CN107294540B - Encoding method and device, decoding method and device - Google Patents

Abstract

The present invention provides an encoding method and device, and a decoding method and device, wherein the encoding method includes: obtaining a message to be sent, wherein the message to be sent includes: a real message of k bits, a (l-k) bit Random message, where l and k are both natural numbers; encode the message to be sent according to the parity check matrix H to obtain the codeword r ^n+k , where n is the codeword length of the real message, and the parity check matrix H The following condition is satisfied: r ^n+k H ^T =0; the code word r ^n+k is sent. By adopting the above-mentioned technical solution, the problem that the coding technology cannot achieve the safety of information theory is solved, and the safe coding and decoding are realized.

Description

Coding method and device, decoding method and device

Technical Field

The present invention relates to the field of communications, and in particular to a coding method and device, and a decoding method and device.

Background Art

In the related art, although Shannon's theorem defined the performance of channel coding as early as 1984, most channel coding algorithms were far from the Shannon limit until the emergence of Turbo codes in 1993. Therefore, the birth of Turbo codes means the beginning of channel coding approaching the Shannon limit in additive white Gaussian noise channels. Two years later, inspired by Turbo codes, Mike Mackay and Neil Neal rediscovered that the long-neglected low-density parity check code (LDPC) has performance closer to the Shannon limit. LDPC code was proposed by Gallager in 1962. The code he proposed is a linear block code based on a sparse check matrix. Gallager elaborated in detail the construction method of LDPC code, iterative probability decoding algorithm and its theoretical description. However, due to the high hardware requirements for its encoding and decoding, and the simple and efficient performance of BCH codes, Reed-Solomon codes and concatenated codes at the time, except for a few researchers such as Pinsker and Margulis, researchers did not pay much attention to LDPC codes and almost forgot about them.

In the 1990s, MacKay et al. rediscovered low-density parity-check codes and proved that when communicating at any code rate below the Shannon limit, the decoding error probability of LDPC codes based on the Maximum A Posteriori (MAP) algorithm is as low as 10 ^-7 , which is very close to 0.

Unfortunately, the optimal decoding algorithm for LDPC codes is a (Non-deterministic Polynomial, abbreviated as NP) complete problem (a non-polynomial time difficult problem). MacKay also demonstrated that the Gallager decoding algorithm has excellent empirical performance. After studying the erasure channel, Luby et al. found that LDPC codes can reach the channel capacity under low complexity decoding, and proposed a simple linear time decoding algorithm on the erasure channel. At present, the main research areas of LDPC codes are concentrated in four different aspects, namely: the construction of the check matrix, the optimization of the decoding algorithm, the analysis of the performance and the application of LDPC codes in practical systems.

The analysis of the security of communication systems from the perspective of information theory can be traced back to 1949, when Shannon published an important article entitled "A Theory of Communication for Secrecy Systems", which laid the foundation for using information theory to analyze the security of communication systems. After that, Wyner and his collaborators proposed two types of wiretap channel models: wiretap channel I and wiretap channel of type II.

In the first type of eavesdropping channel model, the sender wants to transmit a confidential message to a legitimate receiver through a discrete memoryless main channel. At the same time, an eavesdropper tries to eavesdrop on the output of the main channel through another discrete memoryless eavesdropping channel. Wyner used conditional entropy H(W|Z ^N ) to represent the eavesdropper's doubt about the confidential message (here W is the confidential message being sent, and Z ^N is the output of the eavesdropping channel). This doubt is also an important parameter for measuring security in the first type of eavesdropping channel model. Wyner characterized the region composed of all accessible transmission efficiency-doubt pairs. We usually call this region the capacity-doubt region, that is, all points in this region are reachable, and all points outside the region are unreachable. On this basis, Wyner defined and characterized the concept of security capacity, that is, the maximum value of transmission efficiency while ensuring the maximum doubt of the eavesdropper. Wyner systematically demonstrated the trade-off relationship between transmission efficiency and security in communication systems (that is, the security of communication systems and maximum transmission cannot be guaranteed at the same time), which laid the foundation for using information theory to analyze the relationship between security and transmission efficiency of communication systems. In the proof of the existence of the capacity-doubt region, Wyner proposed the random binning coding technique. This technique has become one of the most common coding techniques in the channel model considering security. Random binning means that the message sent corresponds to a codebook (a collection of codewords). When the sender sends a specific message, it first finds the codebook corresponding to the message, and then randomly selects a codeword from the codebook and sends it out. The codeword is used as the output of the encoder.

Soon after Wyner proposed the first type of eavesdropping channel model, he and Ozarow proposed a simplified eavesdropping channel model, namely the second type of eavesdropping channel model. In the second type of eavesdropping channel model, the main channel is noiseless, and the eavesdropper can arbitrarily select μ bits from the N-length codeword output by the main channel for noiseless eavesdropping, that is, the eavesdropper can obtain any μ bits in the N-length codeword. Wyner and Ozarow gave the capacity-doubt region of the second type of eavesdropping channel model.

After the first and second eavesdropping channel models were proposed, constructing practical codewords that can approach information-theoretic security has become a new research direction in the field of coding. In the study of the second type of eavesdropping channel model, V.K.Wei and Forney proposed the concept of generalized Hamming weight by specifically calculating the eavesdropper's suspicion. The introduction of generalized Hamming weight points out the direction for the construction of practical coding schemes that achieve information-theoretic security in the second type of eavesdropping channel model. When the eavesdropping channel is Gaussian noise and the main channel is noise-free, security in the sense of information theory can be achieved by using a coset coding scheme and the subcode is a dual code of any good code that can reach the capacity of the eavesdropping channel. In the study of coding schemes for the first type of eavesdropping channel model, Thangaraj pointed out that codes that meet specific structures can make the system secure in the sense of information theory.

There is currently no effective solution to the problem that the coding technology in related technologies cannot achieve information-theoretic security.

Summary of the invention

The present invention provides an encoding method and device, a decoding method and device, so as to at least solve the problem that the encoding technology in the related art cannot achieve information-theoretic security.

According to one aspect of the present invention, there is provided a coding method, comprising:

Obtaining a message to be sent, wherein the message to be sent includes: a real message of k bits and a random message of (l-k) bits, wherein l and k are both natural numbers;

Encode the message to be sent according to the check matrix H to obtain a codeword r ^n+k , wherein n is the codeword length of the real message, and the check matrix H satisfies the following condition: r ^n+k H ^T =0;

The codeword r ^n+k is sent.

Further,

The check matrix H is a check matrix of a low-density parity-check code LDPC code with a codeword length of n+k bits and a message length of l bits, wherein k<l<n+k.

Further, the (1-k)-bit random message is determined in the following manner:

Randomly generate a (l-k)-bit random message;

The (l-k)-bit random message is used to generate a codeword corresponding to the random message through a generator matrix of a linear block code.

Further, before sending the codeword r ^n+k , the method further includes one of the following:

The codeword r ^n+k is divided into 2 ^k subcodes, each of which corresponds to a message of k bits in length;

Randomly select a codeword from the subcode corresponding to the k-bit real message and send it;

It is determined that the actual transmission rate of the codeword r ^n+k is less than the channel capacity of the main channel, and the actual transmission rate of the subcode is equal to the channel capacity of the wiretap channel.

Further, it is determined that the actual transmission rate of the codeword r ^n+k is less than the channel capacity of the main channel, and the actual transmission rate of the subcode is equal to the channel capacity of the wiretap channel by the following method:

所述码字r^n+k的实际传输速率为

是主信道高斯噪声的噪声方差，

是窃听信道噪声的噪声方差，P是所述码字r^n+k的发送功率，主信道的信道容量maxI(X；Y)为

窃听信道的信道容量maxI(X；Z)为

Among them, the actual transmission rate of the subcode is

The actual transmission rate of the codeword r ^n+k is

is the noise variance of the main channel Gaussian noise,

is the noise variance of the eavesdropping channel noise, P is the transmission power of the codeword r ^n+k , and the channel capacity maxI(X; Y) of the main channel is

The channel capacity maxI(X; Z) of the eavesdropping channel is

Further, the method of solving the codeword r ^n+k includes:

From r ^{n+k HT} = 0, we get (c ^n+kl , ^sk , d ^lk ) ^HT = 0, and solve for c ^n+kl , where ^sk is the real message vector, d ^lk is the random message vector, and c ^n+kl represents the n+kl-bit check bit after encoding;

According to one aspect of the present invention, there is provided a decoding method, comprising:

Receive a codeword r ^n+k , wherein the codeword r ^n+k is obtained by: encoding a message to be sent according to a check matrix H to obtain the codeword r ^n+k , wherein the message to be sent includes: a real message of k bits and a random message of (lk) bits, wherein l and k are both natural numbers, n is the codeword length of the real message, and the check matrix H satisfies the following condition: r ^n+k H ^T =0;

The codeword r ^n+k is parsed.

According to another aspect of the present invention, there is provided an encoding device, comprising:

A first acquisition module is used to acquire a message to be sent, wherein the message to be sent includes: a real message of k bits and a random message of (l-k) bits, wherein l and k are both natural numbers;

A second acquisition module is used to encode the message to be sent according to a check matrix H to obtain a codeword r ^n+k , wherein n is the codeword length of the real message, and the check matrix H satisfies the following condition: r ^n+k H ^T =0;

A sending module is used to send the codeword r ^n+k .

Further, the method of solving the codeword r ^n+k includes:

From r ^{n+k HT} = 0, we get (c ^n+kl , ^sk , d ^lk ) ^HT = 0, and solve for c ^n+kl , where ^sk is the real message vector, d ^lk is the random message vector, and c ^n+kl represents the n+kl-bit check bit after encoding;

According to another aspect of the present invention, there is provided a decoding device, comprising:

A receiving module, configured to receive a codeword r ^n+k , wherein the codeword r ^n+k is obtained by: encoding a message to be sent according to a check matrix H to obtain the codeword r ^n+k , wherein the message to be sent includes: a real message of k bits and a random message of (lk) bits, wherein l and k are both natural numbers, n is the codeword length of the real message, and the check matrix H satisfies the following condition: r ^n+k H ^T =0;

A parsing module is used to parse the codeword r ^n+k .

Through the present invention, a message to be sent is obtained, wherein the message to be sent includes: a real message of k bits and a random message of (lk) bits, wherein l and k are both natural numbers; the message to be sent is encoded according to a check matrix H to obtain a code word r ^n+k , wherein n is the code word length of the real message, and the check matrix H satisfies the following condition: r ^n+k H ^T = 0; and the code word r ^n+k is sent. The problem that the coding technology cannot achieve information-theoretic security is solved, and secure coding and decoding is realized.

BRIEF DESCRIPTION OF THE DRAWINGS

The drawings described herein are used to provide a further understanding of the present invention and constitute a part of this application. The exemplary embodiments of the present invention and their descriptions are used to explain the present invention and do not constitute an improper limitation of the present invention. In the drawings:

FIG1 is a flow chart of an encoding method according to an embodiment of the present invention;

FIG2 is a flow chart of a decoding method according to an embodiment of the present invention;

FIG3 is a structural block diagram of an encoding device according to an embodiment of the present invention;

FIG4 is a structural block diagram of a decoding device according to an embodiment of the present invention;

FIG5 is a schematic diagram of a channel model applicable to a preferred embodiment of the present invention;

6 is a schematic diagram of an encoder construction method designed according to a preferred embodiment of the present invention;

FIG. 7 is a graph according to a preferred embodiment of the present invention.

DETAILED DESCRIPTION

The present invention will be described in detail below with reference to the accompanying drawings and in combination with embodiments. It should be noted that the embodiments and features in the embodiments of the present application can be combined with each other without conflict.

It should be noted that the terms "first", "second", etc. in the specification and claims of the present invention and the above-mentioned drawings are used to distinguish similar objects, and are not necessarily used to describe a specific order or sequence.

In this embodiment, a coding method is provided. FIG. 1 is a flow chart of a coding method according to an embodiment of the present invention. As shown in FIG. 1 , the process includes the following steps:

Step S102, obtaining a message to be sent, wherein the message to be sent includes: a real message of k bits and a random message of (l-k) bits, wherein l and k are both natural numbers;

Step S104, encoding the message to be sent according to the check matrix H to obtain a codeword ^rn+k , wherein n is the codeword length of the real message, and the check matrix H satisfies the following condition: ^rn+k H ^T = 0;

Step S106: Send the codeword r ^n+k .

Through the above steps, a message to be sent is obtained, wherein the message to be sent includes: a real message of k bits and a random message of (lk) bits, wherein l and k are both natural numbers; the message to be sent is encoded according to a check matrix H to obtain a codeword r ^n+k , wherein n is the codeword length of the real message, and the check matrix H satisfies the following condition: r ^n+k H ^T = 0; and the codeword r ^n+k is sent. The problem that the coding technology cannot achieve information-theoretic security is solved, and secure coding and decoding is realized.

In this embodiment, the check matrix H is a check matrix of a low-density parity-check code LDPC code with a codeword length of n+k bits and a message length of l bits, wherein k<l<n+k.

In this embodiment, the (1-k)-bit random message is determined in the following manner:

Randomly generate a (l-k)-bit random message;

The (l-k)-bit random message is used to generate a codeword corresponding to the random message through a generator matrix of a linear block code.

In this embodiment, before sending the codeword r ^n+k , the method further includes one of the following:

The codeword r ^n+k is divided into 2 ^k subcodes, each of which corresponds to a message of k bits in length;

A codeword is randomly selected from the subcode corresponding to the k-bit true message and sent;

It is determined that the actual transmission rate of the codeword r ^n+k is less than the channel capacity of the main channel, and the actual transmission rate of the subcode is equal to the channel capacity of the wiretap channel.

In this embodiment, it is determined that the actual transmission rate of the codeword r ^n+k is less than the channel capacity of the main channel, and the actual transmission rate of the subcode is equal to the channel capacity of the wiretap channel in the following manner:

该码字r^n+k的实际传输速率为

是主信道高斯噪声的噪声方差，

是窃听信道噪声的噪声方差，P是该码字r^n+k的发送功率，主信道的信道容量maxI(X；Y)为

窃听信道的信道容量maxI(X；Z)为Among them, the actual transmission rate of the subcode is

The actual transmission rate of the codeword r ^n+k is

is the noise variance of the main channel Gaussian noise,

is the noise variance of the eavesdropping channel noise, P is the transmission power of the codeword r ^n+k , and the channel capacity maxI(X; Y) of the main channel is

The channel capacity maxI(X; Z) of the eavesdropping channel is

In this embodiment, the method of solving the codeword r ^n+k includes:

From r ^{n+k HT} = 0, we get (c ^n+kl , ^sk , d ^lk ) ^HT = 0, and solve for c ^n+kl , where ^sk is the real message vector, d ^lk is the random message vector, and c ^n+kl represents the check bit of n+kl bits after encoding;

FIG. 2 is a flow chart of a decoding method according to an embodiment of the present invention. As shown in FIG. 2 , the flow chart includes the following steps:

Step S202, receiving a codeword r ^n+k , wherein the codeword r ^n+k is obtained by: encoding a message to be sent according to a check matrix H to obtain a codeword r ^n+k , wherein the message to be sent includes: a real message of k bits and a random message of (lk) bits, wherein l and k are both natural numbers, n is the codeword length of the real message, and the check matrix H satisfies the following condition: r ^n+k H ^T = 0;

Step S204: parsing the codeword r ^n+k .

In the present embodiment, a coding device is also provided, which is used to implement the above-mentioned embodiments and preferred implementation modes, and the descriptions that have been made will not be repeated. As used below, the term "module" can implement a combination of software and/or hardware of a predetermined function. Although the devices described in the following embodiments are preferably implemented in software, the implementation of hardware, or a combination of software and hardware is also possible and conceived.

FIG. 3 is a structural block diagram of an encoding device according to an embodiment of the present invention. As shown in FIG. 3 , the device includes

A first acquisition module 32 is used to acquire a message to be sent, wherein the message to be sent includes: a real message of k bits and a random message of (l-k) bits, wherein l and k are both natural numbers;

The second acquisition module 34 is used to encode the message to be sent according to the check matrix H to obtain the codeword r ^n+k , where n is the codeword length of the real message, and the check matrix H satisfies the following condition: r ^n+k H ^T =0;

The sending module 36 is configured to send the codeword r ^n+k .

Through the above steps, the first acquisition module 32 acquires the message to be sent, wherein the message to be sent includes: a k-bit real message and a (lk)-bit random message, wherein l and k are both natural numbers; the second acquisition module 34 encodes the message to be sent according to the check matrix H to obtain the codeword r ^n+k , wherein n is the codeword length of the real message, and the check matrix H satisfies the following condition: r ^n+k H ^T =0; the sending module 36 sends the codeword r ^n+k , which solves the problem that the coding technology cannot achieve information-theoretic security and realizes secure coding and decoding.

In this embodiment, the method of solving the codeword r ^n+k includes:

From r ^{n+k HT} = 0, we get (c ^n+kl , ^sk , d ^lk ) ^HT = 0, and solve for c ^n+kl , where ^sk is the real message vector, d ^lk is the random message vector, and c ^n+kl represents the check bit of n+kl bits after encoding;

FIG. 4 is a structural block diagram of a decoding device according to an embodiment of the present invention. As shown in FIG. 4 , the device includes:

The receiving module 42 is used to receive a codeword r ^n+k , wherein the codeword r ^n+k is obtained by: encoding a message to be sent according to a check matrix H to obtain a codeword r ^n+k , wherein the message to be sent includes: a real message of k bits and a random message of (lk) bits, wherein l and k are both natural numbers, n is the codeword length of the real message, and the check matrix H satisfies the following condition: r ^n+k H ^T =0;

The parsing module 44 is configured to parse the codeword r ^n+k .

It should be noted that the above modules can be implemented by software or hardware. For the latter, it can be implemented in the following ways, but not limited to: the above modules are all located in the same processor; or the above modules are respectively located in different processors.

The following is a detailed description with reference to the preferred embodiments of the present invention.

The preferred embodiment of the present invention discloses a secure coding method based on LDPC code for Gaussian eavesdropping channels. The coding and decoding designed in the preferred embodiment are relatively simple, and the iterative convergence speed during decoding is relatively fast. Simulation experiments show that the present invention has a very good effect when the signal-to-noise ratio of the eavesdropping channel is small.

Since it is very difficult to calculate the eavesdropper's doubt H(W|Z ^N ) in actual communication scenarios, we define the eavesdropper's bit error rate to approximate the doubt. It should be noted here that from the definition of information entropy, when the eavesdropper's doubt H(W|Z ^N ) is maximized, it is equivalent to the eavesdropper's bit error rate being equal to 0.5, that is, the eavesdropper's decoding error probability is equal to 0.5. Based on this, the preferred embodiment of the present invention hopes that the coding scheme designed for the Gaussian eavesdropping channel model has the following two characteristics: (1) The scheme makes the legitimate receiver's bit error rate arbitrarily small (that is, close to 0); (2) The scheme makes the eavesdropper's bit error rate close to 0.5.

The preferred embodiment of the present invention records a secure encoding and decoding method based on LDPC code, and the encoding scheme is designed as follows:

要小于主信道的信道容量C(SNR₁)，而子码的实际传输效率要等于窃听信道的信道容量C(SNR₂)；(c)给定发送的消息比特k，要随机的从k比特消息所对应的子码中选取一个码字发送出去。Theoretical basis for the design of the secure coding scheme of the preferred embodiment of the present invention: In the existence proof of the secure coding theorem of the eavesdropping channel model, Wyner pointed out that in order to design a coding scheme that achieves information-theoretic security, it is necessary to use a coding technique called "random binning". This coding technique corresponds the transmitted message to a box consisting of a bunch of code words one by one. When a message to be transmitted is given, a code word is randomly selected from the code word box corresponding to the message and sent out. In order to prevent the eavesdropper from correctly deciphering the sent message, the eavesdropper's decoding ability needs to be consumed. Wyner pointed out that if the eavesdropper knows the specific message sent, if the eavesdropper can correctly find ("decode") the random code word sent from the code word box corresponding to the specific message, the eavesdropper's decoding ability is consumed. If the code box corresponding to the specific message is also regarded as a new code word, the preferred embodiment of the present invention hopes that the transmission efficiency corresponding to the new code word is equal to the channel capacity of the eavesdropping channel, because this means that the entire decoding capacity of the eavesdropper is consumed in decoding the new code word, so the eavesdropper has no additional ability to decode which message is actually sent. Based on the above idea of Wyner's secure coding theorem proof, assuming that the message sent is k bits and the length of the code word is n bits, the secure coding scheme designed by the preferred embodiment of the present invention needs to have the following three characteristics: (a) The secure coding code word can be divided into ^2k subcodes, each subcode corresponds to a sent message bit of k bits; (b) The actual transmission efficiency of the code word

It must be smaller than the channel capacity C(SNR ₁ ) of the main channel, while the actual transmission efficiency of the subcode must be equal to the channel capacity C(SNR ₂ ) of the wiretap channel; (c) Given a message bit k to be sent, a codeword is randomly selected from the subcode corresponding to the k-bit message and sent out.

窃听信道噪声的噪声方差

编码之后的码字的发送功率P。由香农的信道容量公式我们可知主信道的容量maxI(X；Y)为

窃听信道的容量maxI(X；Z)为

我们假设发送的消息是k比特的，我们通过随机数产生器随机生成一个l-k比特的随机消息。此外，我们假设码字的长度是n+k比特。Parameter description of the above design scheme: First, we need to know the noise variance of the main channel Gaussian noise

Noise variance of eavesdropping channel noise

The transmission power of the encoded codeword is P. From Shannon's channel capacity formula, we know that the capacity of the main channel maxI(X; Y) is

The capacity of the eavesdropping channel maxI(X; Z) is

We assume that the message to be sent is k bits, and we use a random number generator to randomly generate a random message of lk bits. In addition, we assume that the length of the codeword is n+k bits.

The design steps of the secure encoding and decoding scheme of the preferred embodiment of the present invention are as follows:

First, according to the design idea of the classic LDPC code, a check matrix of an LDPC code with a codeword length of n+k bits and a message length of l bits is designed, denoted as H. The matrix has n+k-l rows and n+k columns.

Second, the l-bit message contains the k-bit real message and the l-k-bit random message. Obviously, l satisfies the following constraint k<l<n+k.

Third, in order to implement the coding method described by Wyner in the proof of the secure coding theorem of the eavesdropping channel model, that is, when the k-bit message to be sent is determined, a codeword is randomly selected from the corresponding codeword box. The preferred embodiment of the present invention first needs to divide the above-designed check matrix H and the LDPC code with a length of n+k bits into ^2k subcodes according to the real message of k bits, and the length of each subcode is n bits. This type of subcode is also a linear block code, and the message bit of the subcode is a random message of lk bits. We use the following method to implement the coding method of "randomly selecting a codeword from the subcode to transmit": (a) randomly generate a random message of lk bits through a random number generator; (b) generate a codeword corresponding to the random message of the lk bits through the generator matrix of the linear block code, and then transmit the codeword.

校验矩阵为H，码字长度为n+k比特，消息长度为l比特的LDPC码的实际传输效率为

为了满足前面所述的安全编码方案的特点(b)，令Fourth, the actual transmission efficiency of the above subcode is

The actual transmission efficiency of an LDPC code with a check matrix of H, a codeword length of n+k bits, and a message length of l bits is

In order to satisfy the characteristic (b) of the secure coding scheme described above, let

5. After the constraints of n, k, and l are given, the design method of LDPC code with check matrix H, codeword length n+k bits, and message length l bits is as follows: (a) The check matrix H is transformed into an [A|B] type matrix by Gaussian elimination. Note that the H matrix is a matrix with n+kl rows and n+k columns, and the A matrix is the unit matrix with n+kl rows and columns. The B matrix is a matrix with n+kl rows and l columns. When the real message s ^k is given and the randomly generated message is d ^{l -k} , according to the definition of the check matrix,

(cn ^+kl , ^sk , ^dlk ) ^HT = 0, (Formula 1)

Here, c ^n+kl represents the n+kl-bit check bit after encoding.

Substituting H = [A | B] into (Formula 1), we have

Rearranging (Formula 2), we can get

c ^n+kl ·A ^T +(s ^k ,d ^lk )·B ^T =0 (Formula 3)

Further arrangement (Formula 3),

c ^n+kl = (s ^k ,d ^lk )·B ^T ·(A ^-1 ) ^T (Formula 4)

(Formula 4) gives the formula for calculating the check digit of the codeword when we know the real message ^sk and the randomly generated message ^dlk . After knowing the check digit, the codeword ^rn+k obtained by the check matrix H can be expressed as

r ^n+k = (c ^n+kl ,s ^k ,d ^lk )=((s ^k ,d ^lk )·B ^T ·(A ^-1 ) ^T ,s ^k ,d ^lk ) (Formula 5)

是小于主信道的信道容量的，所以合法用户可以以趋近于0的译码错误概率同时译出真实消息s^k和随机生成的消息d^l-k。对于窃听者而言，首先我们希望他将其全部的译码能力都消耗在正确译出子码rⁿ上，这里6. For legitimate users, the actual transmission efficiency of codeword r ^n+k

is smaller than the channel capacity of the main channel, so the legitimate user can decode the real message ^sk and the randomly generated message ^dlk at the same time with a decoding error probability close to 0. For the eavesdropper, first we hope that he will consume all his decoding capabilities on correctly decoding the subcode ^rn , where

r ⁿ =(c ^n+kl ,s ^k ,d ^lk )=((s ^k ,d ^lk )·B ^T ·(A ^-1 ) ^T ,d ^lk ) (Formula 6)

由

以及k<l<n+k，我们可以得出Comparing ^rn and rn ^+k , it is easy to find ^that rn is the real message ^sk sent in rn ^+k without being deleted, that is, ^rn is the subcode of rn ^+k . For ^rn , the message is ^dlk , and we hope that the eavesdropper can correctly decode ^dlk and consume all its decoding capabilities in decoding ^dlk , which requires the transmission efficiency of subcode ^rn

Depend on

And k<l<n+k, we can conclude

是大于窃听信道的信道容量的，由香农定理可知，窃听者的译码错误概率是不能趋近于0的。(Formula 7) shows that for an eavesdropper, the actual transmission efficiency of the codeword r ^n+k is

It is greater than the channel capacity of the eavesdropping channel. According to Shannon's theorem, the probability of decoding error of the eavesdropper cannot approach 0.

The decoders of both the legitimate user and the eavesdropper use the classic belief propagation (BP) decoding algorithm, which is divided into the following steps: (1) First, the prior probability of the information bit is preset for the Gaussian channel; (2) The posterior probability of each check node is obtained from the information probability of the information node according to the belief propagation algorithm; (3) The posterior probability of the information node is inferred from the posterior probability of the check node; (4) The posterior probability of the information node is compared with the decision condition to make a hard decision. If it is satisfied, the decoding ends; if it is not satisfied, the above steps (2) to (4) are repeated, and the iteration is repeated until the condition is satisfied and the decoding result is obtained. If the number of iterations reaches a preset maximum number (for example, 100) and the condition is still not satisfied, the decoding is declared to have failed.

FIG5 is a schematic diagram of a channel model applicable to a preferred embodiment of the present invention. As shown in FIG5 , the channel model includes: an encoder, a main channel, a decoder, and an eavesdropping channel.

FIG6 is a schematic diagram of an encoder construction method designed according to a preferred embodiment of the present invention, as shown in FIG6 .

The specific implementation of the example of the preferred embodiment of the present invention adopts the rule (3,2) LDPC security code of the BP decoding algorithm.

即规则(3,2)LDPC码的实际传输效率是远小于主信道的信道容量的。在仿真中我们设置发送的总消息比特l＝5000000×100，合法用户译码错误的比特数是2次，其译码错误比率为4×10^-9。由于窃听信道的信噪比是变化的，我们不可能让固定的n,k,l满足

这里本实例希望发现同一个固定的编码方案对于不同的窃听信道的信噪比情况下的安全性变化趋势。我们发现，当窃听信道的信噪比越小(即窃听信道的噪声方差越大)，窃听者的译码错误概率越逼近0.5，即本发明优选实施例所设计的安全编码方案越安全。表1给出了当主信道信噪比等于14时，窃听信道信噪比与窃听者译码误比特率之间的关系，如表1所示。This example introduces a simple regular (3,2) LDPC security code. Based on the security coding method described above, in this example, n = 280, k = 20, l = 100, SNR ₁ = 14, SNR ₂ takes 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 create a 200-row, 300-column check matrix (n+kl rows, n+k columns). The check matrix consists of 0, 1, with 2 1s in each row and 3 1s in each column. The LDPC code composed of such a check matrix is called a regular (3,2) LDPC code. Each time we generate a 20-bit real message and an 80-bit random message, we encode these messages into a codeword with 100 message bits and 200 check bits through a regular (3,2) LDPC code, and then send the codeword to the legitimate user through the main channel and to the eavesdropper through the eavesdropping channel. The decoders of the legitimate user and the eavesdropper both use the classic BP decoding algorithm for decoding. It should be noted here that we assume that the signal-to-noise ratio of the main channel is fixed, while the signal-to-noise ratio of the eavesdropping channel is variable. From n = 280, k = 20, l = 100, SNR ₁ = 14, we can get

That is, the actual transmission efficiency of the rule (3,2) LDPC code is much lower than the channel capacity of the main channel. In the simulation, we set the total message bits sent to l = 5000000 × 100, the number of bits decoded incorrectly by the legitimate user is 2 times, and the decoding error rate is 4 × 10 ^-9 . Since the signal-to-noise ratio of the eavesdropping channel is variable, we cannot make fixed n, k, l satisfy

Here, this example hopes to find the security change trend of the same fixed coding scheme under different signal-to-noise ratios of the eavesdropping channel. We found that when the signal-to-noise ratio of the eavesdropping channel is smaller (that is, the noise variance of the eavesdropping channel is larger), the eavesdropper's decoding error probability is closer to 0.5, that is, the security coding scheme designed by the preferred embodiment of the present invention is more secure. Table 1 shows the relationship between the signal-to-noise ratio of the eavesdropping channel and the eavesdropper's decoding bit error rate when the main channel signal-to-noise ratio is equal to 14, as shown in Table 1.

Table 1

Fig. 7 is a curve diagram according to a preferred embodiment of the present invention, as shown in Fig. 7, Fig. 7 shows the relationship between the ratio of the signal-to-noise ratio of the main channel to the signal-to-noise ratio of the wiretap channel and the bit error rate of the eavesdropper. It is not difficult to see that when the ratio is larger, the effect of the security encoder is better, that is, when the signal-to-noise ratio of the wiretap channel is smaller, the performance of the security encoder designed by the present invention is safer.

Through the description of the above implementation methods, those skilled in the art can clearly understand that the method according to the above embodiment can be implemented by means of software plus a necessary general hardware platform, and of course can also be implemented by hardware, but in many cases the former is a better implementation method. Based on such an understanding, the technical solution of the present invention, or the part that contributes to the prior art, can be embodied in the form of a software product, which is stored in a storage medium (such as ROM/RAM, a magnetic disk, or an optical disk), and includes a number of instructions for enabling a terminal device (which can be a mobile phone, a computer, a server, or a network device, etc.) to execute the methods described in each embodiment of the present invention.

An embodiment of the present invention further provides a storage medium. Optionally, in this embodiment, the storage medium may be configured to store program codes for executing the following steps:

S1, obtaining a message to be sent, wherein the message to be sent includes: a real message of k bits and a random message of (l-k) bits, wherein l and k are both natural numbers;

S2, encoding the message to be sent according to the check matrix H to obtain a codeword r ^n+k , where n is the codeword length of the real message, and the check matrix H satisfies the following condition: r ^n+k H ^T = 0;

S3, sending the codeword r ^n+k .

Optionally, the storage medium is further configured to store program codes for executing the method steps of the above embodiment:

Optionally, in this embodiment, the above-mentioned storage medium may include but is not limited to: a USB flash drive, a read-only memory (ROM), a random access memory (RAM), a mobile hard disk, a magnetic disk or an optical disk, and other media that can store program codes.

Optionally, in this embodiment, the processor executes the method steps of the above embodiment according to the program code stored in the storage medium.

Optionally, the specific examples in this embodiment may refer to the examples described in the above embodiments and optional implementation modes, and this embodiment will not be described in detail here.

Obviously, those skilled in the art should understand that the above modules or steps of the present invention can be implemented by a general computing device, they can be concentrated on a single computing device, or distributed on a network composed of multiple computing devices, and optionally, they can be implemented by a program code executable by a computing device, so that they can be stored in a storage device and executed by the computing device, and in some cases, the steps shown or described can be executed in a different order than here, or they can be made into individual integrated circuit modules, or multiple modules or steps therein can be made into a single integrated circuit module for implementation. Thus, the present invention is not limited to any specific combination of hardware and software.

The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. For those skilled in the art, the present invention may have various modifications and variations. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention shall be included in the protection scope of the present invention.

Claims (8)

1. A method of encoding, comprising:

obtaining a message to be sent, wherein the message to be sent comprises: k bits of true message, (l-k) bits of random message, wherein l and k are natural numbers;

coding the message to be sent according to the check matrix H to obtain a codeword r ^n+k Wherein n is a codeword length of the real message, and the check matrix H satisfies the following conditions: r is (r) ^n+k H ^T ＝0；

-dividing said codeword r ^n+k Divided into 2 ^k A plurality of subcodes, each of which has a length of n bits;

from said 2 ^k Randomly selecting one sub-code from the sub-codes and transmitting the sub-code;

transmitting the codeword r ^n+k 。

2. The method of claim 1, wherein the step of determining the position of the substrate comprises,

the check matrix H is a check matrix of a low density parity check code LDPC code with a codeword length of n+k bits and a message length of l bits, wherein k is less than l and less than n+k.

3. The method of claim 1, wherein the (l-k) bit random message is determined by:

randomly generating a (l-k) bit random message;

generating a codeword corresponding to the random message by generating a matrix of the linear block code from the random message of the (l-k) bits.

4. The method of claim 1, wherein the codeword r ^n+k The actual transmission rate of the sub-code is smaller than the channel capacity of the main channel, and the actual transmission rate of the sub-code is equal to the channel capacity of the eavesdropping channel.

5. The method of claim 4, wherein the codeword r is determined by ^n+k The actual transmission rate of the subcode is less than the channel capacity of the primary channel and the actual transmission rate of the subcode is equal to the channel capacity of the eavesdropping channel:

wherein the actual transmission rate of the subcode is

The codeword r ^n+k Is +.>

Is the noise variance of the gaussian noise of the main channel,

is the noise variance of the eavesdropping channel noise, P is the codeword r ^n+k Is equal to or greater than the transmission power of the main channel>

The channel capacity maxI (X; Z) of the eavesdropping channel is +.>

6. A method of decoding, comprising:

receive Slave 2 ^k Randomly selecting one subcode from the subcodes, wherein the number 2 ^k The subcode is to code the code word r ^n+k The length of each subcode is n bits, which is obtained after division;

receiving codeword r ^n+k Wherein the codeword r ^n+k Is a codeword obtained by: coding the message to be transmitted according to the check matrix H to obtain a codeword r ^n+k Wherein the message to be sent comprises: a real message of k bits is provided,

(l-k) bits of random message, wherein l, k are natural numbers, n is the codeword length of the real message, and the check matrix H satisfies the following condition: r is (r) ^n+k H ^T ＝0；

Parsing the codeword r ^n+k 。

7. An encoding device, comprising:

the first acquisition module is configured to acquire a message to be sent, where the message to be sent includes: k bits of true message, (l-k) bits of random message, wherein l and k are natural numbers;

a second obtaining module, configured to encode the message to be sent according to a check matrix H, to obtain a codeword r ^n+k Wherein n is a codeword length of the real message, and the check matrix H satisfies the following conditions: r is (r) ^n+k H ^T ＝0；

A transmitting module for transmitting the codeword r ^n+k ；

Wherein the encoding device is further configured to, when transmitting the codeword r ^n+k BeforeThe codeword r ^n+k Divided into 2 ^k A plurality of subcodes, each of which has a length of n bits; from said 2 ^k And randomly selecting one subcode from the subcodes to send.

8. A decoding apparatus, comprising:

a receiving module for receiving the code word r ^n+k Wherein the codeword r ^n+k Is a codeword obtained by: coding the message to be transmitted according to the check matrix H to obtain a codeword r ^n+k Wherein the message to be sent comprises: k-bit true message, (l-k) -bit random message, wherein l and k are natural numbers, n is the codeword length of the true message, and the check matrix H satisfies the following conditions: r is (r) ^n+k H ^T ＝0；

A parsing module for parsing the codeword r ^n+k ；

Wherein the decoding device is further configured to, upon receiving the codeword r ^n+k Previously, receive from 2 ^k Randomly selecting one subcode from the subcodes; wherein said 2 ^k The subcode is to code the code word r ^n+k And the length of each subcode is n bits, which is obtained after division.

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