CN103414540A - Degraded eavesdropping channel rate compatible method based on Polar code - Google Patents

Abstract

The invention discloses a degenerate wiretapping channel rate compatible method based on punctured Polar codes. The method combines punctured Polar codes with a degenerated wiretapping channel model, and according to the construction characteristics of Polar codes, secure bits for transmitting information are given. channel; according to the channel rate requirements of the degenerate eavesdropping channel, a suitable puncturing matrix is constructed, and a rate-compatible method of degenerate eavesdropping channel coding based on Polar codes is realized; since the eavesdropper does not know the puncturing matrix, and the puncturing operation makes the encoded The length of the codeword is reduced, the information is hidden through the puncturing operation, and the complexity of the eavesdropper's recovery of the original information by eavesdropping the received codeword on the channel increases, which ensures the security of the system; moreover, the puncturing method makes the same All the codes in the group rate compatible codes can be implemented by the same group encoder and decoder, which greatly reduces the complexity of the transmitter and receiver.

Description

A kind of tapping channel of degeneration based on Polar code rate-compatible method

Technical field

The present invention relates to wireless communication information safe practice field, particularly a kind of tapping channel of degeneration based on Polar code rate-compatible method.

Background technology

In recent years, along with the development of wireless communication technology and the people continuous increase to demand for services, require more and more higher to safety and the rate-compatible of wireless communication system.Physical layer becomes safely an important branch of information security, causes that people pay close attention to widely.Wyner tapping channel (Wiretap Channel) model is an important models of physical layer security study, and its important indicator " safe capacity " becomes the key of information security research.

Wyner tapping channel model comprises main channel (main channel) between validated user Alice and Bob and the channel that wiretaps (eavesdropping channel) between disabled user Eve and sender Alice.Usually supposing to wiretap interchannel noise will be higher than the main channel noise, and the channel that namely wiretaps is the degenerate channel of main channel.Channel coding method is to guarantee that wireless system reaches the important means of " safe capacity ".2005, the people such as Thangaraj for main channel be noiseless channel, the channel that wiretaps is that binary system can be smeared channel (BEC), provided based on random low density parity check code (LDPC), transmission rate reaches the method for safe capacity.2011, the people such as V.Rathi further, when main channel is all the BEC channel with the channel that wiretaps, used convolutional LDPC code, make transmission rate reach whole achievable rate region.The Polar code be 2007 by Arikan propose, unique channel coding method that reaches shannon limit in theory up to now, and be the coding and decoding method with low complex degree.2010, the people such as E.Hof were applied to the Polar code in the Wyner tapping channel, the Polar code structure that has provided the safe capacity of the discrete memoryless symmetrical tapping channel of binary system and obtained safe capacity.Due to main channel and bit channel (bit-channel) difference of channel by " channel-polarization " (channel polarization) acquisition that wiretap, allow information only by for main channel, being for the channel that wiretaps, can obtain safe transmission when entirely making an uproar bit channel without making an uproar bit channel, these bit channels that are used for transmission information are called as " safe bit " channel.The structure of Polar code in the degeneration tapping channel takes full advantage of these characteristics of degenerate channel that the channel that wiretaps is main channel.

Because the time-varying characteristics of radio communication channel environment are stronger, the code check of chnnel coding should meet the demands adaptively, therefore needs a kind of coding method of rate-compatible.More than deleting, be a kind of common method that builds the rate-compatible coding, more than the deleting of code, make all codes in same group of rate-compatible code can be by same group of volume, decoder realization, this greatly reduces the complexity of transmitter and receiver.And, more than deleting, also can improve the fail safe of wyner tapping channel model, as people such as Klinc 2011 in Gauss's tapping channel model, utilization is deleted remaining (puncturing) technology and is combined with LDPC code structure, while making the channel signal to noise ratio that wiretaps be less than the minimum signal to noise ratio of main channel, the listener-in obtains less than any effective information.The present invention utilizes the design of Polar code and the structure of residual matrix, can solve well fail safe and the rate-compatible two aspect problems of degeneration tapping channel.

Summary of the invention

The object of the invention has been to propose a kind of degeneration tapping channel rate-compatible method based on deleting remaining Polar code, the method will be deleted remaining Polar code and be combined with degeneration tapping channel model, according to the construction features of Polar code and the channel circumstance of degeneration tapping channel, construct applicable residual matrix, realize the rate-compatible of degeneration tapping channel coding.Because the listener-in does not know residual matrix, and delete remaining operation and make the code word size after coding reduce, information exchange is crossed and is deleted remaining operation and be hidden.The complexity that the reception code word that the listener-in obtains by the channel that wiretaps is recovered prime information increases, and has guaranteed the fail safe of system.

The technical solution adopted for the present invention to solve the technical problems is: the present invention be take degeneration tapping channel model and is basis, the building method of Polar code of take is prerequisite, utilize puncturing method, design based on the rate-compatible method of deleting remaining Polar code, realize the rate-compatible of degeneration tapping channel and the assurance of fail safe.

Polar code Common Parameters (N, K, A,

) expression, wherein N(N=2 ⁿ, n>=0) and be code length, K is information bit length, A is information bit subscript collection,

For freezing position, these freeze an information and will remain unchanged before and after coding.By channel-polarization, the bit channel that in the Polar code, the A indexed set is corresponding is without making an uproar bit channel (noiseless bit-channel), and A ^cThe bit channel that the subscript set pair is answered is the bit channel of entirely making an uproar (noisy bit-channel).In the design of degeneration tapping channel model Polar code, the code length of main channel and the channel Polar code that wiretaps is all N, makes A _mWith Be the information bit set of main channel and freeze position set, A _wWith

Be wiretap channel the information bit set and freeze position set.Due to the channel that wiretaps, be the degenerate channel of main channel, therefore

Can select like this validated user Bob is for listener-in Eve, to be that the bit channel of entirely making an uproar carries out the breath transmission as safe bit channel without making an uproar.Therefore, in degeneration tapping channel model, set corresponding to safe bit channel may be defined as S=A _mA _w, i.e. A _mCollection removes A _wIndexed set.In order to make the Polar encoding scheme be applicable to degeneration tapping channel parameter, change with environmental change, can delete remaining operation to the generator matrix of Polar code.By deleting remaining operation, reduced the bit number transmitted in channel after Polar code coding, improved the transmission rate between validated user; Simultaneously, owing to deleting remaining operation, make the code word size after coding reduce, some information are hidden.The signal to noise ratio of channel is lower if wiretap, listener-in Eve wants that the reception code word obtained by the channel that wiretaps recovers the complexity of prime information and increase, the bit error rate of listener-in Eve will be more near 0.5, and this is equivalent to the listener-in and is close to 0 from the channel that wiretaps, obtaining Useful Information.Therefore, by deleting remaining operation, the fail safe of Wyner tapping channel model can be guaranteed.

But deleting remaining operation meeting affects a little the safe capacity theoretical value.Main channel and tapping channel are W and W' if suppose, its channel capacity is respectively I (W) and I (W'), and the theoretically secure capacity is:

$\mathrm{Cs}=I\left(W\right)-I\left(W^{\′}\right)=\frac{n(I\left(W\right)-I\left(W^{\′}\right))}{n}---\left(1\right)$

In Polar code coding, make N of channel W to copy merge and split together, adopted delete remaining after, some copy channel is transmission information not, at the decoding end, the likelihood ratio of these positions will assignment ' 1 ' be worth, show receive ' 0 ' identical with the probability of ' 1 ' symbol, so capacity of these copy channels can think 0.If deleting remaining bit number is np, wherein p is deleted the probability of remaining bit in the n bit information after coding, and safe capacity can be calculated as:

${\mathrm{Cs}}^{\′}=(\mathrm{nI}\left(W\right)-\mathrm{npI}\left(W\right)-(n-\mathrm{np})I\left(W^{\′}\right))/n=\frac{(n-\mathrm{np})(I\left(W\right)-I\left(W^{\′}\right))}{n}---\left(2\right)$

As can be seen here, delete remaining rear safe capacity and will relatively be reduced to original (n-np)/n.If p<<1, the safe capacity value remains unchanged substantially.

Below provide and be applied to degenerate the concrete construction process of the Polar code tapping channel model, the achievable rate compatibility.

Method flow:

The invention provides a kind of tapping channel of degeneration based on Polar code rate-compatible method, the method comprises the steps:

Step 1: at transmitting terminal, Alice is by information u, random noise v and freeze position

Encode, the coding formula is:

$X=u{G}_N\left(S\right)+v{G}_N\left(A_w\right)+u_{A_m^c}{G}_N\left(A_m^c\right)---\left(3\right)$

Wherein, noise v is that a length is | A _w| random sequence, G _N(A) be G _NIn under be designated as the generator matrix that row that the A set pair answers forms,

B _NBe the bit permutation matrix of one N * N, F is matrix $\left[\begin{array}{cc}1& 0\\ 1& 1\end{array}\right],$

For the Kronecker tensor product; Like this, information is only at safe bit channel, and namely subscript integrates as the S position and transmits, with the fail safe of guarantee information;

The sequence X that step 2:Alice obtains coding is deleted remaining operation, obtain sequence X ',

X'＝XG _punc (4)

Wherein, G _PuncFor the residual matrix on rank of N * (N-d), d deletes the number of bits do not passed; According to the construction features of Polar code, existing employing cut-off tree (stopping-tree) is deleted remaining method, the participation cut-off is set to the code word node of least number of times and leaves out; According to the cut-off tree, delete the basic principle of remaining method, in conjunction with the characteristics of linear block codes, the code that can obtain every row in Polar code coding generator matrix is exactly heavily the number of times that after coding, this code word participates in the cut-off tree; The position collection that calculates the d row of weight minimum in Polar code generator matrix is labeled as to A _d, the unit matrix of N * N is removed to A _dMatrix after set is made as residual matrix G _Punc

Step 3: at receiving terminal, validated user Bob can obtain the d column position collection A of weight minimum in generator matrix according to a preconcerted arrangement _d, then the sequence Y ' received is carried out to extended operation, namely at A _dBit is added in position, obtains sequence YY, and wherein bit information is that " 0 " is the same large with the probability for " 1 ";

Step 4: the sequence YY that expansion is obtained carries out decoding, and interpretation method is as follows:

${\hat{u}}_i=\left\{\begin{array}{cc}0& \mathrm{ifi}\&Element;S^c\\ h_i({\mathrm{yy}}_1^N,{\hat{u}}_1^{i-1}),& \mathrm{ifi}\&Element;S\end{array}\right.---\left(5\right)$

H wherein _i: YY ^N* X ^I-1→ X, i ∈ S is defined as

Step 5: listener-in Eve is owing to not knowing residual matrix, and it can not determine that those information bits are deleted, reaches N length so only can supplement at random receiving code; Simultaneously, for the smaller channel that wiretaps of noise, due to the remaining operation of deleting of transmitting terminal Alice, make the performance of the channel that wiretaps poorer, thus obtained bit error rate, closer to 0.5, has guaranteed the fail safe of Wyner tapping channel model.

Beneficial effect:

1, the present invention is by deleting the remaining structure of Polar code in the degeneration tapping channel, in the tapping channel that obtains degenerating, obtains a kind of rate-compatible method of high safe capacity.

2, the present invention has guaranteed the fail safe of Wyner tapping channel model, has reduced the complexity of transmitter and receiver.

The accompanying drawing explanation

Fig. 1 deletes remaining Polar code degeneration tapping channel illustraton of model.

Fig. 2 is the service condition schematic diagram of deleting bit channel in remaining Polar code cataloged procedure.

Fig. 3 deletes impact (Polar code code length the be 256) schematic diagram of remaining Polar code on degeneration tapping channel system safety capacity.

Fig. 4 is based on code check (Polar code code length the is 256) schematic diagram of deleting remaining Polar code degeneration tapping channel system.

Fig. 5 is based on the error rate schematic diagram of deleting remaining Polar code degeneration tapping channel system.

Embodiment

Below in conjunction with Figure of description, patent of the present invention is described in further detail.

The invention provides a kind of tapping channel of degeneration based on Polar code rate-compatible method, the method is by deleting the remaining structure of Polar code in the degeneration tapping channel, in the tapping channel that obtains degenerating, obtains a kind of rate-compatible method of high safe capacity.In the method by transmitting terminal Alice to more than the deleting of code word after Polar coding, make the performance of the smaller channel that wiretaps of noise poorer, thus obtained bit error rate, closer to 0.5, has guaranteed the fail safe of Wyner tapping channel model.Simultaneously, in the method the Polar code only need the female code of design, all codes can be by same group of volume, decoder realization, this greatly reduces the complexity of transmitter and receiver.

In the present invention, all to adopt code length be the Polar code of N=256 in numerical simulation, but, because its generator matrix will be 256 * 256 matrixes, be not suitable for describing.For Polar code structure being described and deleting remaining process, existing Polar code of take code length N=8 is described method of the present invention as example:

(1) at transmitting terminal, Alice is by information u, random noise v and freeze position

Encode, the coding formula is $X=u{G}_N\left(S\right)+v{G}_N\left(A_w\right)+u_{A_m^c}{G}_N\left(A_m^c\right).$ Generator matrix expression formula by the Polar code obtains $G_N={\left[\begin{array}{cc}1& 0\\ 1& 1\end{array}\right]}^{\&CircleTimes;n},$ $N=2^{\&CircleTimes;n},$ Can obtain N=2 ³=8 generator matrix:

${\mathrm{<figure-callout\; id="8"\; label="G"\; filenames="HDA00003663610400021.png,HDA00003663610400022.png"\; state="\{\{state\}\}">G</figure-callout>}}_8=\left(\begin{array}{cccccccc}1& 0& 0& 0& 0& 0& 0& 0\\ 1& 0& 0& 0& 1& 0& 0& 0\\ 1& 0& 1& 0& 0& 0& 0& 0\\ 1& 0& 1& 0& 1& 0& 1& 0\\ 1& 1& 0& 0& 0& 0& 0& 0\\ 1& 1& 0& 0& 1& 1& 0& 0\\ 1& 1& 1& 1& 0& 0& 0& 0\\ 1& 1& 1& 1& 1& 1& 1& 1\end{array}\right)---\left(7\right)$

(2) according to cut-off tree, delete the basic principle of remaining method, in conjunction with the characteristics of linear block codes, the code that calculates all row in the Polar code generator matrix of N=8 heavily is respectively { 8,4,4,2,4,2,2,1}, wherein x ₄x ₆x ₇Code is heavily 2, x ₈Column weight is 1, and they are namely the number of times that after coding, this code word participates in the cut-off tree.According to the column weight of every row, the code word sequence number being carried out to descending or ascending order arrangement, is d if delete remaining bit number, selects the wherein sequence number of the minimum row of column weight, forms set A _d, then, in the unit matrix of N * N, delete set A _dThe d row of middle correspondence, can obtain residual matrix G _PuncWhen if the column weight of multiple row is identical, can select random column to delete.

If make d=2, for the Polar code of N=8, to its each row code descending again, obtain (1,2,3,5,4,6,7,8).When the dibit of code word does not need to transmit, can delete code word the 7th and 8, i.e. x ₇x ₈, also can delete x ₄x ₈, x ₆x ₈.When deleting x ₇x ₈While not transmitting, its residual matrix is as follows:

$G_{\mathrm{punc}}=\left(\begin{array}{cccccc}1& 0& 0& 0& 0& 0\\ 0& 1& 0& 0& 0& 0\\ 0& 0& 1& 0& 0& 0\\ 0& 0& 0& 1& 0& 0\\ 0& 0& 0& 0& 1& 0\\ 0& 0& 0& 0& 0& 1\\ 0& 0& 0& 0& 0& 0\\ 0& 0& 0& 0& 0& 0\end{array}\right)---\left(8\right)$

Work as x ₄x ₈While not transmitting, its residual matrix is as follows:

$G_{\mathrm{punc}}=\left(\begin{array}{cccccc}1& 0& 0& 0& 0& 0\\ 0& 1& 0& 0& 0& 0\\ 0& 0& 1& 0& 0& 0\\ 0& 0& 0& 0& 0& 0\\ 0& 0& 0& 1& 0& 0\\ 0& 0& 0& 0& 1& 0\\ 0& 0& 0& 0& 0& 1\\ 0& 0& 0& 0& 0& 0\end{array}\right)---\left(9\right)$

Work as x ₆x ₈While not transmitting, its residual matrix is as follows:

$G_{\mathrm{punc}}=\left(\begin{array}{cccccc}1& 0& 0& 0& 0& 0\\ 0& 1& 0& 0& 0& 0\\ 0& 0& 1& 0& 0& 0\\ 0& 0& 0& 1& 0& 0\\ 0& 0& 0& 0& 1& 0\\ 0& 0& 0& 0& 0& 0\\ 0& 0& 0& 0& 0& 1\\ 0& 0& 0& 0& 0& 0\end{array}\right)---\left(10\right)$

Code word X and the residual matrix G that (3) will obtain through Polar coding _PuncThe code word that obtains needing to transmit that multiplies each other is X '=XG _Punc, by main channel, X ' is passed to validated user Bob (recipient) afterwards.Due to the imperfection of channel, the recipient obtains Y '=X '+n, and wherein n is interchannel noise.At receiving terminal, Bob can obtain the d column position collection A of weight minimum in generator matrix according to a preconcerted arrangement _d.Bob, before decoding, at first expands sequence Y ', is deleting remaining position A _dPlace adds bit and obtains sequence YY, and the bit information added meets,

$L_1^1\left(A_d\right)=\frac{W\left(A_d\right|0)}{W\left(A_d\right|1)}=1---\left(11\right)$

Namely this position occurs that the probability of " 0 " and " 1 " is the same large.And the likelihood ratio of other positions can be tried to achieve in conjunction with channel parameter according to the information received.

(4) according to Polar code SC (Successive Cancellation) interpretation method, carry out decoding, expression formula in its Chinese style (6)

$L_N^{\left(i\right)}({\mathrm{yy}}_1^N,{\hat{u}}_1^i)=\frac{W_N^i({\mathrm{yy}}_1^N,{\hat{u}}_1^{i-1}|0)}{W_N^i({\mathrm{yy}}_1^N,{\hat{u}}_1^{i-1}|1)}---\left(12\right)$

Available following iterative formula is tried to achieve:

$L_N^{(2i-1)}({\mathrm{yy}}_1^N,{\hat{u}}_1^{2i-2})=$

$\frac{L_{N/2}^{\left(i\right)}({\mathrm{yy}}_1^{N/2},{\hat{u}}_{1,o}^{2i-2}\&CirclePlus;{\hat{u}}_{1,e}^{2i-2})L_{N/2}^{\left(i\right)}({\mathrm{yy}}_{N/2+1}^N,{\hat{u}}_{1,e}^{2i-2})+1}{L_{N/2}^{\left(i\right)}({\mathrm{yy}}_1^{N/2},{\hat{u}}_{1,o}^{2i-2}\&CirclePlus;{\hat{u}}_{1,e}^{2i-2})+L_{N/2}^{\left(i\right)}({\mathrm{yy}}_{N/2+1}^N,{\hat{u}}_{1,e}^{2i-2})}---\left(13\right)$

$L_N^{\left(2i\right)}({\mathrm{yy}}_1^N,{\hat{u}}_1^{2i-1})=[L_{N/2}^{\left(i\right)}({\mathrm{yy}}_1^{N/2},{\hat{u}}_{1,o}^{2i-2}\&CirclePlus;{\hat{u}}_{1,e}^{2i-2}){]}^{1-2{\hat{u}}_{2i-1}}---\left(14\right)$

$\&CenterDot;L_{N/2}^{\left(i\right)}({\mathrm{yy}}_{N/2+1}^N,{\hat{u}}_{1,e}^{2i-2})$

Validated user Bob can obtain the information of transmission at receiving terminal like this.

(5) listener-in Eve is owing to not knowing residual matrix, and it can not determine that those information bits are deleted, reaches N length so only can supplement at random receiving code; Simultaneously, due to the remaining operation of deleting of transmitting terminal Alice, make the performance of the channel that wiretaps poorer, thus obtained bit error rate, closer to 0.5, has guaranteed the fail safe of Wyner tapping channel model.

Fig. 3 deletes the impact of remaining Polar code on degeneration tapping channel system safety capacity according to what Fig. 2 method for designing obtained, and in numerical simulation, the signal to noise ratio of tapping channel is made as-1dB.After result of study showed that remaining operation is deleted in introducing, the safe capacity of tapping channel had minimizing slightly; When deleting complementary probability p<<1, this impact can drop to very little.By deleting remaining operation, reduced the code word bits number transmitted in noisy channel, thereby also increased the transfer rate of code in the main channel.Fig. 4 is that the error rate is less than 10 ^-5The time, delete and remaining 32 and delete and remaining the comparison diagram of the maximum transmitted code check when not deleting remaining operation of main channel maximum transmitted code check 64 time.Numerical Simulation Results shows that in main channel, the maximum transmitted code check is improved by deleting remaining operation, and deletes the main channel maximum transmitted code check of remaininging 64 time and will remaining main channel maximum transmitted code check 32 time higher than deleting; Further analyze and delete remaining operation to main channel, the channel bit error rate that wiretaps impact.Fig. 5 does not introduce to delete when remaining, the bit error rate comparison diagram of main channel when the main channel bit error rate that code check is 0.5, code length is 512 Polar code and deleting is remaininged 32 and 64.Numerical result shows deletes the bit error rate decline slightly that remaining operation makes main channel.But listener-in's bit error rate (delete remaining 32 time) all remains on 0.5 left and right, show that deleting listener-in in remaining operation can not obtain any useful information.In fact, when more than deleting, figure place was more, listener-in's bit error rate, more near 0.5, showed and deletes the fail safe that remaining operation does not have influence on system.

Claims (4)

1. a kind of degraded eavesdropping channel rate compatible method based on punctured Polar code, it is characterized in that, described method comprises the steps: Step 1: At the sender, Alice combines information u, random noise v and frozen bits

To encode, the encoding formula is: $\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; u</span>}{\mathrm{<span\; class="notranslate">\; G</span>}}_{\mathrm{<span\; class="notranslate">\; N</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; S</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; v</span>}{\mathrm{<span\; class="notranslate">\; G</span>}}_{\mathrm{<span\; class="notranslate">\; N</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; A</span>}}_{\mathrm{<span\; class="notranslate">\; w</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; u</span>}}_{{\mathrm{<span\; class="notranslate">\; A</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}}^{\mathrm{<span\; class="notranslate">\; c</span>}}}{\mathrm{<span\; class="notranslate">\; G</span>}}_{\mathrm{<span\; class="notranslate">\; N</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; A</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}}^{\mathrm{<span\; class="notranslate">\; c</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 15</span>}<span\; class="notranslate">\; )</span>$ Among them, the noise v is a random sequence with a length of |A _w |, G _N (A) is a generator matrix composed of rows corresponding to the subscript A in G _N , and

B _N is a N×N bit permutation matrix, F is the matrix $\left[\begin{array}{cc}1& 0\\ 1& 1\end{array}\right],$

is the Kronecker tensor product; Step 2: Alice performs a puncturing operation on the encoded sequence X to obtain the sequence X', X'＝XG _punc (16) Wherein, G _punc is a punctured matrix of N×(Nd) order, and d is the number of bits to be deleted and not transmitted; Step 3: At the receiving end, the legal user Bob can obtain the d-column position set A _d with the smallest weight in the generator matrix according to the agreement, and then perform an expansion operation on the received sequence Y', that is, add bits at the A _d position to obtain the sequence YY , where the probability of bit information being "0" is as high as being "1"; Step 4: Decode the extended sequence YY, the decoding method is as follows: ${\stackrel{<span\; class="notranslate">\; ^</span>}{\mathrm{<span\; class="notranslate">\; u</span>}}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; =</span>\left\{\begin{array}{cc}\mathrm{<span\; class="notranslate">\; 0</span>}& \mathrm{<span\; class="notranslate">\; ifi</span>}<span\; class="notranslate">\; \&Element;</span>{\mathrm{<span\; class="notranslate">\; S</span>}}^{\mathrm{<span\; class="notranslate">\; c</span>}}\\ {\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; yy</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}^{\mathrm{<span\; class="notranslate">\; N</span>}}<span\; class="notranslate">\; ,</span>{\stackrel{<span\; class="notranslate">\; ^</span>}{\mathrm{<span\; class="notranslate">\; u</span>}}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}^{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ,</span>& \mathrm{<span\; class="notranslate">\; ifi</span>}<span\; class="notranslate">\; \&Element;</span>\mathrm{<span\; class="notranslate">\; S</span>}\end{array}\right.<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 17</span>}<span\; class="notranslate">\; )</span>$ where h _i : YY ^N ×X ⁱ - ¹ →X,i∈S is defined as

Step 5: The eavesdropper can only randomly supplement the receiving code to reach N length; for the eavesdropping channel with a small signal-to-noise ratio, the sending end punctures the operation to make the bit error rate closer to 0.5. 2. a kind of degraded eavesdropping channel rate compatible method based on punctured Polar code according to claim 1, it is characterized in that: in above-mentioned step 2, also comprise: Delete the code word node with the least number of participation in the cut-off tree; combined with the characteristics of linear block codes, the code weight of each column in the Polar code encoding generation matrix is obtained after encoding. The position set A _d of the column d with the smallest weight in the matrix, the matrix obtained by removing the set A _d from the N×N unit matrix is set as the puncturing matrix G _punc . 3. a kind of degraded eavesdropping channel rate compatible method based on punctured Polar code according to claim 1, is characterized in that: The method is channel rate compatible. 4. a kind of degraded eavesdropping channel rate compatible method based on punctured Polar code according to claim 1, is characterized in that: The method combines punctured Polar codes with a degenerate eavesdropping channel model.

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