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WO2017177609A1 - 编码方法及装置，译码方法及装置 - Google Patents

编码方法及装置，译码方法及装置 Download PDF

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Publication number
WO2017177609A1
WO2017177609A1 PCT/CN2016/098727 CN2016098727W WO2017177609A1 WO 2017177609 A1 WO2017177609 A1 WO 2017177609A1 CN 2016098727 W CN2016098727 W CN 2016098727W WO 2017177609 A1 WO2017177609 A1 WO 2017177609A1
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message
codeword
check matrix
bit
channel
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PCT/CN2016/098727
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English (en)
French (fr)
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胡婧婷
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中兴通讯股份有限公司
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Publication of WO2017177609A1 publication Critical patent/WO2017177609A1/zh

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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
    • 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
    • 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

Definitions

  • This document relates to, but is not limited to, the field of communications, and in particular, to an encoding method and apparatus, a decoding method and apparatus.
  • LDPC codes Unfortunately, the optimal decoding algorithm for LDPC codes is a complete problem (Non-deterministic Polynomial, NP for short) (a difficult problem with non-polynomial time). MacKay also demonstrated that the Gallager decoding algorithm has excellent empirical performance. Luby et al. studied the Erasure Channel and found that the LDPC code can achieve channel capacity under lower complexity decoding, and proposed a simple linear time decoding algorithm on the deleted channel. The main research of LDPC codes The research field focuses on 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 the LDPC code in the actual system.
  • the sender wants to transmit the confidential message to the legitimate recipient via a discrete, unmemorized primary channel.
  • an eavesdropper attempts to eavesdrop on the output of the primary channel through another discrete, unvoiced eavesdropping channel.
  • Wyner uses conditional entropy H(W
  • W is the secret message being sent
  • Z N is the output of the eavesdropping channel. This confusion is also the first type of eavesdropping channel.
  • this area a capacity-doubt area, where all points in the area are reachable, and all points outside the area are It is unreachable.
  • Wyner defines and characterizes the concept of safe capacity, which is the maximum transmission efficiency in case the eavesdropper's doubts are maximized.
  • the Wyner system demonstrates the trade-off between transmission efficiency and security in communication systems (ie, the security of the communication system and the maximization of transmission cannot be guaranteed at the same time), which establishes the use of information theory to analyze the security of communication systems and the efficiency of transmission. The basis of the relationship.
  • Wyner proposed a random binning coding technique.
  • Random boxing means that the sent message is in one-to-one correspondence with a codebook (a collection of codewords).
  • a codebook a collection of codewords.
  • the second type of eavesdropping channel model Shortly after Wyner proposed the first type of eavesdropping channel model, he and Ozarow proposed a simplified eavesdropping channel model, the second type of eavesdropping channel model.
  • the main channel is noise-free, and the eavesdropper can arbitrarily select the ⁇ bit from the N-length codeword outputted by the main channel for noise-free eavesdropping, that is, the eavesdropper can obtain N-long. Any ⁇ bit in the code word.
  • Wyner and Ozarow give the capacity-doubt area of the second type of eavesdropping channel model.
  • the coset coding scheme is adopted and the subcode is any good coded dual code that can reach the eavesdropping channel capacity, and the information theory security can be achieved.
  • the first type of eavesdropping channel model coding scheme Thangaraj pointed out that satisfying the code of a specific structure can make the system safe in the sense of information theory.
  • the embodiment of the invention provides an encoding method and device, a decoding method and a device, which can realize the security of the coding technology to achieve the meaning of information theory.
  • an encoding method including:
  • Obtaining a to-be-sent message where the to-be-sent message includes: a k-bit real message, a (1-k)-bit random message, where l, k are natural numbers;
  • the check matrix H is a check matrix of a low density parity check code LDPC code having a codeword length of n+k bits and a message length of 1 bit, where k ⁇ l ⁇ n+k.
  • the (1 - k) bit random message is determined by:
  • the (1 - k)-bit random message is generated by a generation matrix of a linear block code to generate a codeword corresponding to the random message.
  • the codeword r n+k is divided into 2 k subcodes, and each of the subcodes corresponds to a message of a length of k bits;
  • the actual transmission rate of the codeword rn +k 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.
  • the actual transmission rate of the codeword r n+k is determined to be smaller 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:
  • 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 channel noise, P is the transmission power of the code word 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
  • a decoding method including:
  • the codeword r n+k is a codeword obtained by encoding a message to be transmitted according to a check matrix H, to obtain a codeword r n+k
  • parsing the codeword r n+k includes:
  • p k is the first k-dimensional vector of the check matrix H
  • q lk is the back (lk)-dimensional vector of the check matrix H.
  • an encoding apparatus including:
  • the first obtaining module is configured to obtain a to-be-sent message, where the to-be-sent message includes: a k-bit real message, and a (1-k)-bit random message, where l, k are natural numbers;
  • the sending module is configured to send the codeword r n+k .
  • a decoding apparatus including:
  • the receiving module is configured to receive the codeword r n+k , wherein the codeword r n+k is a codeword obtained by encoding a message to be sent according to the check matrix H, and obtaining a codeword r n+k
  • a parsing module configured to parse the codeword r n+k .
  • the parsing module is configured to parse the codeword r n+k by :
  • p k is the first k-dimensional vector of the check matrix H
  • q lk is the back (lk)-dimensional vector of the check matrix H.
  • the to-be-sent message is obtained, where the to-be-sent message includes: a k-bit real message, a (lk)-bit random message, where l, k are all natural numbers; the to-be-sent is sent according to the check matrix H
  • the security of the coding technology to achieve the meaning of information theory is realized, and the secure coding and decoding is realized.
  • FIG. 1 is a flow chart of an encoding method in accordance with an embodiment of the present invention.
  • FIG. 2 is a flow chart of a decoding method in accordance with an embodiment of the present invention.
  • FIG. 3 is a structural block diagram of an encoding apparatus according to an embodiment of the present invention.
  • FIG. 4 is a block diagram showing the structure of a decoding apparatus according to an embodiment of the present invention.
  • FIG. 5 is a schematic diagram of a suitable channel model in accordance with an alternative embodiment of the present invention.
  • FIG. 6 is a schematic diagram of a method of constructing an encoder designed in accordance with an alternative embodiment of the present invention.
  • Figure 7 is a graph of an alternative embodiment in accordance with the present invention.
  • FIG. 1 is a flowchart of an encoding method according to an embodiment of the present invention. As shown in FIG. 1, the process includes the following steps:
  • Step S102 Acquire a to-be-sent message, where the to-be-sent message includes: a k-bit real message, a (1-k)-bit random message, where l, k are natural numbers;
  • step S106 the code word r n+k is transmitted.
  • the message to be sent is obtained by the foregoing steps, where the to-be-sent message includes: a k-bit real message, a (lk)-bit random message, where l, k are natural numbers; and the to-be-sent message is performed according to the check matrix H.
  • the security of the coding technology to achieve the meaning of information theory is realized, and the secure coding and decoding is realized.
  • the check matrix H is a check matrix of a low density parity check code LDPC code having a codeword length of n+k bits and a message length of 1 bit, where k ⁇ l ⁇ n+k .
  • the (l-k)-bit random message is determined by:
  • the (l-k)-bit random message is generated by the generation matrix of the linear block code to generate a codeword corresponding to the random message.
  • the method 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, and each subcode corresponds to a message of length k bits;
  • the actual transmission rate of the codeword r n+k is smaller 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.
  • the actual transmission rate of the codeword rn +k is determined to be smaller 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:
  • 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 channel noise, P is the transmission power of the code word 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
  • the manner of solving the codeword r n+k includes:
  • FIG. 2 is a flowchart of a decoding method according to an embodiment of the present invention. As shown in FIG. 2, the process includes the following steps:
  • Step S202 receiving a codeword r n+k , wherein the codeword r n+k is a codeword obtained by encoding a message to be sent according to a check matrix H, to obtain a codeword r n+k , where
  • step S204 the codeword r n+k is parsed.
  • an encoding device is also provided, which is used to implement the above-mentioned embodiments and optional embodiments, and has not been described again.
  • the term “module” may implement a combination of software and/or hardware of a predetermined function.
  • the apparatus described in the following embodiments is preferably implemented in software, hardware, or a combination of software and hardware, is also possible and contemplated.
  • FIG. 3 is a structural block diagram of an encoding apparatus according to an embodiment of the present invention. As shown in FIG. 3, the apparatus includes
  • the first obtaining module 32 is configured to obtain a to-be-sent message, where the to-be-sent message includes: a k-bit real message, and a (1-k)-bit random message, where l, k are natural numbers;
  • the transmitting module 36 is arranged to transmit the codeword r n+k .
  • the sending module 36 sends the code word r n+k , which realizes the security of the coding technology to achieve information theory meaning, and realizes secure coding and decoding.
  • the manner of solving the codeword r n+k includes:
  • FIG. 4 is a structural block diagram of a decoding apparatus according to an embodiment of the present invention. As shown in FIG. 4, the apparatus includes:
  • the receiving module 42 is configured to receive the codeword r n+k , wherein the codeword r n+k is a codeword obtained by encoding a message to be sent according to the check matrix H, and obtaining a codeword r n+k
  • the parsing module 44 is arranged to parse the codeword r n+k .
  • each of the above modules may be implemented by software or hardware.
  • the foregoing may be implemented by, but not limited to, the foregoing modules are all located in the same processor; or, the above modules are respectively located. Different processors.
  • An optional embodiment of the present invention discloses an LDPC code-based secure coding and decoding method for a Gaussian eavesdropping channel.
  • the coding and decoding designed by this alternative embodiment are relatively simple, and the iteration convergence speed during decoding is faster. Simulation experiments show that the embodiment of the present invention has a very good effect when the signal-to-noise ratio of the eavesdropping channel is small.
  • the eavesdropper's bit error rate is the largest when the eavesdropper's bit error rate is equal to 0.5, that is, the eavesdropper's decoding error probability is equal to 0.5.
  • the codec scheme designed by the optional embodiment of the present invention for the Gaussian eavesdropping channel model has the following two features: (1) the scheme makes the bit error rate of the legal receiver arbitrarily small (ie, approximates 0); 2) This scheme makes the eavesdropper's bit error rate close to 0.5.
  • An optional embodiment of the present invention describes a secure coding and decoding method based on an LDPC code, and the coding scheme is designed as follows:
  • the theoretical basis for the design of the secure coding scheme in the alternative embodiment of the present invention In the existence proof of the security coding theorem of the eavesdropping channel model, Wyner pointed out that to design a coding and decoding scheme to achieve information theory security, it is necessary to use a type called Random packing" coding technology.
  • the encoding technique corresponds one-to-one correspondence between the transmitted message and the stack of codewords. When a message to be transmitted is given, a codeword is randomly selected from the codeword box corresponding to the message and sent out. In order for the eavesdropper to not correctly translate the sent message, it is necessary to consume the ability of the eavesdropper to decode.
  • Wyner points out that if the eavesdropper knows the specific message sent, if the eavesdropper can correctly find it from the codeword box corresponding to the specific message.
  • the "random" codeword is sent ("translated"), the eavesdropper's decoding ability is consumed.
  • the codeword box corresponding to the specific message is also regarded as a new codeword, the optional embodiment of the present invention hopes that the transmission efficiency corresponding to the new codeword is equal to the channel capacity of the eavesdropping channel, because this represents The entire decoding ability of the eavesdropper is consumed by translating the new codeword so that the eavesdropper has no additional ability to translate which message was sent.
  • the secure coding scheme designed by the alternative embodiment of the present invention needs to have the following three characteristics: (a) Secure coding The transmission efficiency is equal to the channel capacity C (SNR 2 ) of the eavesdropping channel; (c) given the transmitted message bit k, a codeword is randomly selected from the subcode corresponding to the k-bit message to be transmitted.
  • a check matrix of LDPC code with a codeword length of n+k bits and a message length of 1 bit is designed, denoted as H, and the matrix has n+kl rows with n+k Column.
  • the 1-bit message contains a k-bit real transmission message and a 1-k-bit random message. Obviously, l satisfies the following constraint k ⁇ l ⁇ n + k.
  • a random encoding method is selected from a corresponding codeword box.
  • the optional embodiment of the present invention first needs to design the check matrix of the above as H, and the LDPC code of length n+k bits is divided into 2 k subcodes according to the k-bit real message, and each subcode has a length of n bits. .
  • This type of subcode is also a linear block code, and the message bits of the subcode are lk-bit random messages.
  • the actual transmission efficiency of the above subcode is
  • the parity transmission matrix is H
  • the codeword length is n+k bits
  • the actual transmission efficiency of the LDPC code with a message length of 1 bit is In order to meet the characteristics of the security coding scheme described above (b),
  • the parity check matrix is H
  • the codeword length is n+k bits
  • the design method of the LDPC code with the message length of 1 bit is as follows: (a) the school The matrix H is reduced to a [A
  • the B matrix is a matrix with a row number of n+kl and a column number of l.
  • c n+kl represents the parity of the n+k1 bits after encoding.
  • Equation 4 gives the formula for calculating the check digit of the codeword when we know the real message s k and the randomly generated message d lk . After knowing the parity bit, the codeword r n+k obtained by checking the matrix H can be expressed as
  • the actual transmission efficiency of the codeword r n+k It is smaller than the channel capacity of the primary channel, so the legitimate user can simultaneously decode the real message s k and the randomly generated message d lk with a decoding error probability close to zero.
  • the legitimate user can simultaneously decode the real message s k and the randomly generated message d lk with a decoding error probability close to zero.
  • eavesdroppers first we want him to consume all of his decoding power on the correct translation subcode r n , here
  • r n is to delete the real message s k sent in r n+k , that is, r n is a subcode of r n+k .
  • the message is d lk , we hope that the eavesdropper can correctly decode d lk and consume all its decoding capabilities on the translated d lk , which requires the transmission of the subcode r n effectiveness by And k ⁇ l ⁇ n+k, we can get
  • Equation 7 shows the actual transmission efficiency of the codeword r n+k for the eavesdropper 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 be close to zero.
  • Both the legitimate user and the eavesdropper's decoder use the classic Belief Propagation (BP) decoding algorithm, which is divided into the following steps: (1) Firstly, the prior probability of the information bits is preset for the Gaussian channel. (2) The posterior probability of each check node is obtained by the information probability of the information node according to the belief propagation algorithm; (3) the posterior probability of the information node is derived from the posterior probability of the check node; (4) The posterior probability of the information node is hard decision according to the decision condition. If it is satisfied, the decoding ends; if not, 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 of times (for example, 100) and the condition is still not met, then the decoding fails.
  • BP Belief Propagation
  • FIG. 5 is a schematic diagram of a suitable channel model according to an alternative embodiment of the present invention, as shown in FIG. 5, including: an encoder, a primary channel, a decoder, and an eavesdropping channel; in the figure, X N , Y N , and Z N are output signal.
  • FIG. 6 is a schematic diagram of a method of constructing an encoder designed in accordance with an alternative embodiment of the present invention, as shown in FIG.
  • a specific embodiment of an alternative embodiment of the present invention employs a rule (3, 2) LDPC security code of a BP decoding algorithm.
  • This example introduces a simple rule (3, 2) LDPC security code.
  • a check matrix 200 rows and 300 columns (n+k1 rows, n+k columns).
  • the check matrix consists of 0,1, and the number of 1s in each row is 2, in each column.
  • the number of 1 is 3.
  • the LDPC code composed of such a check matrix is called a regular (3, 2) LDPC code.
  • Table 1 shows the relationship between the eavesdropping channel signal-to-noise ratio and the eavesdropper decoding bit error rate when the primary channel SNR is equal to 14, as shown in Table 1.
  • FIG. 7 is a graph of an alternative 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 primary channel to the signal to noise ratio of the eavesdropping channel and the eavesdropper bit error rate. It is not difficult to see that the larger the ratio, the better the effect of the security encoder, that is, the smaller the signal-to-noise ratio of the eavesdropping channel, the present invention The safer the performance of the safety encoder designed in the embodiment.
  • the method according to the above embodiment can be implemented by means of software plus a necessary general hardware platform, and of course, by hardware, but in many cases, the former is A better implementation.
  • the technical solution of the present invention which is essential or contributes to the prior art, may be embodied in the form of a software product stored in a storage medium (such as ROM/RAM, disk,
  • the optical disc includes a number of instructions for causing a terminal device (which may be a cell phone, a computer, a server, or a network device, etc.) to perform the methods described in various embodiments of the present invention.
  • Embodiments of the present invention also provide a storage medium.
  • the foregoing storage medium may be configured to store program code for performing the following steps:
  • S1 Acquire a to-be-sent message, where the to-be-sent message includes: a k-bit real message, a (1-k)-bit random message, where l, k are natural numbers;
  • the storage medium is further arranged to store program code for performing the method steps of the above-described embodiments:
  • the foregoing storage medium may include, but not limited to, a USB flash drive, a Read-Only Memory (ROM), a Random Access Memory (RAM), a mobile hard disk, and a magnetic memory.
  • ROM Read-Only Memory
  • RAM Random Access Memory
  • a mobile hard disk e.g., a hard disk
  • magnetic memory e.g., a hard disk
  • the processor performs the method steps of the foregoing embodiments according to the stored program code in the storage medium.
  • modules or steps of the present invention described above can be implemented by a general-purpose computing device that can be centralized on a single computing device or distributed.
  • they may be implemented by program code executable by the computing device such that they may be stored in the storage device by the computing device and, in some cases,
  • the steps shown or described may be performed in an order different than that herein, or they may be separately fabricated into individual integrated circuit modules, or a plurality of the modules or steps may be implemented as a single integrated circuit module.
  • the invention is not limited to any specific combination of hardware and software.
  • the above technical solution realizes the security of the coding technology to achieve the meaning of information theory, and realizes secure coding and decoding.

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Abstract

一种编码方法及装置，译码方法及装置，其中，该编码方法包括：获取待发送消息，其中，该待发送消息包括：k比特的真实消息，(l-k)比特的随机消息，其中l，k均为自然数；依据校验矩阵H对该待发送消息进行编码，获取码字rn+k，其中，该n为该真实消息的码字长度，该校验矩阵H满足以下条件：rn+kHT＝0；发送该码字rn+k。采用上述技术方案实现了安全编码译码。

Description

编码方法及装置，译码方法及装置 技术领域
本文涉及但不限于通信领域，具体而言，涉及一种编码方法及装置，译码方法及装置。
背景技术
在相关技术中，尽管早在1984年香农定理就界定了信道编码的性能，然而直到1993年涡轮Turbo码出现之前，大多数信道编码算法都远不及香农限。所以，Turbo码的诞生意味着在加性高斯白噪声信道中信道编码接近香农限的开始。在两年之后，迈克Mackay和尼尔Neal受Turbo码的启发重新发现，很长时间以来被人们忽视的低密度校验码(Low Density Parity Check code，简称为LDPC)，有着更为接近香农限的性能。LDPC码是在1962年由Gallager提出的，他所提出的这种码是一种基于稀疏校验矩阵的线性分组码。Gallager详细阐述了LDPC码的构造方法、迭代概率译码算法以及其理论描述。然而因为其编码和译码需要较高的硬件需求，以及当时BCH码、Reed-Solomon码和级联码表现出的简单而高效的性能，除了少数的研究人员，例如Pinsker和Margulis之外，大部分研究人员们并不怎么关注LDPC码，甚至于几乎将其遗忘。
在上个世纪九十年代，MacKay等人对低密度奇偶校验码进行了再发现，并且证明了当以低于香农限的任意码率进行通信时，基于最大后验概率译码(Maximum A Posteriori，简称为MAP)算法的LDPC码的译码错误概率低至10-7，非常接近于0。
遗憾的是，LDPC码的最优译码算法是一个(Non-deterministic Polynomial，简称为NP)完全问题(非多项式时间的困难问题)。MacKay同时还论证了Gallager译码算法有着出色的经验性能。Luby等人研究了删除信道(Erasure Channel)之后发现，LDPC码能够在较低复杂度的译码下达到信道容量，并且提出了一种在删除信道上的简单线性时间译码算法。目前LDPC码的主要研 究领域集中于四个不同的方面，它们分别是：校验矩阵的构造、译码算法优化、性能的分析及LDPC码在实际系统中的应用。
从信息论的角度来分析通信系统的安全性要追溯到1949年，香农在该年发表了一篇名为《保密系统的通信理论》的重要文章，从而奠定了用信息论去分析通信系统安全性的基础。在此之后，Wyner及其合作者提出了两类窃听信道模型：第一类窃听信道(wiretap channel I)和第二类窃听信道(wiretap channel of type II)。
在第一类窃听信道模型中，发送方想将机密消息通过一个离散无记忆的主信道传送给合法接收者。与此同时，一个窃听者试图通过另外一个离散无记忆的窃听信道来窃听主信道的输出。Wyner用条件熵H(W|ZN)来表示窃听者对机密消息的疑惑度(这里W为正在发送的机密消息，ZN为窃听信道的输出)，这个疑惑度也就是第一类窃听信道模型中衡量安全性的重要参数。Wyner刻画了由所有可达的传输效率-疑惑度对组成的区域，我们通常把这个区域叫做容量-疑惑度区域，即这个区域内所有的点都是可达的，而区域外所有的点都是不可达的。在此基础上，Wyner定义并刻画了安全容量这个概念，即在保证窃听者的疑惑度最大的情况下传输效率的最大值。Wyner系统论证了通信系统中传输效率与安全性之间的折衷关系(即通信系统的安全性和最大化传输不能同时得到保证)，这奠定了用信息论去分析通信系统安全性和传输效率之间关系的基础。在容量-疑惑度区域的存在性证明中，Wyner提出了随机装箱(random binning)的编码技术。在考虑安全的信道模型中，该技术已经成为一种最常见的编码技术。随机装箱是指发送的消息和一个码本(一堆码字组成的集合)一一对应。当发送方发送一个具体的消息时，首先找出和此消息相对应的码本，然后随机地于此码本中选取一个码字发送出去，该码字就做为编码器的输出。
在Wyner提出了第一类窃听信道模型之后不久，他和Ozarow又提出了一个简化了的窃听信道模型，即第二类窃听信道模型。在第二类窃听信道模型中，主信道是无噪的，同时窃听者可以从主信道输出的N长的码字中任意地选取μ位进行无噪窃听，也即窃听者可以得到N长的码字中任意的μ位。Wyner和Ozarow给出了第二类窃听信道模型的容量-疑惑度区域。
第一、二类窃听信道模型提出之后，构造实际的能逼近信息论意义安全的码字就成为了编码领域一个新的研究方向。在第二类窃听信道模型的研究中，通过具体计算窃听者的疑惑度，V.K.Wei以及Forney提出了广义汉明重量的概念。广义汉明重量的提出为第二类窃听信道模型中达到信息论意义安全的实际编码方案的构造指明了方向。当窃听信道是高斯噪声，主信道无噪声的情况下，采用陪集编码方案且子码是任意一种可达窃听信道容量的好码的对偶码时，可以达到信息论意义上的安全。在第一类窃听信道模型编码方案的研究中，Thangaraj指出满足特定结构的码可以使系统达到信息论意义上的安全。
由于实际信道无法同时满足窃听信道是高斯噪声，主信道无噪声的情况,因此相关技术中的编码技术不能达到信息论意义上的安全。针对这一问题，目前还没有有效地解决方案。
发明内容
以下是对本文详细描述的主题的概述。本概述并非是为了限制权利要求的保护范围。
本发明实施例提供了一种编码方法及装置，译码方法及装置，能够实现编码技术达到信息论意义的安全。
根据本发明实施例的一个方面，提供了一种编码方法，包括：
获取待发送消息，其中，所述待发送消息包括：k比特的真实消息，(l-k)比特的随机消息，其中l，k均为自然数；
依据校验矩阵H对所述待发送消息进行编码，获取码字rn+k，其中，所述n为所述真实消息的码字长度，所述校验矩阵H满足以下条件：rn+kHT＝0；
发送所述码字rn+k。
可选地，
所述校验矩阵H为码字长度为n+k比特，并且消息长度为l比特的低密度奇偶校验码LDPC码的校验矩阵，其中，k＜l＜n+k。
可选地，通过以下方式确定所述(l-k)比特的随机消息：
随机产生一个(l-k)比特的随机消息；
将所述(l-k)比特的随机消息通过线性分组码的生成矩阵生成与所述随机消息对应的码字。
可选地，发送所述码字rn+k之前，执行以下至少一种：
所述码字rn+k划分为2k个子码，每一个所述子码对应一个k比特长度的消息；
从所述k比特真实消息所对应的子码中随机选取一个码字发送；
确定所述码字rn+k的实际传输速率小于主信道的信道容量，以及所述子码的实际传输速率等于窃听信道的信道容量。
可选地，通过以下方式确定所述码字rn+k的实际传输速率小于主信道的信道容量，以及所述子码的实际传输速率等于窃听信道的信道容量：
Figure PCTCN2016098727-appb-000001
Figure PCTCN2016098727-appb-000002
其中，所述子码的实际传输速率为
Figure PCTCN2016098727-appb-000003
所述码字rn+k的实际传输速率为
Figure PCTCN2016098727-appb-000004
Figure PCTCN2016098727-appb-000005
是主信道高斯噪声的噪声方差，
Figure PCTCN2016098727-appb-000006
是窃听信道噪声的噪声方差，P是所述码字rn+k的发送功率，主信道的信道容量maxI(X；Y)为
Figure PCTCN2016098727-appb-000007
窃听信道的信道容量maxI(X；Z)为
Figure PCTCN2016098727-appb-000008
根据本发明实施例的一个方面，提供了一种译码方法，包括：
接收码字rn+k，其中，所述码字rn+k为通过以下方式得到的码字：依据校验矩阵H对待发送消息进行编码，得到码字rn+k，其中，所述待发送消息包括：k比特的真实消息，(l-k)比特的随机消息，其中l，k均为自然数，所述n为所述真实消息的码字长度，所述校验矩阵H满足以下条件：rn+kHT＝0；
解析所述码字rn+k。
可选地，解析所述码字rn+k包括：
由rn+kHT＝0得出(cn+k-l，sk,dl-k)HT＝0，解得cn+k-l，其中，所述sk为所述真实消息向量，所述dl-k为所述随机消息向量，所述cn+k-l表示编码之后的n+k-l比特的校验位；
Figure PCTCN2016098727-appb-000009
pk为校验矩阵H的前k维向量，ql-k为校验矩阵H的后(l-k)维向量。
根据本发明实施例的另一方面，提供了一种编码装置，包括：
第一获取模块，设置为获取待发送消息，其中，所述待发送消息包括：k比特的真实消息，(l-k)比特的随机消息，其中l，k均为自然数；
第二获取模块，设置为依据校验矩阵H对所述待发送消息进行编码，获取码字rn+k，其中，所述n为所述真实消息的码字长度，所述校验矩阵H满足以下条件：rn+kHT＝0；
发送模块，设置为发送所述码字rn+k。
根据本发明实施例的另一方面，提供了一种译码装置，包括：
接收模块，设置为接收码字rn+k，其中，所述码字rn+k为通过以下方式得到的码字：依据校验矩阵H对待发送消息进行编码，得到码字rn+k，其中，所述待发送消息包括：k比特的真实消息，(l-k)比特的随机消息，其中l，k均为自然数，所述n为所述真实消息的码字长度，所述校验矩阵H满足以下条件：rn+kHT＝0；
解析模块，设置为解析所述码字rn+k。
可选地，解析模块是设置为通过如下方式实现解析所述码字rn+k：
由rn+kHT＝0得出(cn+k-l，sk,dl-k)HT＝0，解得cn+k-l，其中，所述sk为所述真实消息向量，所述dl-k为所述随机消息向量，所述cn+k-l表示编码之后的n+k-l比特的校验位；
Figure PCTCN2016098727-appb-000010
pk为校验矩阵H的前k维向量，ql-k为校验矩阵H的后(l-k)维向量。
通过本发明实施例，获取待发送消息，其中，该待发送消息包括：k比 特的真实消息，(l-k)比特的随机消息，其中l，k均为自然数；依据校验矩阵H对该待发送消息进行编码，获取码字rn+k，其中，该n为该真实消息的码字长度，该校验矩阵H满足以下条件：rn+kHT＝0；发送该码字rn+k。实现了编码技术达到信息论意义的安全，实现了安全编码译码。
在阅读并理解了附图和详细描述后，可以明白其他方面。
附图概述
图1是根据本发明实施例的一种编码方法的流程图；
图2是根据本发明实施例的一种译码方法的流程图；
图3是根据本发明实施例的一种编码装置的结构框图；
图4是根据本发明实施例的一种译码装置的结构框图；
图5是根据本发明可选实施例的适用的信道模型示意图；
图6是根据本发明可选实施例设计的编码器构造方法示意图；
图7是根据本发明可选实施例的曲线图。
本发明的实施方式
下文中将参考附图并结合实施例来详细说明本发明。需要说明的是，在不冲突的情况下，本申请中的实施例及实施例中的特征可以相互组合。
需要说明的是，本发明的说明书和权利要求书及上述附图中的术语“第一”、“第二”等是用于区别类似的对象，而不必用于描述特定的顺序或先后次序。
在本实施例中提供了一种编码方法，图1是根据本发明实施例的一种编码方法的流程图，如图1所示，该流程包括如下步骤：
步骤S102，获取待发送消息，其中，该待发送消息包括：k比特的真实消息，(l-k)比特的随机消息，其中l，k均为自然数；
步骤S104，依据校验矩阵H对该待发送消息进行编码，获取码字rn+k，其中，该n为该真实消息的码字长度，该校验矩阵H满足以下条件：rn+kHT＝0；
步骤S106，发送该码字rn+k。
通过上述步骤，获取待发送消息，其中，该待发送消息包括：k比特的真实消息，(l-k)比特的随机消息，其中l，k均为自然数；依据校验矩阵H对该待发送消息进行编码，获取码字rn+k，其中，该n为该真实消息的码字长度，该校验矩阵H满足以下条件：rn+kHT＝0；发送该码字rn+k。实现了编码技术达到信息论意义的安全，实现了安全编码译码。
在本实施例中，该校验矩阵H为码字长度为n+k比特，并且消息长度为l比特的低密度奇偶校验码LDPC码的校验矩阵，其中，k＜l＜n+k。
在本实施例中，通过以下方式确定该(l-k)比特的随机消息：
随机产生一个(l-k)比特的随机消息；
将该(l-k)比特的随机消息通过线性分组码的生成矩阵生成与该随机消息对应的码字。
在本实施例中，发送该码字rn+k之前，该方法还包括以下之一：
该码字rn+k划分为2k个子码，每一个子码对应一个k比特长度的消息；
从该k比特真实消息所对应的子码中随机选取一个码字发送；
确定该码字rn+k的实际传输速率小于主信道的信道容量，以及该子码的实际传输速率等于窃听信道的信道容量。
在本实施例中，通过以下方式确定该码字rn+k的实际传输速率小于主信道的信道容量，以及该子码的实际传输速率等于窃听信道的信道容量：
Figure PCTCN2016098727-appb-000011
Figure PCTCN2016098727-appb-000012
其中，该子码的实际传输速率为
Figure PCTCN2016098727-appb-000013
该码字rn+k的实际传输速率为
Figure PCTCN2016098727-appb-000014
Figure PCTCN2016098727-appb-000015
是主信道高斯噪声的噪声方差，
Figure PCTCN2016098727-appb-000016
是窃听信道噪声的噪声方差，P是该码字rn+k的发送功率，主信道的信道容量maxI(X；Y)为
Figure PCTCN2016098727-appb-000017
窃听信道的 信道容量maxI(X；Z)为
Figure PCTCN2016098727-appb-000018
在本实施例中，求解该码字rn+k的方式包括：
由rn+kHT＝0得出(cn+k-l，sk,dl-k)HT＝0，解得cn+k-l，其中，该sk为该真实消息向量，该dl-k为该随机消息向量，该cn+k-l表示编码之后的n+k-l比特的校验位；
Figure PCTCN2016098727-appb-000019
图2是根据本发明实施例的一种译码方法的流程图，如图2所示，该流程包括如下步骤：
步骤S202，接收码字rn+k，其中，该码字rn+k为通过以下方式得到的码字：依据校验矩阵H对待发送消息进行编码，得到码字rn+k，其中，该待发送消息包括：k比特的真实消息，(l-k)比特的随机消息，其中l，k均为自然数，该n为该真实消息的码字长度，该校验矩阵H满足以下条件：rn+kHT＝0；
步骤S204，解析该码字rn+k。
在本实施例中还提供了一种编码装置，该装置用于实现上述实施例及可选实施方式，已经进行过说明的不再赘述。如以下所使用的，术语“模块”可以实现预定功能的软件和/或硬件的组合。尽管以下实施例所描述的装置较佳地以软件来实现，但是硬件，或者软件和硬件的组合的实现也是可能并被构想的。
图3是根据本发明实施例的一种编码装置的结构框图，如图3所示，该装置包括
第一获取模块32，设置为获取待发送消息，其中，该待发送消息包括：k比特的真实消息，(l-k)比特的随机消息，其中l，k均为自然数；
第二获取模块34，设置为依据校验矩阵H对该待发送消息进行编码，获取码字rn+k，其中，该n为该真实消息的码字长度，该校验矩阵H满足以下条件：rn+kHT＝0；
发送模块36，设置为发送该码字rn+k。
通过上述步骤，第一获取模块32获取待发送消息，其中，该待发送消息 包括：k比特的真实消息，(l-k)比特的随机消息，其中l，k均为自然数；第二获取模块34依据校验矩阵H对该待发送消息进行编码，获取码字rn+k，其中，该n为该真实消息的码字长度，该校验矩阵H满足以下条件：rn+kHT＝0；发送模块36发送该码字rn+k，实现了编码技术达到信息论意义的安全，实现了安全编码译码。
在本实施例中，求解该码字rn+k的方式包括：
由rn+kHT＝0得出(cn+k-l，sk,dl-k)HT＝0，解得cn+k-l，其中，该sk为该真实消息向量，该dl-k为该随机消息向量，该cn+k-l表示编码之后的n+k-l比特的校验位；
Figure PCTCN2016098727-appb-000020
图4是根据本发明实施例的一种译码装置的结构框图，如图4所示，该装置包括：
接收模块42，设置为接收码字rn+k，其中，该码字rn+k为通过以下方式得到的码字：依据校验矩阵H对待发送消息进行编码，得到码字rn+k，其中，该待发送消息包括：k比特的真实消息，(l-k)比特的随机消息，其中l，k均为自然数，该n为该真实消息的码字长度，该校验矩阵H满足以下条件：rn+kHT＝0；
解析模块44，设置为解析该码字rn+k。
需要说明的是，上述各个模块是可以通过软件或硬件来实现的，对于后者，可以通过以下方式实现，但不限于此：上述各个模块均位于同一处理器中；或者，上述各个模块分别位于不同的处理器中。
下面结合本发明可选实施例进行详细说明。
本发明可选实施例公开了一种用于高斯窃听信道的基于LDPC码的安全编译码方法。本可选实施例所设计的编码译码都相对简单，译码时的迭代收敛速度较快。仿真实验表明本发明实施例在窃听信道信噪比较小时具有非常好的效果。
由于在实际通信场景中，计算窃听者的疑惑度H(W|ZN)是一件非常困难的事情，于是我们定义窃听者的误比特率来近似代替疑惑度。这里需要注意的 是从信息熵的定义来看，窃听者的疑惑度H(W|ZN)取得最大时等价于窃听者的误比特率等于0.5，也即窃听者的译码错误概率等于0.5。基于此，本发明可选实施例希望为高斯窃听信道模型设计出的编译码方案具有如下两个特征：(1)该方案使得合法接收者的误比特率任意小(即逼近于0)；(2)该方案使得窃听者的误比特率逼近0.5。
本发明可选实施例记载了一种基于LDPC码的安全编译码方法，设计编码方案如下：
本发明可选实施例安全编译码方案设计的理论依据：在窃听信道模型的安全编码定理的存在性证明中，Wyner指出要设计出达到信息论安全的编译码方案，需要使用一种被称为“随机装箱”的编码技术。该编码技术将发射的消息和一堆码字所组成的箱子一一对应，当给定要传输的消息时，随机的从该消息所对应的码字箱子中选取一个码字发送出去。为了让窃听者不能正确译出发送的消息，需要消耗窃听者的译码能力，Wyner指出假设窃听者知道发送的具体消息时，如果窃听者能从该具体消息所对应的码字箱子中正确找到(“译出”)发送的那个随机码字时，则窃听者的译码能力就得到了消耗。如果将该具体消息所对应的码字箱子也看成是一种新的码字的话，本发明可选实施例希望该新的码字所对应的传输效率等于窃听信道的信道容量，因为这代表着窃听者的全部译码能力都消耗在译出该新码字上，这样窃听者就没有额外的能力去译出究竟发送的是哪个消息上了。基于Wyner的安全编码定理证明的上述思想，假设发送的消息是k比特，码字的长度为n比特，则本发明可选实施例设计的安全编码方案需要具备以下三个特点：(a)该安全编码
Figure PCTCN2016098727-appb-000021
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。
上述设计方案的参数说明：首先我们需要知道主信道高斯噪声的噪声方差
Figure PCTCN2016098727-appb-000022
窃听信道噪声的噪声方差
Figure PCTCN2016098727-appb-000023
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
Figure PCTCN2016098727-appb-000024
窃听信道 的容量maxI(X；Z)为
Figure PCTCN2016098727-appb-000025
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。
本发明可选实施例安全编译码方案的设计步骤如下：
一，按照经典的LDPC码的设计思路设计一个码字长度为n+k比特，消息长度为l比特的LDPC码的校验矩阵，记为H，该矩阵有n+k-l行，有n+k列。
二，l比特的消息中包含了k比特的真实的发送消息和l-k比特的随机消息。显而易见，l满足如下约束条件k＜l＜n+k。
三，为了实现Wyner在窃听信道模型的安全编码定理证明中所描述的编码方法，即当发送的k比特消息确定时，随机的从其对应的码字箱子中选取一个码字这种编码方式，本发明可选实施例首先需要将上述所设计的校验矩阵为H，长度为n+k比特的LDPC码按照k比特的真实消息划分为2k个子码，每一个子码的长度为n比特。该类子码也是一种线性分组码，该子码的消息比特即是l-k比特的随机消息。我们采用如下方式实现“随机从子码中选取一个码字传送”的编码方式：(a)通过随机数生成器随机产生一个l-k比特的随机消息；(b)将该l-k比特的随机消息通过线性分组码的生成矩阵生成一个和其一一对应的码字，然后该将码字传送。
四，上述子码的实际传输效率为
Figure PCTCN2016098727-appb-000026
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
Figure PCTCN2016098727-appb-000027
为了满足前面所述的安全编码方案的特点(b)，令
Figure PCTCN2016098727-appb-000028
五，在给出了上述n,k,l的约束关系之后，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码设计方法如下：(a)将该校验矩阵H通过高斯消元法化为[A|B]型矩阵，这里注意H矩阵为n+k-l行，n+k列的矩阵，A矩阵为单位矩阵，其行数和列数均为n+k-l。B矩阵为一个行数为n+k-l，列数为l的矩阵。当给定发送的真实消息sk，随机生成的消息为dl-k时，由校 验矩阵的定义，
(cn+k-l，sk,dl-k)HT＝0，           (公式1)
这里cn+k-l表示编码之后的n+k-l比特的校验位。
将H＝[A|B]代入(公式1)中，我们有
Figure PCTCN2016098727-appb-000029
将(公式2)整理，我们可得
cn+k-l·AT+(sk,dl-k)·BT＝0          (公式3)
进一步整理(公式3)，
cn+k-l＝(sk,dl-k)·BT·(A-1)T           (公式4)
(公式4)给出了当我们知道真实消息sk和随机生成的消息dl-k时，计算码字的校验位的公式。知道了校验位之后，通过校验矩阵H而得到的码字rn+k可表示为
rn+k＝(cn+k-l,sk,dl-k)＝((sk,dl-k)·BT·(A-1)T,sk,dl-k)       (公式5)
六，对于合法用户来说，码字rn+k的实际传输效率
Figure PCTCN2016098727-appb-000030
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sk和随机生成的消息dl-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
rn＝(cn+k-l,sk,dl-k)＝((sk,dl-k)·BT·(A-1)T,dl-k)        (公式6)
将rn和rn+k相比，很容易发现rn是将rn+k中发送的真实消息sk删掉，即rn是rn+k的子码。对于rn而言，其中的消息为dl-k，我们希望窃听者能正确译出dl-k，且将其全部的译码能力都消耗在译出dl-k上，这就需要子码rn的传输效率由
Figure PCTCN2016098727-appb-000032
以及k＜l＜n+k，我们可以得出
Figure PCTCN2016098727-appb-000033
(公式7)说明对于窃听者而言，码字rn+k的实际传输效率
Figure PCTCN2016098727-appb-000034
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。
合法用户和窃听者的译码器均采用经典置信传播(Belief Propagation，简称为BP)译码算法，该译码算法分为以下步骤：(1)首先对高斯信道预设信息比特的先验概率；(2)由信息节点的信息概率按照置信传播算法得出每个校验节点的后验概率；(3)由校验节点的后验概率推算出信息节点的后验概率；(4)将信息节点的后验概率对照判决条件作硬判决，若满足则译码结束；若不满足，则重复以上的(2)～(4)步骤，反复迭代，直到满足条件，得出译码结果。如果迭代次数达到一个预设的最大次数(例如100)，条件仍然不满足，则宣布译码失败。
图5是根据本发明可选实施例的适用的信道模型示意图，如图5所示，包括：编码器，主信道，译码器，窃听信道；图中，XN、YN和ZN为输出信号。
图6是根据本发明可选实施例设计的编码器构造方法示意图，如图6所示。
本发明可选实施例的具体实施方式采用BP译码算法的规则(3,2)LDPC安全码。
本实例介绍一种简单的规则(3,2)LDPC安全码。基于如前所述的安全编码方法，在此例中，n＝280，k＝20，l＝100，SNR1＝14，SNR2取10个不同的值(0.5,0.1,0.05,0.02,0.01,0.0085,0.005,0.0035,0.002,0.001)。首先，我们造一个200行，300列的校验矩阵(n+k-l行，n+k列)，该校验矩阵由0,1构成，每行中1的个数为2个，每列中1的个数为3个。这样的校验矩阵构成的LDPC码叫做规则(3,2)LDPC码。每次我们产生一个20比特的真实消息，以及一个80比特的随机消息，我们将这些消息通过规则(3,2)LDPC码编码成一个拥有100比特消息位，200比特校验位的码字，然后将该码字通过主信道发送给合法用户，通过窃听信道发送给窃听者，且合法用户和窃听者的译码器均采用经典BP译码算法进行译码。这里需要注意的是我们假设主信道的信噪比固定，而窃听信道的信噪比是变化的。由n＝280，k＝20，l＝100，SNR1＝14，我们可以得到
Figure PCTCN2016098727-appb-000035
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
Figure PCTCN2016098727-appb-000036
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，即本发明可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。
表1
Figure PCTCN2016098727-appb-000037
图7是根据本发明可选实施例的曲线图，如图7所示，图7给出了主信道的信噪比与窃听信道信噪比的比值和窃听者误比特率之间的关系。不难看出当比值越大，安全编码器的效果越好，即当窃听信道信噪比越小，本发明 实施例所设计的安全编码器的性能越安全。
通过以上的实施方式的描述，本领域的技术人员可以清楚地了解到根据上述实施例的方法可借助软件加必需的通用硬件平台的方式来实现，当然也可以通过硬件，但很多情况下前者是更佳的实施方式。基于这样的理解，本发明的技术方案本质上或者说对现有技术做出贡献的部分可以以软件产品的形式体现出来，该计算机软件产品存储在一个存储介质(如ROM/RAM、磁碟、光盘)中，包括若干指令用以使得一台终端设备(可以是手机，计算机，服务器，或者网络设备等)执行本发明各个实施例所述的方法。
本发明的实施例还提供了一种存储介质。可选地，在本实施例中，上述存储介质可以被设置为存储用于执行以下步骤的程序代码：
S1，获取待发送消息，其中，该待发送消息包括：k比特的真实消息，(l-k)比特的随机消息，其中l，k均为自然数；
S2，依据校验矩阵H对该待发送消息进行编码，获取码字rn+k，其中，该n为该真实消息的码字长度，该校验矩阵H满足以下条件：rn+kHT＝0；
S3，发送该码字rn+k。
可选地，存储介质还被设置为存储用于执行上述实施例的方法步骤的程序代码：
可选地，在本实施例中，上述存储介质可以包括但不限于：U盘、只读存储器(ROM，Read-Only Memory)、随机存取存储器(RAM，Random Access Memory)、移动硬盘、磁碟或者光盘等各种可以存储程序代码的介质。
可选地，在本实施例中，处理器根据存储介质中已存储的程序代码执行上述实施例的方法步骤。
可选地，本实施例中的具体示例可以参考上述实施例及可选实施方式中所描述的示例，本实施例在此不再赘述。
显然，本领域的技术人员应该明白，上述的本发明的各模块或各步骤可以用通用的计算装置来实现，它们可以集中在单个的计算装置上，或者分布 在多个计算装置所组成的网络上，可选地，它们可以用计算装置可执行的程序代码来实现，从而，可以将它们存储在存储装置中由计算装置来执行，并且在某些情况下，可以以不同于此处的顺序执行所示出或描述的步骤，或者将它们分别制作成各个集成电路模块，或者将它们中的多个模块或步骤制作成单个集成电路模块来实现。这样，本发明不限制于任何特定的硬件和软件结合。
以上所述仅为本发明的可选实施例而已，并不用于限制本发明，对于本领域的技术人员来说，本发明可以有各种更改和变化。凡在本发明的精神和原则之内，所作的任何修改、等同替换、改进等，均应包含在本发明的保护范围之内。
工业实用性
上述技术方案实现了编码技术达到信息论意义的安全，实现了安全编码译码。

Claims (10)

  1. 一种编码方法，包括：
    获取待发送消息，其中，所述待发送消息包括：k比特的真实消息，(l-k)比特的随机消息，其中l，k均为自然数；
    依据校验矩阵H对所述待发送消息进行编码，获取码字rn+k，其中，所述n为所述真实消息的码字长度，所述校验矩阵H满足以下条件：rn+kHT＝0；
    发送所述码字rn+k。
  2. 根据权利要求1所述的方法，其中，
    所述校验矩阵H为码字长度为n+k比特，并且消息长度为l比特的低密度奇偶校验码LDPC码的校验矩阵，其中，k＜l＜n+k。
  3. 根据权利要求1所述的方法，其中，通过以下方式确定所述(l-k)比特的随机消息：
    随机产生一个(l-k)比特的随机消息；
    将所述(l-k)比特的随机消息通过线性分组码的生成矩阵生成与所述随机消息对应的码字。
  4. 根据权利要求1所述的方法，还包括：发送所述码字rn+k之前，执行以下至少一种：
    所述码字rn+k划分为2k个子码，每一个所述子码对应一个k比特长度的消息；
    从所述k比特真实消息所对应的子码中随机选取一个码字发送；
    确定所述码字rn+k的实际传输速率小于主信道的信道容量，以及所述子码的实际传输速率等于窃听信道的信道容量。
  5. 根据权利要求4所述的方法，其中，通过以下方式确定所述码字rn+k的实际传输速率小于主信道的信道容量，以及所述子码的实际传输速率等于窃听信道的信道容量：
    Figure PCTCN2016098727-appb-100001
    Figure PCTCN2016098727-appb-100002
    其中，所述子码的实际传输速率为
    Figure PCTCN2016098727-appb-100003
    所述码字rn+k的实际传输速率为
    Figure PCTCN2016098727-appb-100004
    是主信道高斯噪声的噪声方差，
    Figure PCTCN2016098727-appb-100005
    是窃听信道噪声的噪声方差，P是所述码字rn+k的发送功率，主信道的信道容量maxI(X；Y)为
    Figure PCTCN2016098727-appb-100006
    窃听信道的信道容量maxI(X；Z)为
    Figure PCTCN2016098727-appb-100007
  6. 一种译码方法，包括：
    接收码字rn+k，其中，所述码字rn+k为通过以下方式得到的码字：依据校验矩阵H对待发送消息进行编码，得到码字rn+k，其中，所述待发送消息包括：k比特的真实消息，(l-k)比特的随机消息，其中l，k均为自然数，所述n为所述真实消息的码字长度，所述校验矩阵H满足以下条件：rn+kHT＝0；
    解析所述码字rn+k。
  7. 根据权利要求6所述的方法，其中，解析所述码字rn+k包括：
    由rn+kHT＝0得出(cn+k-l，sk,dl-k)HT＝0，解得cn+k-l，其中，所述sk为所述真实消息向量，所述dl-k为所述随机消息向量，所述cn+k-l表示编码之后的n+k-l比特的校验位；
    Figure PCTCN2016098727-appb-100008
    pk为校验矩阵H的前k维向量，ql-k为校验矩阵H的后(l-k)维向量。
  8. 一种编码装置，包括：
    第一获取模块，设置为获取待发送消息，其中，所述待发送消息包括：k比特的真实消息，(l-k)比特的随机消息，其中l，k均为自然数；
    第二获取模块，设置为依据校验矩阵H对所述待发送消息进行编码，获取码字rn+k，其中，所述n为所述真实消息的码字长度，所述校验矩阵H满足以下条件：rn+kHT＝0；
    发送模块，设置为发送所述码字rn+k。
  9. 一种译码装置，包括：
    接收模块，设置为接收码字rn+k，其中，所述码字rn+k为通过以下方式得到的码字：依据校验矩阵H对待发送消息进行编码，得到码字rn+k，其中，所述待发送消息包括：k比特的真实消息，(l-k)比特的随机消息，其中l，k均为自然数，所述n为所述真实消息的码字长度，所述校验矩阵H满足以下条件：rn+kHT＝0；
    解析模块，设置为解析所述码字rn+k。
  10. 根据权利要求9所述的装置，其中，
    解析模块是设置为通过如下方式实现解析所述码字rn+k：
    由rn+kHT＝0得出(cn+k-l，sk,dl-k)HT＝0，解得cn+k-l，其中，所述sk为所述真实消息向量，所述dl-k为所述随机消息向量，所述cn+k-l表示编码之后的n+k-l比特的校验位；
    Figure PCTCN2016098727-appb-100009
    pk为校验矩阵H的前k维向量，ql-k为校验矩阵H的后(l-k)维向量。
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