embodiment in the application can be mutually combined.
It should be noted that term " first " in description and claims of this specification and above-mentioned accompanying drawing, "
Two " etc. be for distinguishing similar object, without for describing specific order or precedence.
A kind of coding method is provided in the present embodiment, and Fig. 1 is a kind of coding method according to embodiments of the present invention
Flow chart, as shown in figure 1, the flow comprises the following steps：
Step S102, obtains message to be sent, wherein, the message to be sent includes：The true messages of k bits, (l-k) ratio
Special random message, wherein l, k is natural number；
Step S104, is encoded according to check matrix H to the message to be sent, obtains code word rn+k, wherein, the n is should
The code word size of true messages, the check matrix H meets following condition：rn+kHT=0；
Step S106, sends code word rn+k。
By above-mentioned steps, message to be sent is obtained, wherein, the message to be sent includes：The true messages of k bits, (l-
K) random message of bit, wherein l, k is natural number；The message to be sent is encoded according to check matrix H, code is obtained
Word rn+k, wherein, the n is the code word size of the true messages, and the check matrix H meets following condition：rn+kHT=0；Sending should
Code word rn+k.The problem of implication in information theory is safe can not be reached by solving coding techniques, realize safe coding decoding.
In the present embodiment, the check matrix H is that code word size is n+k bits, and message-length is the low close of l bits
The check matrix of parity check code LDPC code is spent, wherein, k<l<n+k.
In the present embodiment, the random message of (l-k) bit is somebody's turn to do in determination in the following manner：
Randomly generate the random message of (l-k) bit；
The random message that (l-k) bit will be somebody's turn to do is corresponding with the random message by the generator matrix generation of linear block codes
Code word.
In the present embodiment, code word r is sentn+kBefore, this method also includes one below：
Code word rn+kIt is divided into 2kIndividual subcode, the message of each subcode one k bit length of correspondence；
A code word transmission is randomly selected from the subcode corresponding to the k bit true messages；
Determine code word rn+kActual transfer rate be less than main channel channel capacity, and the subcode actual transmissions
Speed is equal to the channel capacity of tapping channel.
In the present embodiment, code word r is determined in the following mannern+kActual transfer rate be less than main channel channel
Capacity, and the subcode actual transfer rate be equal to tapping channel channel capacity：
Wherein, the actual transfer rate of the subcode isCode word rn+kActual transfer rate be It is main
The noise variance of channel Gaussian noise,It is the noise variance of tapping channel noise, P is code word rn+kTransmit power, main letter
Channel capacity maxI (the X in road；Y) it isChannel capacity maxI (the X of tapping channel；Z) it is
In the present embodiment, code word r is solvedn+kMode include：
By rn+kHT=0 draws (cn+k-l, sk,dl-k)HT=0, solve cn+k-l, wherein, the skFor true messages vector, it is somebody's turn to do
dl-kFor random message vector, the cn+k-lThe check bit of n+k-l bits after presentation code；
Fig. 2 is a kind of flow chart of interpretation method according to embodiments of the present invention, as shown in Fig. 2 the flow is including as follows
Step：
Step S202, receives code word rn+k, wherein, code word rn+kFor the code word obtained in the following manner：According to verification
Matrix H is encoded to message to be sent, obtains code word rn+k, wherein, the message to be sent includes：The true messages of k bits,
(l-k) random message of bit, wherein l, k is natural number, and the n is the code word size of the true messages, and the check matrix H expires
It is enough lower condition：rn+kHT=0；
Step S204, parses code word rn+k。
A kind of code device is additionally provided in the present embodiment, and the device is used to realize above-described embodiment and the side of being preferable to carry out
Formula, had carried out repeating no more for explanation.As used below, term " module " can realize the software of predetermined function
And/or the combination of hardware.Although the device described by following examples is preferably realized with software, hardware, or soft
The realization of the combination of part and hardware is also that may and be contemplated.
Fig. 3 is a kind of structured flowchart of code device according to embodiments of the present invention, as shown in figure 3, the device includes
First acquisition module 32, for obtaining message to be sent, wherein, the message to be sent includes：The true of k bits disappears
Breath, the random message of (l-k) bit, wherein l, k is natural number；
Second acquisition module 34, for being encoded according to check matrix H to the message to be sent, obtains code word rn+k, its
In, the n is the code word size of the true messages, and the check matrix H meets following condition：rn+kHT=0；
Sending module 36, for sending code word rn+k。
By above-mentioned steps, the first acquisition module 32 obtains message to be sent, wherein, the message to be sent includes：K bits
True messages, the random message of (l-k) bit, wherein l, k is natural number；Second acquisition module 34 is according to check matrix H
The message to be sent is encoded, code word r is obtainedn+k, wherein, the n is the code word size of the true messages, the check matrix H
Meet following condition：rn+kHT=0；Sending module 36 sends code word rn+k, solving coding techniques can not reach that information theory is anticipated
The problem of Yian city is complete, realizes safe coding decoding.
In the present embodiment, code word r is solvedn+kMode include：
By rn+kHT=0 draws (cn+k-l, sk,dl-k)HT=0, solve cn+k-l, wherein, the skFor true messages vector, it is somebody's turn to do
dl-kFor random message vector, the cn+k-lThe check bit of n+k-l bits after presentation code；
Fig. 4 is a kind of structured flowchart of code translator according to embodiments of the present invention, as shown in figure 4, the device includes：
Receiving module 42, for receiving code word rn+k, wherein, code word rn+kFor the code word obtained in the following manner：According to
Message to be sent is encoded according to check matrix H, code word r is obtainedn+k, wherein, the message to be sent includes：K bits it is true
Message, the random message of (l-k) bit, wherein l, k is natural number, and the n is the code word size of the true messages, the verification square
Battle array H meets following condition：rn+kHT=0；
Parsing module 44, for parsing code word rn+k。
It should be noted that above-mentioned modules can be by software or hardware to realize, for the latter, Ke Yitong
Cross in the following manner realization, but not limited to this：Above-mentioned modules are respectively positioned in same processor；Or, above-mentioned modules point
In processor that Wei Yu be not different.
It is described in detail with reference to the preferred embodiment of the present invention.
The preferred embodiment of the present invention discloses a kind of safe coding and decoding side based on LDPC code for Gauss tapping channel
Method.Coding and decoding designed by this preferred embodiment is all relatively easy, and iterative convergence speed during decoding is very fast.Emulation experiment table
The bright present invention has extraordinary effect when tapping channel signal to noise ratio is smaller.
Due in practical communication scene, calculate listener-in doubt degree H (W | ZN) it is an extremely difficult thing, in
It is that we define the bit error rate of listener-in approximately to replace doubt degree.It is noted herein that coming from the definition of comentropy
See, and the doubt degree H of listener-in (W | ZN) bit error rate that is equivalent to listener-in when obtaining maximum is equal to 0.5, namely listener-in
Decoding error probability is equal to 0.5.Based on this, the preferred embodiment of the present invention wishes the compiling gone out for Gauss tapping channel modelling
Code scheme has following two features：(1) program causes the bit error rate of legitimate receiver arbitrarily small (approaching 0)；(2)
The program causes the bit error rate of listener-in to approach 0.5.
The preferred embodiment of the present invention describes a kind of safe coding and decoding method based on LDPC code, and design encoding scheme is such as
Under：
The theoretical foundation of the safe coding and decoding conceptual design of the preferred embodiment of the present invention：In the safe coding of tapping channel model
In the existence proof of theorem, Wyner points out to design the coding and decoding scheme for reaching Information theoretical secure, it is necessary to using a kind of quilt
The coding techniques referred to as " cased at random ".A pair of the coding techniques chest 1 that is constituted the message of transmitting and a pile code word
Should, when the given message to be transmitted, a random code word of being chosen from the code word chest corresponding to the message is sent.
In order to allow listener-in correctly to translate the message of transmission, it is necessary to consume the decoding capability of listener-in, Wyner points out to assume eavesdropping
When person knows the specific message of transmission, (" translated if listener-in can be correctly found from the code word chest corresponding to the specific message
Go out ") send that random code word when, then the decoding capability of listener-in is just consumed.If the specific message institute is right
If the code word chest answered is also considered as a kind of new code word, the preferred embodiment of the present invention wishes the biography corresponding to the new code word
Defeated efficiency is equal to the channel capacity of tapping channel, because this whole decoding capability that represent listener-in is all consumed to translate this new
In code word, it is in that such listener-in just goes to translate send actually without extra ability for which message.Peace based on Wyner
The above-mentioned thought of full coding theorem proving, it is assumed that the message of transmission is k bits, and the length of code word is n-bit, then the present invention is preferred
The secure coding schemes of embodiment design need to have three below feature：(a) code word of the safe coding can be divided into 2kIt is individual
Subcode, the message bit of the k bit lengths of each subcode one transmission of correspondence；(b) the actual transmissions efficiency of the code wordIt is less than
Channel capacity C (the SNR of main channel1), and the actual transmissions efficiency of subcode will be equal to the channel capacity C (SNR of tapping channel2)；
(c) the message bit k sent is given, a code word of being chosen from the subcode corresponding to k bit messages that be random is sent.
The parameter declaration of above-mentioned design：We need to know the noise variance of main channel Gaussian noise firstSurreptitiously
Listen the noise variance of interchannel noiseThe transmit power P of code word after coding.From Shannon channel capacity formula we
Capacity maxI (the X of main channel；Y) it isCapacity maxI (the X of tapping channel；Z) it is
We assume that the message sent is k bits, we are generated the random of l-k bits by tandom number generator and disappeared at random
Breath.In addition, it will be assumed that the length of code word is n+k bits.
The design procedure of the safe coding and decoding scheme of the preferred embodiment of the present invention is as follows：
One, it is n+k bits to design a code word size according to the mentality of designing of classical LDPC code, and message-length is l ratios
The check matrix of special LDPC code, is designated as H, the matrix has n+k-l rows, there is n+k row.
The real transmission message of k bits and the random message of l-k bits are contained in the message of two, l bit.It is aobvious and easy
See, l meets following constraints k<l<n+k.
Three, in order to realize coding methods of the Wyner described in the safe coding theorem proving of tapping channel model, i.e.,
When the k bit messages of transmission are determined, random chooses a this coded system of code word from its corresponding code word chest, this
Invention preferred embodiment is firstly the need of being H by above-mentioned designed check matrix, and length is the LDPC code of n+k bits according to k ratios
Special true messages are divided into 2kIndividual subcode, the length of each subcode is n-bit.Such subcode is also a kind of Linear codes
Code, the message bit of the subcode is the random message of l-k bits.We realize in the following way " selects from subcode at random
Take the transmission of code word " coded system：(a) random message of a l-k bit is randomly generated by random number generator；
(b) random message of the l-k bits is generated into one and its one-to-one code word by the generator matrix of linear block codes, so
This transmits code word afterwards.
Four, the actual transmissions efficiency of above-mentioned subcode isCheck matrix is H, and code word size is n+k bits, and message is long
Degree is that the actual transmissions efficiency of the LDPC code of l bits isThe characteristics of in order to meet foregoing secure coding schemes
(b), make
Five, after above-mentioned n, k, l restriction relation is given, check matrix is H, and code word size is n+k bits, message
Length is as follows for the LDPC code design method of l bits：(a) turn to the check matrix H by Gaussian elimination method [A | B] type square
Battle array, it is noted here that H-matrix is n+k-l rows, the matrix of n+k row, A matrixes are unit matrix, and its line number and columns are n+k-l.B
Matrix is that a line number is n+k-l, and columns is l matrix.As the given true messages s sentk, the message generated at random is dl -kWhen, by the definition of check matrix,
(cn+k-l, sk,dl-k)HT=0, (formula 1)
Here cn+k-lThe check bit of n+k-l bits after presentation code.
H=[A | B] is substituted into (formula 1), Wo Menyou
(formula 2) is arranged, we can obtain
cn+k-l·AT+(sk,dl-k)·BT=0 (formula 3)
(formula 3) further is arranged,
cn+k-l=(sk,dl-k)·BT·(A-1)T(formula 4)
(formula 4) is given when it is understood that true messages skThe message d generated at randoml-kWhen, calculate the verification of code word
The formula of position.It is aware of after check bit, passes through code word r obtained from check matrix Hn+kIt is represented by
rn+k=(cn+k-l,sk,dl-k)=((sk,dl-k)·BT·(A-1)T,sk,dl-k) (formula 5)
Six, for validated user, code word rn+kActual transmissions efficiencyIt is less than the channel capacity of main channel
, thus validated user can with level off to 0 decoding error probability while translating true messages skThe message generated at random
dl-k.For listener-in, first it is desirable that he, which consumes its whole decoding capability, is correctly translating subcode rnOn,
Here
rn=(cn+k-l,sk,dl-k)=((sk,dl-k)·BT·(A-1)T,dl-k) (formula 6)
By rnAnd rn+kCompare, it is easy to find rnIt is by rn+kThe true messages s of middle transmissionkDelete, i.e. rnIt is rn+kSubcode.
For rnFor, message therein is dl-k, it is intended that listener-in can correctly translate dl-k, and its whole decoding capability is all disappeared
Consumption is translating dl-kOn, this is accomplished by subcode rnEfficiency of transmissionByAnd k<l<N+k, we can draw
(formula 7) illustrates for listener-in, code word rn+kActual transmissions efficiencyIt is greater than tapping channel
Channel capacity, from Shannon's theorems, the decoding error probability of listener-in can not level off to 0.
(Belief Propagation are referred to as using classical belief propagation for validated user and the decoder of listener-in
BP) decoding algorithm, the decoding algorithm is divided into following steps：(1) prior probability first to Gaussian channel presupposed information bit；
(2) posterior probability of each check-node is drawn according to belief propagation algorithm by the informational probability of information node；(3) by check-node
Posterior probability extrapolate the posterior probability of information node；(4) the posterior probability control judgment condition of information node is made to sentence firmly
Certainly, decode and terminate if meeting；If it is not satisfied, (2)~(4) step more than then repeating, iterates, until meeting condition,
Draw decoding result.If iterations reaches a default maximum times (such as 100), condition is still unsatisfactory for, then is declared
Cloth decoding failure.
Fig. 5 is applicable channel model schematic diagram according to the preferred embodiment of the invention, as shown in figure 5, including：Coding
Device, main channel, decoder, tapping channel.
Fig. 6 is the encoder building method schematic diagram designed according to the preferred embodiment of the present invention, as shown in Figure 6.
The embodiment of the example of the preferred embodiment of the present invention is safe using rule (3,2) LDPC of BP decoding algorithms
Code.
This example introduces a kind of simple regular (3,2) LDPC safety codes.Based on foregoing secure coding method,
In this example, n=280, k=20, l=100, SNR1=14, SNR2Take 10 different values (0.5,0.1,0.05,0.02,0.01,
0.0085,0.005,0.0035,0.002,0.001).First, we make 200 rows, the check matrix (n+k-l of 300 row
OK, n+k is arranged), the check matrix is constituted by 0,1, and 1 number is 2 in often going, and 1 number is 3 in each column.Such school
The LDPC code for testing matrix composition is called regular (3,2) LDPC code.We produce the true messages of 20 bits, Yi Jiyi every time
The random message of individual 80 bit, these message are encoded into one by regular (3,2) LDPC code and possess 100 bit messages by us
Position, the code word of 200 bit checks position, is then sent to validated user by main channel by the code word, is sent by tapping channel
To listener-in, and validated user and the decoder of listener-in enter row decoding using classic BP decoding algorithm.It is noted here that
Be that we assume that the signal to noise ratio of main channel is fixed, and the signal to noise ratio of tapping channel is change.By n=280, k=20, l=
100, SNR1=14, we can obtainThe reality of i.e. regular (3,2) LDPC code
Efficiency of transmission is the channel capacity much smaller than main channel.We set total message bit l=5000000 of transmission in simulations
× 100, the bit number of validated user decoding error is 2 times, and its decoding error ratio is 4 × 10-9.Due to the noise of tapping channel
Than being change, we can not possibly allow fixed n, k, l to meetHere
This example wishes that the encoding scheme for finding same fixation becomes for the security under the state of signal-to-noise of different tapping channels
Change trend.It was found that when the signal to noise ratio of tapping channel is smaller (i.e. the noise variance of tapping channel is bigger), the decoding of listener-in
The secure coding schemes that error probability is more approached designed by 0.5, the i.e. preferred embodiment of the present invention are safer.Table 1 is given as master
When channel SNRs are equal to 14, the relation between tapping channel signal to noise ratio and listener-in's decoding bit error rate, as shown in table 1.
Table 1
Fig. 7 is curve map according to the preferred embodiment of the invention, as shown in fig. 7, Fig. 7 give the signal to noise ratio of main channel with
Relation between the ratio and listener-in's bit error rate of tapping channel signal to noise ratio.Be not difficult to find out when ratio it is bigger, safe coding device
Effect it is better, i.e., when tapping channel signal to noise ratio is smaller, the performance of the safe coding device designed by the present invention is safer.
Through the above description of the embodiments, those skilled in the art can be understood that according to above-mentioned implementation
The method of example can add the mode of required general hardware platform to realize by software, naturally it is also possible to by hardware, but a lot
In the case of the former be more preferably embodiment.Understood based on such, technical scheme is substantially in other words to existing
The part that technology contributes can be embodied in the form of software product, and the computer software product is stored in a storage
In medium (such as ROM/RAM, magnetic disc, CD), including some instructions are to cause a station terminal equipment (can be mobile phone, calculate
Machine, server, or network equipment etc.) perform method described in each of the invention embodiment.
Embodiments of the invention additionally provide a kind of storage medium.Alternatively, in the present embodiment, above-mentioned storage medium can
The program code for performing following steps to be arranged to storage to be used for：
S1, obtains message to be sent, wherein, the message to be sent includes：The true messages of k bits, (l-k) bit with
Machine message, wherein l, k are natural number；
S2, is encoded according to check matrix H to the message to be sent, obtains code word rn+k, wherein, the n truly disappears for this
The code word size of breath, the check matrix H meets following condition：rn+kHT=0；
S3, sends code word rn+k。
Alternatively, storage medium is also configured to the program code that storage is used to perform the method and step of above-described embodiment：
Alternatively, in the present embodiment, above-mentioned storage medium can include but is not limited to：USB flash disk, read-only storage (ROM,
Read-Only Memory), random access memory (RAM, Random Access Memory), mobile hard disk, magnetic disc or
CD etc. is various can be with the medium of store program codes.
Alternatively, in the present embodiment, processor performs above-mentioned implementation according to the program code stored in storage medium
The method and step of example.
Alternatively, the specific example in the present embodiment may be referred to described in above-described embodiment and optional embodiment
Example, the present embodiment will not be repeated here.
Obviously, those skilled in the art should be understood that above-mentioned each module of the invention or each step can be with general
Computing device realize that they can be concentrated on single computing device, or be distributed in multiple computing devices and constituted
Network on, alternatively, the program code that they can be can perform with computing device be realized, it is thus possible to they are stored
Performed in the storage device by computing device, and in some cases, can be shown to be performed different from order herein
The step of going out or describe, they are either fabricated to each integrated circuit modules respectively or by multiple modules in them or
Step is fabricated to single integrated circuit module to realize.So, the present invention is not restricted to any specific hardware and software combination.
The preferred embodiments of the present invention are the foregoing is only, are not intended to limit the invention, for the skill of this area
For art personnel, the present invention can have various modifications and variations.Within the spirit and principles of the invention, that is made any repaiies
Change, equivalent substitution, improvement etc., should be included in the scope of the protection.
Claims (10)
1. a kind of coding method, it is characterised in that including：
Message to be sent is obtained, wherein, the message to be sent includes：The true messages of k bits, the random of (l-k) bit disappears
Breath, wherein l, k is natural number；
The message to be sent is encoded according to check matrix H, code word r is obtainedn+k, wherein, the n truly disappears to be described
The code word size of breath, the check matrix H meets following condition：rn+kHT=0；
Send the code word rn+k。
2. according to the method described in claim 1, it is characterised in that
The check matrix H is that code word size is n+k bits, and message-length is the low density parity check code of l bits
The check matrix of LDPC code, wherein, k<l<n+k.
3. according to the method described in claim 1, it is characterised in that (l-k) bit is random described in determining in the following manner
Message：
Randomly generate the random message of (l-k) bit；
The random message of (l-k) bit is generated corresponding with the random message by the generator matrix of linear block codes by described in
Code word.
4. according to the method described in claim 1, it is characterised in that send the code word rn+kBefore, methods described also include with
It is one of lower：
The code word rn+kIt is divided into 2kIndividual subcode, the message of each one k bit length of the subcode correspondence；
A code word transmission is randomly selected from the subcode corresponding to the k bits true messages；
Determine the code word rn+kActual transfer rate be less than main channel channel capacity, and the subcode actual transmissions
Speed is equal to the channel capacity of tapping channel.
5. method according to claim 4, it is characterised in that determine the code word r in the following mannern+kActual biography
Defeated speed be less than main channel channel capacity, and the subcode actual transfer rate be equal to tapping channel channel capacity：
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Wherein, the actual transfer rate of the subcode isThe code word rn+kActual transfer rate be It is main
The noise variance of channel Gaussian noise,It is the noise variance of tapping channel noise, P is the code word rn+kTransmit power, it is main
Channel capacity maxI (the X of channel；Y) it isChannel capacity maxI (the X of tapping channel；Z) it is
6. method according to claim 5, it is characterised in that solve the code word rn+kMode include：
By rn+kHT=0 draws (cn+k-l, sk,dl-k)HT=0, solve cn+k-l, wherein, the skFor true messages vector, institute
State dl-kFor random message vector, the cn+k-lThe check bit of n+k-l bits after presentation code；
rn+k=(cn+k-l, sk⊕pk,dl-k⊕ql-k)。
7. a kind of interpretation method, it is characterised in that including：
Receive code word rn+k, wherein, the code word rn+kFor the code word obtained in the following manner：According to check matrix H to pending
Send message to be encoded, obtain code word rn+k, wherein, the message to be sent includes：The true messages of k bits, (l-k) bit
Random message, wherein l, k is natural number, and the n is the code word size of the true messages, and the check matrix H is met
Following condition：rn+kHT=0；
Parse the code word rn+k。
8. a kind of code device, it is characterised in that including：
First acquisition module, for obtaining message to be sent, wherein, the message to be sent includes：The true messages of k bits,
(l-k) random message of bit, wherein l, k is natural number；
Second acquisition module, for being encoded according to check matrix H to the message to be sent, obtains code word rn+k, wherein,
The n is the code word size of the true messages, and the check matrix H meets following condition：rn+kHT=0；
Sending module, for sending the code word rn+k。
9. device according to claim 8, it is characterised in that solve the code word rn+kMode include：
By rn+kHT=0 draws (cn+k-l, sk,dl-k)HT=0, solve cn+k-l, wherein, the skFor true messages vector, institute
State dl-kFor random message vector, the cn+k-lThe check bit of n+k-l bits after presentation code；
rn+k=(cn+k-l, sk⊕pk,dl-k⊕ql-k)。
10. a kind of code translator, it is characterised in that including：
Receiving module, for receiving code word rn+k, wherein, the code word rn+kFor the code word obtained in the following manner：According to school
Test matrix H to encode message to be sent, obtain code word rn+k, wherein, the message to be sent includes：The true of k bits disappears
Breath, the random message of (l-k) bit, wherein l, k is natural number, and the n is the code word size of the true messages, the school
Test matrix H and meet following condition：rn+kHT=0；
Parsing module, for parsing the code word rn+k。
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