JP7040761B2 - Evaluation device - Google Patents

Description

The present invention relates to an evaluation device.

Conventionally, in a communication channel model in which an eavesdropper exists, a technique for finding a limit of a coding rate for performing secure communication has been disclosed (see, for example, Non-Patent Document 1).

Ke Zhang, Martin Tomlinson, Mohammed Zaki Ahmed, Marcel Ambroze, Miguel R.D. Rodrigues, Best binary equivocation code construction forsyndrome coding, IET Commun., 2014, Vol.8, Iss. 10, pp. 1696-1704

However, in the above-mentioned conventional technique, since the inspection matrix H is represented by a set of integers, there is no consistency in the case of substituting a specific numerical value for calculation, which is special for z-transform. There was a problem that calculation was required. That is, in the above-mentioned conventional technique, there is a problem that the calculation by a practical procedure cannot always be performed.

The present invention has been made to solve the above problems, and an object of the present invention is to provide an evaluation device capable of obtaining an evaluation value of a coding rate in eavesdropping communication path coding by a practical procedure. ..

One embodiment of the present invention includes an inspection matrix which is a public parameter in an eavesdropping communication path coding method, a bit inversion probability of the eavesdropping communication path, an eavesdropper reception bit string acquired via the eavesdropping communication path, and the inspection matrix. The acquisition unit for acquiring the input vector of the function obtained by multivariate discrete Fourier transforming the probability distribution of the noise vector, which is a bit string indicating the noise based on the bit inversion probability, included in the eavesdropper estimation message obtained from Based on the input vector acquired by the acquisition unit, the vector component of either the vertical vector or the horizontal vector of the inspection matrix, and the bit inversion probability, a noise characteristic function which is a characteristic function of the probability distribution of the noise vector is obtained. An evaluation value for calculating the evaluation value of the inspection matrix for each bit inversion probability based on the noise characteristic function calculation unit to be calculated, the noise characteristic function calculated by the noise characteristic function calculation unit, and the bit inversion probability. It is an evaluation device including a calculation unit.

Further, in one embodiment of the present invention, in the above-mentioned evaluation device, a uniform characteristic function calculation unit that calculates a uniform characteristic function, which is a characteristic function of uniform distribution, based on the input vector acquired by the acquisition unit. Further, the evaluation value calculation unit calculates the norm of the noise characteristic function and the uniform characteristic function calculated by the uniform characteristic function calculation unit as the evaluation value of the inspection matrix for each bit inversion probability. do.

Further, in one embodiment of the present invention, in the above-mentioned evaluation device, the evaluation value calculation unit calculates two norms of the noise characteristic function and the uniform characteristic function, and the calculated two norms are reduced to one norm. By converting, the evaluation value is calculated.

Further, in one embodiment of the present invention, in the above-mentioned evaluation device, the noise characteristic function is indicated by the inner product of the input vector and the vector component of the inspection matrix, and the evaluation value calculation unit is the inner product. The evaluation value is calculated based on the value of.

Further, one embodiment of the present invention includes a first procedure for calculating the count value of the input vectors whose inner product values match each other among the plurality of input vectors in the above-mentioned evaluation device for each evaluation value. Using the count value calculated by the first procedure, the second procedure of obtaining the total sum of the input vectors whose inner product value is 1 among the input vectors for each bit inversion probability. The evaluation value is calculated by.

According to the present invention, it is possible to provide an evaluation device capable of obtaining an evaluation value of a safety reference value in eavesdropping communication path coding by a practical procedure.

It is a figure which shows an example of the functional structure of the evaluation apparatus of this embodiment. It is a figure which shows an example of the schematic operation which calculates the evaluation value of the evaluation apparatus of this embodiment. It is a figure which shows an example of the calculation procedure of the noise characteristic function by the noise characteristic function calculation part of this embodiment. It is a figure which shows an example (the 1) of the plot of the evaluation value by the evaluation apparatus of this embodiment. It is a figure which shows an example (the 2) of the plot of the evaluation value by the evaluation apparatus of this embodiment. It is a figure which shows an example of the evaluation value near the theoretical value of this embodiment. It is a figure which shows an example of the evaluation value when (n, k) = (40, 10) in this embodiment. It is a figure which shows an example of the evaluation value when (n, k) = (60,30) in this embodiment. It is a figure which shows an example of the experimental result of the evaluation value when (n, k) = (400,370) in this embodiment. It is a figure which shows an example of the experimental result of the evaluation value when (n, k) = (400,370) in this embodiment. It is a figure which shows an example of the schematic operation which calculates the evaluation value of the evaluation apparatus which concerns on the modification of this embodiment. It is a figure which shows an example of the calculation procedure of the evaluation value by the evaluation apparatus which concerns on the modification of this embodiment. It is a figure which shows an example of the experimental result of the evaluation value by the algorithm of the modification of this embodiment. It is a figure which shows an example of the channel model in which an eavesdropper exists. It is a figure which shows an example of an eavesdropping communication path coding model. It is a figure which shows an example of the concept of cosset decomposition. It is a figure which shows an example of the concept of coset coding. (N, k) It is a figure which shows an example of the relationship between a random number rate of a code, and a bit inversion probability. It is a figure which shows an example of the relationship between a random number rate and a set of (n, k).

[Summary of prerequisites and embodiments]
Hereinafter, before explaining the embodiment of the present invention, the premise of the embodiment and the outline of the embodiment will be described with reference to the drawings.

[Eavesdropping channel coding]
FIG. 14 is a diagram showing an example of a channel model in which an eavesdropper exists. Winner has devised an eavesdropping channel coding problem that allows secure communication in a channel model in which an eavesdropper is present. The communication path from the sender Alice to the eavesdropper Eve defined in FIG. 14 is referred to as an eavesdropping communication path. There are two requests for the eavesdropping channel coding model.

In the asymptotic situation of n → ∞,
Request 1: The sender Alice conveys the message to the regular receiver Bob with an error probability ≈ 0.
Request 2: No message information is transmitted to the eavesdropper Eve.

The eavesdropping channel coding problem considers the limit of the coding rate of the code that simultaneously satisfies the above requirements, and the rate is called the eavesdropping channel capacity. The following three equations (1) to (3) are considered as safety criteria for Request 2.

However, in equation (3), PZ ⁿ _i and _PZ ⁿ _j (n is the upper right subscript of _z . i and j are the lower right subscripts of z) are the i-th and j-th messages when they are input. Probability distribution for communication. Since the standard 2 shown by the formula (2) is stronger than the standard 1 shown by the formula (1), if the standard 2 is satisfied, the standard 1 naturally holds. For this reason, Criterion 1 is called weak safety and Criterion 2 is called strong safety. Criteria 1 and Criteria 2 mean that S and Zn are asymptotically independent when ⁿ → ∞. Criterion 3 is the average value of 1-norm regarding the difference in output distribution when different messages are input. Even if the eavesdropper Eve observes the channel output, no information about the message can be obtained because the probability distribution does not depend on the message. The following eavesdropping channel coding theorem holds when the channel to the eavesdropper Eve contains more noise than the channel to the regular receiver Bob.

[Eavesdropping channel coding theorem]
The eavesdropping channel capacity (T (W, V)), which is the upper limit of the coding rate that can be achieved by the above two requests (request 1 and request 2), is the communication path of the regular receiver Bob (regular channel B). Is W, and the communication path of the eavesdropper Eve (eavesdropping communication path E) is V, the following equation (4) is satisfied.

The case where the bit inversion probability of the binary symmetric channel BSC (Binary Symmetric Channel) is the bit inversion probability α is referred to as the binary symmetric channel BSC _α . When the regular channel B is noiseless and the eavesdropping channel E is the binary symmetric channel BSC _α , the equal sign holds for the inequality sign in equation (4), and the eavesdropping channel capacity is given by the following equation (5). It is known.

[Eavesdropping channel coding model]
FIG. 15 is a diagram showing an example of an eavesdropping channel coding model. In the eavesdropping communication path coding model shown in FIG. 15, a noiseless communication path is used for the regular communication path B shown in FIG. 14, and a binary symmetric communication path BSC is used for the eavesdropping communication path E. Hereinafter, the eavesdropping channel coding model shown in FIG. 15 will be used as the eavesdropping channel coding model. The above-mentioned Criterion 2 is considered as a safety index. Regarding the request for eavesdropping communication path coding, for request 1, a noiseless communication path is used as the communication path from the sender Alice to the regular receiver Bob. Request 2 will be considered as a condition for satisfying equation (6).

[Linear code]
When a vector of length k is converted into a vector of length n, the linear code C is referred to as a (n, k) linear code or a (n, k) code. Hereinafter, it will be discussed as m: = nk. Consider the original m × n matrix H whose component is F ₂ . Here, H assumes that all row vectors are first-order independent, that is, row full rank. By this matrix H, the linear code C is designated as in Eq. (7).

The matrix H that specifies this linear code C is called an inspection matrix. In the designation method using the check matrix H, the linear code C is designated as the solution space of the linear simultaneous equations of the same order. On the other hand, since it is assumed that the inspection matrix H has a row full rank, the equation (8) holds.

From the dimension theorem, because it is equation (9)

The following equation (10) is obtained, and a code of the same dimension as in the case of the generator matrix is given.

[Coset]
Next, the cosset will be described with reference to FIG.
FIG. 16 is a diagram showing an example of the concept of cosset decomposition. As shown in Eq. (11), the inverse image of the inspection matrix H: F ⁿ ₂ → F ^m ₂ corresponding to any syndrome s = (s ₀ , ..., s _m-1 ) ∈ F ^m ₂ is obtained from the syndrome s. It is called a coset corresponding to.

[Cosset encoding]
FIG. 17 is a diagram showing an example of the concept of coset coding. Cosset encoding equates a message with the sender's syndrome. By making a one-to-one correspondence between a message and a cosset, a cosset code, which is one of the stochastic codes, can be constructed. When sending an arbitrary message s ∈ M (# M = 2 ^m ) (that is, a bit string of m bits), a uniform random number u ∈ U (# U = 2 ^k ) (# U = 2 k) from the elements of the cosset associated in advance. That is, the codeword x is determined using the k-bit bit string) and input to the communication path. At this time, the message rate _RS and the random number rate _RU are given as follows.

[Realization of eavesdropping channel coding by coset coding]
The realization of eavesdropping channel coding by coset coding using the eavesdropping channel coding model shown in FIG. 15 will be described.
It is assumed that the communication quality between the sender Alice and the regular receiver Bob and the communication environment between the sender Alice and the eavesdropper Eve exceed the former communication quality. Examples include the inside and outside of a room with a wireless LAN, the line-of-sight range of satellite communication and the outside. By utilizing the difference in communication quality in such a situation, secure communication can be performed between the sender Alice and the regular receiver Bob.
For the sake of simplicity, it is assumed that the communication path from the sender Alice to the regular receiver Bob is a noiseless communication path. Further, it is assumed that the communication path from the sender Alice to the eavesdropper Eve is the binary symmetric channel BSC.

The form of the inspection matrix H used below will be described. Considering the above-mentioned (n, k) code, m: = n−k.

The vertical vector representation of the inspection matrix H is written in the form of equation (15) using equation (14).

Attempts have been made to search for (n, k) codes that can realize eavesdropping channel coding in coset coding.

1: One inspection matrix H is fixed and used as a public parameter.
2: Sender Alice phase:
Generate syndromes s corresponding to the message.
The x satisfying Hx = s is obtained by coset coding and transmitted to the regular receiver Bob.
3: Phase of regular receiver Bob:
By receiving x _r = x from the sender Alice, s = Hx _r is calculated.
4: Eavesdropper Eve Phase:
By receiving x _e = x + e with the error vector by the binary symmetric channel BSC as e, s'= Hx _e is calculated.

However, for the random variable S related to the message of the sender Alice and the random variable S ′ related to the information possessed by the eavesdropper Eve, the above-mentioned equation (6) is secured by using the mutual information amount which is the amount of information representing the index of correlation. Used as a definition of sex.

[About encoders and decoders]
A technique is presented in which a method of encoder and decoder of a message is given and safety evaluation is performed using entropy.
H = (I, H2) is specified. The sender Alice generates x ∈ F ⁿ ₂ satisfying Hx = s in the following three steps.

1: The sender Alice defines the codeword x ₁ ∈ F ⁿ ₂ as follows by using the generator matrix G of a ∈ F ^k ₂ and n × k, which are uniformly and randomly determined.

2: Sender Alice generates x ₂ ∈ F ⁿ ₂ using the message s ∈ F ^m ₂ as follows.

3: Sender Alice uses Eqs. (16) and (17) to generate x ∈ F ⁿ ₂ as follows.

In this way, the sender Alice

It is possible to generate x that satisfies.
The regular receiver Bob calculates the syndrome of the received vector by the equation (20). Since the communication path from the sender Alice to the regular receiver Bob is noiseless, x _r = x. Therefore, the regular receiver Bob can be decoded as shown in the equation (20).

On the other hand, the eavesdropper Eve is the vector shown in the equation (21).

を受信し、式（２２）を計算することが想定される。

Is received and equation (22) is calculated.

Therefore, the eavesdropper Eve is as shown in the equation (23).

It is thought that the message is guessed as. The reason why we can assume that the random variables for a message follow a uniform distribution is that the uniform distribution is easy to handle, and that the sender Alice constructs a code with the same security regardless of which message is selected. Because I want to. If the distribution of messages is biased, the information of messages frequently used by eavesdroppers Eve may be inferred and targeted by frequency attacks.

[Safety evaluation using characteristic functions]
When the random variables S and Se are independent and S follows a uniform distribution, the random variables S + Se also follow a uniform distribution. When the equation (24) is satisfied, Se shown in the equation (25) is a random variable.

If other letters are written in capital letters, S and Se are independent. At this time, if the random variable S + Se is set to S', the equation (27) is established by the equation (26).

From this equation (27), it can be seen that the above-mentioned equation (6) has the same value as the following equation (28).

Hereinafter, instead of the formula (6), the formula (28) is used for the safety evaluation of the (n, k) code.

[Characteristic function]
By defining a characteristic function and examining its properties, we consider performing a safety evaluation of the (n, k) code without directly calculating the mutual information amount. In the following description, the symbol i is an imaginary unit.

2 ≤ a ∈ N and x = (x ₀ , ..., _x ^m _-1 ) ∈ Z ma, ^t ₌ (t ₀ , ..., t _m-1 ) ∈ Z ma, the characteristic of the probability distribution p The function φp is shown in Eq. (29).

Here, t is an input vector of a function obtained by performing a multivariable discrete Fourier transform on the probability distribution of a bit string.
When the characteristic function φp is defined as described above, the inverse transformation of the equation (29) exists, and the input and output of the characteristic function φp store the result of the inner product (that is, unitarity is established).

This characteristic function ^φp (t) includes the square root of am, and the theorem regarding the sum of independent random variables does not hold. Therefore, when conducting a numerical experiment, the characteristic function φp (t) is defined by the equation (30).

With this definition, it is no longer a unitary transformation, but the existence of the inverse transformation is satisfied and the theorem regarding the sum of independent random variables holds. Therefore, in the following, the equation (30) is defined as a characteristic function. When defined in this way, the following equation (31) holds.

[Safety evaluation]
For the random variable _X that follows the probability distribution PX on the alphabet χ, the 1-norm of the random variable X is defined by the equation (32).

Similarly, the 2-norm of the random variable X is defined by the equation (33).

Here, the Juanes-type inequality is an inequality that expresses the relationship between entropy and norm. Also known as an inequality for entropy continuity.
Let X ₁ and X ₂ be random variables that follow a probability distribution on the alphabet χ. At this time, if the equation (34) is satisfied, the equation (35) holds.

This equation (35) is an equation that holds in 1-norm, but it is easier to find 2-norm when considering the characteristic function. Therefore, the relationship between 1-norm and 2-norm will be described below.

The relationship shown in the following equation (36) holds for the random variable _X that follows the probability distribution PX on the alphabet χ.

Safety evaluation is performed from inequality related to norm and fanes type inequality. First, from the Juanes-type inequality, the equation (38) is established, paying attention to the relationship shown in the equation (37).

From this, the following holds. That is, note that the random variable S regarding the message of the sender Alice follows a uniform distribution, the entropy Ent (S) of the random variable S becomes m. From this, considering that the entropy Ent (U) of the uniform distribution U is m, the following equation (39) holds.

That is, when the equation (40) is satisfied under the assumption that the positive number ε is sufficiently small,

It can be considered that the situation is the same as the case shown in the above-mentioned equation (28). Therefore, the above object can be achieved by searching for a (n, k) code that satisfies the equation (41).

[Derivation of numerical experimental algorithm]
The equation is transformed so that the above-mentioned characteristic function can be used in the numerical experiment. Hereinafter, the case where a = 2 in the equation (30) will be considered. At this time, the modulo ring Z _a is equal to the finite field Fa if _a is _a prime number, so Z ^ma ₌ F ^ma . That is, as shown in equations (42) and (43),

Then, the characteristic function φp (t) is as shown in the equation (44).

In general, AND is used for the product of elements of F ₂ (for example, 0 (zero) and 1 (1)), and XOR is used for addition, but here, the same notation as normal addition or multiplication is used.

[Charistical function of uniform distribution]
First, consider the characteristic function of uniform distribution shown in Eq. (45).

By transforming the equation shown in equation (46), there are two ways for the value of the uniform characteristic function φU (t), which is a characteristic function of uniform distribution, when the input vector t is zero vector 0 and when it is not. Is reduced to.

[Charistical function for random variable Se]
Consider the characteristic function for the random variable Se. Hereinafter, the vertical vector component of the inspection matrix H is expressed as equation (49) using equations (47) and (48).

At this time, the random variable Se can be written as in Eq. (50).

Here, el ( _l = 0, ..., N-1) is a component of the error vector of the binary symmetric channel BSC, and is a random variable given independently. Therefore, f _l ( _l = 0, ..., N-1) can be seen as a random variable determined by el. That is, since f _l (l = 0, ..., N-1) is independent, the characteristic function of the random variable Se that follows the distribution of the sum of f _l is the characteristic function of f _l as shown in Eq. (51). Can be decomposed into products.

Here, the contents of the infinite product of the equation (51) are simplified as shown in the equation (52).

Further, as shown in the equation (53), due to the above-mentioned property of 2-norm, the evaluation function F of 2-norm is used by using the random variable S related to the uniform distribution and the random variable Se related to the information possessed by the eavesdropper Eve. ,

Defined as. In the numerical experiment conducted as an example of this embodiment, the behavior of the evaluation function F of 2-norm is observed by moving the bit inversion probability α of the binary symmetric communication path BSC in the range of 0.0 to 0.5.
Further, the equation (54) is established from the above-mentioned relationship between 1-norm and 2-norm.

[Algorithm for calculating characteristic function of random variable Se]
As described above, it has been stated that the equation (55) can be calculated by using the equation (52).

However, as it is, it is necessary to perform the inner product calculation nm = k times for one input vector t. In this section, we consider a method for speeding up the k-time internal product calculation for equation (55). On the computer, the inner product on F ^m ₂ is reduced to the operation of taking the product AND and adding the results using XOR. By using this, it is possible to speed up the inner product calculation by applying the following procedure.

Step 1: Initialize the variable temp to 0.
Step 2: for loop: l = m, ..., n-1 {
Step 3: Considering t and hl as a bit string, temp1 = (t) ₂ AND ( _hl ) ₂ is calculated.
Step 4: Count the 1 part of temp1 and store it in temp2.
Step 5: When temp2 = 1mod2, the temp is incremented. }
Step 6: Return the temp as the number of repetitions k'.

By this procedure, the value of equation (55) is given by equation (56). Here, the algorithm for counting the part of the bit string in which 1 stands is generally population.
It is called the count algorithm (popcnt). popcnt is defined as in equation (57).

Further, regarding the product of the parts where t _l = 1 in the first half of the equation (52), the part where 1 of the input vector t stands may be counted, and this may be set as the number of repetitions. From the above, the numerical experiment algorithm is summarized as follows.

Step 1: Let α be the bit inversion probability of the binary symmetric channel BSC.
Step 2: H ₂ = [(h _m ) ₁₀ , ..., (h _n-1 ) ₁₀ ] is generated using random numbers.
Step 3: for loop: α = 0.0, ..., 0.5 {
Step 4: Initialize temp2 with 0.0.
Procedure 5: for loop: (t) ₁₀ = 0, ..., 2 ^m -1 {
Procedure 6: s = φU ((t) ₁₀ )
Step 7: temp1 = popcnt ((t) ₁₀ )
Procedure 8: for loop: l = m, ..., n-1 {
Step 9: temp1 = temp1 + {popcnt ((t) ₁₀ ANDh _l ) mod2}}
Step 10: s _e = (-2α + 1) ^temp1
Step 11: temp = | s-s _e | ²
Step 12: temp2 = temp2 + temp}
Step 13: Plot α and Root (temp1) / Root (2 ^m ). }

Here, among the above algorithms, the power of (-2α + 1) performed in the procedure 10 is calculated as shown in the equation (58).

However, in the equation (58), when the bit inversion probability α = 0.5, (-2α + 1) = 0, so log (-2α + 1) = −∞, and the calculation cannot be performed. Therefore, the bit inversion probability α = 0.5 will be excluded.

[Performance of (n, k) code]
(N, k) The fact that the code has good performance is the bit inversion probability α at which the random number rate of coset coding and the channel capacity of BSC match, and the message possessed by the sender Alice and the information possessed by the eavesdropper Eve. There is no correlation. First, the condition for the bit inversion probability α is shown in the equation (59).

Equation (59) can be seen as an equation for α when n and k are fixed. Considering finding the intersection of the left side and the right side of the equation (59), this is illustrated as shown in FIG.

FIG. 18 is a diagram showing an example of the relationship between the random number rate of the (n, k) code and the bit inversion probability α. Here, the line L4 indicates a random number rate (k / n in this example). Further, L5 indicates 1-h (α). It is assumed that the range in which the desired bit inversion probability α can be obtained is 0.0 to 0.5. The random number rate (that is, n and k) of the (n, k) code may be fixed, and the bit inversion probability α satisfying the number (54) may be numerically obtained by using an algorithm for finding the solution of the equation. Newton's method and dichotomy can be considered as typical numerical solutions for finding solutions to equations, but this time we will adopt the values found using the dichotomy. Just in case, plot the obtained numerical solution on the graph to reconfirm whether it is the value you really wanted to find. The value plotted using this is line L3 in FIG. This value is defined as the theoretical value α _BSC of the bit inversion probability of the (n, k) code, and it is defined that the smaller the value taken by the evaluation value F near the theoretical value α _BSC , the better the performance of the (n, k) code. As a standard for numerical experiments, in the evaluation of 2-norm, if the value of the evaluation value F is at most a constant multiple of 10 ^-3 near the theoretical value α _BSC , it is judged that the evaluation value F is sufficiently close to 0. It is assumed that the (n, k) code can be selected. Even in the evaluation of 1-norm, if the product of the square root of (2 ^m ) and the evaluation value F is at most a constant multiple of ^10-2 , it is judged that the evaluation value F is sufficiently close to 0 (n, k) It is assumed that the code can be selected. Further, a (n, k) code that satisfies both the 2-norm evaluation and the 1-norm evaluation is defined as a code having performance close to complete confidentiality.

[Generation of parameters for numerical calculation]
To see the performance of the (n, k) sign, consider the set of (n, k) to plot. Here, there is a problem of how much m should be increased in order to construct a code having good performance.

According to the conventional method, since the mutual information amount J (S; S') is directly calculated, constraints are given to the parameters by fixing the value of m to a small value or restricting the input of a message. ..
In the present embodiment, since the mutual information amount is not directly calculated, the calculation amount can be reduced, so that the parameter generation can be devised. Since 2 ^m of input is required in the numerical experiment algorithm, there is a concern that the calculation time will increase when m is large. Therefore, by paying attention to the change in the value of m when the random number rate is fixed, we considered a method to calculate without taking a large m.

FIG. 19 is a diagram showing an example of the relationship between the random number rate and the sample of m. As shown in FIG. 19, it can be seen that if the random number rate is determined, a plurality of sets (n, k) satisfying the equation (59) can be generated. The merit of this method is that the larger i is, the larger the value of m is, so that it is possible to compare the case where m is large and the case where m is small. From this, it is more efficient than thinking by fixing n and moving k sequentially. By using this method, it is possible to check whether or not there is a code having almost the same performance as the performance when m is large by searching for a code having the same random number rate. Therefore, it is possible to confirm whether or not the same performance is obtained even if m is made relatively small.

So far, the prerequisites and the outline of the present embodiment have been described. Next, an example of an evaluation device that evaluates the inspection matrix H by the above-mentioned calculation procedure will be described.

[Evaluator configuration]
FIG. 1 is a diagram showing an example of the functional configuration of the evaluation device 10 of the present embodiment. The evaluation device 10 includes a uniform characteristic function calculation unit 110, a noise characteristic function calculation unit 120, and an evaluation value calculation unit 130. Further, the evaluation device 10 includes an acquisition unit (not shown) for acquiring the bit inversion probability α, the inspection matrix H, and the input vector t. Here, the bit inversion probability α is the bit inversion probability of the eavesdropping communication path E. The inspection matrix H is a public parameter in the wiretapping channel coding method. The input vector t is an input vector of a function obtained by performing a multivariate discrete Fourier transform on the probability distribution of the random variable Se. Here, the random variable Se is also referred to as a noise vector Se. The noise vector Se is a bit string indicating noise based on the bit inversion probability α included in the eavesdropper estimation message ^s'obtained from the eavesdropper reception bit string Zn acquired via the eavesdropping communication path E and the inspection matrix H. Is.

Of these parameters, the inspection matrix H and the input vector t are calculated by the vertical vector component calculation unit 20 of the input vector / inspection matrix. In this example, the evaluation device 10 and the vertical vector component calculation unit 20 of the input vector / inspection matrix will be described as separate devices, but the evaluation device 10 is the vertical vector component calculation unit of the input vector / inspection matrix. 20 may be provided.

As shown in the above equation (46), the uniform characteristic function calculation unit 110 calculates the uniform characteristic function φU (t), which is a characteristic function of uniform distribution, based on the input vector t.

As shown in the above equation (30), the noise characteristic function calculation unit 120 has a probability distribution of the noise vector Se based on the input vector t, the vertical vector component h _l of the inspection matrix H, and the bit inversion probability α. The noise characteristic function φSe (t), which is the characteristic function of, is calculated.
It should be noted that the noise characteristic function φSe (t) is calculated based on the vertical vector component h _l of the inspection matrix H as an example, and the noise characteristic function φSe (t) is used as the horizontal vector component of the inspection matrix H. It may be calculated based on.

The evaluation value calculation unit 130 sets the evaluation value F (φU, φSe) of the inspection matrix H as the bit inversion probability based on the noise characteristic function φSe (t) calculated by the noise characteristic function calculation unit 120 and the bit inversion probability α. Calculated for each α. The evaluation value F (φU, φSe) of the inspection matrix H is also simply described as the evaluation value F.

Here, as shown in the equations (51) and (52), the noise characteristic function φSe (t) includes the inner product of the input vector t and the vertical vector component h _l of the inspection matrix H, and the bit inversion probability α. Demanded by. As shown in the equation (53), the evaluation value calculation unit 130 calculates the evaluation value F by obtaining the inner product of the input vector t and the vertical vector component h _l of the inspection matrix H.

Further, the evaluation value calculation unit 130 sets the norm of the noise characteristic function φSe (t) and the uniform characteristic function φU (t) calculated by the uniform characteristic function calculation unit 110 in the check matrix H for each bit inversion probability α. Calculated as the evaluation value F.

Further, the evaluation value calculation unit 130 calculates two norms of the noise characteristic function φSe (t) and the uniform characteristic function φU (t), and converts the calculated 2-norm into 1-norm for evaluation. The value F may be calculated.

[Operation of evaluation device]
Next, an example of the procedure for calculating the evaluation value F by the evaluation device 10 will be described with reference to FIG. 2.
FIG. 2 is a diagram showing an example of a schematic operation for calculating an evaluation value F of the evaluation device 10 of the present embodiment.
(Step St10) The acquisition unit (not shown) of the evaluation device 10 acquires the vertical vector component h _l of the inspection matrix H.
(Step St20) The acquisition unit (not shown) of the evaluation device 10 acquires the input vector t.
(Step St30) The evaluation device 10 updates the bit inversion probability α. Here, the evaluation device 10 updates the bit inversion probability α by increasing the bit inversion probability α by a predetermined increment in the range of 0.0 to 0.5. For example, the evaluation device 10 repeatedly executes the processes of steps St40 to St90 until the bit inversion probability α reaches 0.5 while increasing the bit inversion probability α = 0.0 by 0.1 as an initial value.

(Step St40) The uniform characteristic function calculation unit 110 calculates the uniform characteristic function φU (t) based on the input vector t acquired in step St20.
(Step St50) The noise characteristic function calculation unit 120 calculates the noise characteristic function φSe (t) based on the vertical vector component h _l acquired in step St10 and the input vector t acquired in step St20. Here, the details of the calculation procedure of the noise characteristic function φSe (t) will be described with reference to FIG.

FIG. 3 is a diagram showing an example of a calculation procedure of the noise characteristic function φSe (t) by the noise characteristic function calculation unit 120 of the present embodiment.
(Step St510) Initialize the variable temp and the variable l.
(Step St520) Both the input vector t and the vertical vector component h _l are regarded as a bit string, and the logical product of the input vector t and the vertical vector component h _l is calculated.
(Step St530) Among the bit strings, the number of bit strings whose logical product calculated in step St520 is "1" is counted.
(Step St540) When the remainder (remainder) obtained by dividing the result counted in step St530 by 2 is "1", the variable temp is incremented.
(Step St550) It is determined whether or not the variable l has reached (n-1). If the variable l has not reached (n-1) (step St550; NO), the variable l is incremented (step St560) and the process returns to step St520. When the variable l has reached (n-1) (step St550; YES), the process proceeds to step St570.
(Step St570) The noise characteristic function φSe (t) is calculated as the noise characteristic function φSe (t) = ( ^-2α + 1) emp.

(Step St60) Returning to FIG. 2, the evaluation value calculation unit 130 is based on the uniform characteristic function φU (t) calculated in step St40 and the noise characteristic function φSe (t) calculated in step St50. The evaluation value F is calculated.
(Step St70) The evaluation device 10 plots the evaluation value F with the horizontal axis as the bit inversion probability α and the vertical axis as the evaluation value F.
Here, the evaluation device 10 calculates the evaluation value F for all the components when the input vector t is regarded as a bit string (step St80), and repeats the plotting of the evaluation value F. Further, the evaluation device 10 updates the bit inversion probability α until the bit inversion probability α reaches 0.5 (step St90), and repeats plotting the evaluation value F. An example of the plot of the evaluation value F by the evaluation device 10 is shown in FIGS. 4 and 5.

[Example of evaluation result by evaluation device]
FIG. 4 is a diagram showing an example (No. 1) of the plot of the evaluation value F by the evaluation device 10 of the present embodiment. FIG. 5 is a diagram showing an example (No. 2) of the plot of the evaluation value F by the evaluation device 10 of the present embodiment. In this example, FIG. 4 shows a graph of experimental results for (n, k) = (10, 5), (40, 20), (60, 30) when T (BSC) = 0.5. Was plotted. FIG. 5 shows the experimental results for (n, k) = (20,10), (30,15), (50,25), (60,30) when T (BSC) = 0.5. The graph of is plotted. In each case, the vertical axis is the evaluation value F of 2-norm, and the horizontal axis is the bit inversion probability α of the binary symmetric channel BSC. In addition, in order to check the performance of the code, the theoretical value α _BSC was plotted by the line L1 in these figures. Further, in order to make it easier to understand the difference between the evaluation values F near the theoretical value α _BSC , FIG. 6 shows the relationship between the value n near the theoretical value α _BSC and the evaluation value F.

FIG. 6 is a diagram showing an example of the evaluation value F near the theoretical value α _BSC of the present embodiment. From these data, the evaluation value F near the theoretical value α _BSC is (n, k) = (60, 30), which is about 1.449 × 10 ^-3 . Therefore, in 2-norm (n, k). In the case of = (60, 30), the above-mentioned condition of the (n, k) code was satisfied. From this result, it was judged that m = n−k = 30 was sufficient for the evaluation of the inspection matrix H, and the experiment was repeated by setting (n, k) = (40, 10). FIG. 7 shows the results when (n, k) = (40, 10).

FIG. 7 is a diagram showing an example of the evaluation value F when (n, k) = (40, 10) in the present embodiment. In the case of the figure, the evaluation value F near the theoretical value α _BSC was about 3.233 × 10 ^-3 . Therefore, it can be said that the same result as the case where (n, k) = (60, 30) was obtained when (n, k) = (40, 10).

FIG. 8 is a diagram showing an example of the evaluation value F when (n, k) = (60, 30) in the present embodiment. When (n, k) = (60, 30) in 2-norm, the inspection matrix H having good performance could be constructed. Therefore, using this result, the horizontal axis is plotted with the bit inversion probability α of the binary symmetric channel BSC, and the vertical axis is plotted as Rot ⁽ 230) · F. Here, Root ⁽ 230) is the square root of ²³⁰ . In the 1-norm evaluation, the correspondence between the vertical axis and the horizontal axis of the graph is very difficult to understand, so the line L2 is drawn on the value of Root ⁽ 230) · F to be observed.

At (n, k) = (60, 30), for the evaluation of 2-norm, the evaluation value F was close to 0 in the vicinity of the theoretical value α _BSC , but in the evaluation of 1-norm. , The theoretical value α The value of Rot ⁽ 230) · F near _BSC was about 47.466. In this case, it cannot be said that Rot ⁽ 230) · F → 0, so it can be seen that (n, k) = (60, 30) is not suitable for the evaluation of 1-norm.

In 2-norm, when m = nk = 30, it was found that the evaluation value F approaches 0 near the theoretical value α _BSC , so when m = ³⁰ , Root (230) · F → We will search for a (n, k) code that will be 0. In general, the effect of the law of large numbers appears when n is large, so this time we re-experimented with n = 400. From the above-mentioned experimental results, it was found that the evaluation value F sufficiently approaches 0 when m = 30 for the evaluation of 2-norm, so the experiment was conducted with (n, k) = (400,370).

FIG. 9 is a diagram showing an example of the experimental result of the evaluation value F when (n, k) = (400,370) in the present embodiment. In the figure, the horizontal axis is plotted with the bit inversion probability α of the binary symmetric channel BSC, and the vertical axis is plotted with the evaluation value F.
FIG. 10 is a diagram showing an example of an experimental result of the evaluation value F when (n, k) = (400,370) in the present embodiment. The graph is a graph plotted with Rot ⁽ 230) and F on the vertical axis, with the horizontal axis as the bit inversion probability α of the binary symmetric channel BSC. In this section, in order to make it easier to understand the correspondence between the vertical axis and the horizontal axis of the graph, for Root ⁽ 230) and F, the line L2 is drawn on the value of Root ⁽ 230) and F that you want to observe in the same way as above. do.

In the result of the numerical experiment (n, k) = (400,370), the value near αBSC was F = || PS-PSe || 2≈1.636 × 10-6. Further, when Root ⁽ 230) was applied to both sides, Root ⁽ 230) · F≈0.054 was obtained. Therefore, when (n, k) = (400,370), the (n, k) code having performance close to the complete confidentiality defined in the present embodiment is satisfied in order to satisfy the above-mentioned (n, k) code standard. I was able to select. In this case, by substituting || PS-PSe || 1 = Root ⁽ 230) · F≈0.054 on the right side of the Juanes type inequality, a value of about 1.847 was obtained.

[Modification example]
In the method used in the numerical experiment shown above, the evaluation value F of 2-norm was calculated for each step width (increment) of the bit inversion probability α of the binary symmetric communication path BSC. In the calculation of the evaluation value F, there are 2 ^m of inputs. Therefore, a loop of 2 ^m is required for each step width (increment) of the bit inversion probability α. Hereinafter, the calculation procedure for reducing the loop of 2 ^m times will be described.
First, if the inputs of the uniform characteristic function φU (t) for the uniform distribution and the noise characteristic function φSe (t) for the information possessed by the eavesdropper are both zero vectors 0, then φU (0) = φSe (0) = 1. Since it holds, the equation (60) holds.

Hereinafter, if K: = F ^m _2- {0}, the generality is not lost as t ∈ K in the sum when calculating the evaluation value F of 2-norm. Further, for t ∈ K, the equation (61) and the equation (62) hold.

Therefore, the equation (63) holds.

By utilizing this, by storing the number of infinite products in the list b of the storage area n, it is not necessary to execute a loop of 2 ^m times for each step width of the bit inversion probability α, so that it is only once 2 ^m times. All you have to do is execute the loop of. This preprocessing algorithm is summarized below.

Step 1: Initialize the list b of the storage area n with 0.
Step 2: for loop: (t) ₁₀ = 1, ..., 2 ^m -1 {
Step 3: j = popcnt ((t) ₁₀ )
Step 4: for loop: l = m, ..., n-1 {
Step 5: if popcnt ((t) ₁₀ AND (hl) ₁₀ ) = _1mod2 {
Step 6: j = j + 1}}
Step 7: Increment b [j]. }

By applying this preprocessing algorithm, K can be divided into n subsets by the inverse image of equation (64). That is, since the equation (65) is obtained, the equation (66) is established.

From this, the evaluation value F of 2-norm can be rewritten as in the equation (67).

さらに、ビット反転確率α＝０の場合には、評価値Ｆの定義に直接、α＝０を代入することで、ノイズ特性関数φＳｅ（ｔ）は、式（６８）として表される。

Further, when the bit inversion probability α = 0, the noise characteristic function φSe (t) is expressed as the equation (68) by directly substituting α = 0 into the definition of the evaluation value F.

Even in the case of the bit inversion probability α = 0.5, the noise characteristic function φSe (t) is expressed as the equation (69) by directly substituting it into the definition of the evaluation value F.

Further, the party function shown in the equation (70) will also be used.

Taking the above considerations into consideration, the numerical experimental algorithms are summarized below.

Step 1: Let α be the bit inversion probability of the binary symmetric channel BSC.
Step 2: H ₂ = [(h _m ) ₁₀ , ..., (h _n-1 ) ₁₀ ] is generated using random numbers.
Step 3: Initialize the list b [] of the storage area n with 0.
Step 4: for loop: (t) ₁₀ = 1, ..., 2 ^m -1 {
Step 5: j = popcnt ((t) ₁₀ )
Step 6: for loop: l = m, ..., n-1
Step 7: if party ((t) ₁₀ AND (hl) ₁₀ ) = ₁ {
Step 8: j = j + 1}}
Step 9: Increment b [j]. }
Step 10: for loop: α = 0.0, ..., 0.5 {
Step 11: Initialize temp1 with 0.0.
Step 12: if α = 0.0 or α = 0.5 {
Step 13: if α = 0.0 {
Step 14: temp1 = 2 ^m -1}}
Step 15: else {
Step 16: Initialize temp4 with 0.0.
Step 17: for loop: j = 1, ..., n {
Step 18: if j = 1 {
Step 19: temp3 = 2 * log (-2α + 1)
Step 20: temp4 = temp3}
Step 21: else {
Step 22: temp4 = temp4 + temp3}
Step 23: if b [j] ≠ 0 {
Step 24: temp2 = b [j] * exp [temp4]
Step 25: temp1 = temp1 + temp2}}}
Step 26: Plot Root (temp1) / Root (2 ^m ). }

An example of the procedure for calculating the evaluation value F by the evaluation device 10 in this modification will be described more specifically.
FIG. 11 is a diagram showing an example of a schematic operation for calculating the evaluation value F of the evaluation device 10 according to the modified example of the present embodiment.
(Step St100) The acquisition unit (not shown) of the evaluation device 10 acquires the vertical vector component h _l of the inspection matrix H.
(Step St110) The acquisition unit (not shown) of the evaluation device 10 acquires the input vector t.
(Step St120) The evaluation device 10 calculates the evaluation value F. Here, with reference to FIG. 12, the details of the calculation procedure of the evaluation value F will be described.

FIG. 12 is a diagram showing an example of a procedure for calculating the evaluation value F by the evaluation device 10 according to the modified example of the present embodiment. The computer included in the evaluation device 10 becomes the main operating body, and processes each subsequent step St.
(Step St210) Initialize the list b (each element of b [j]) of the storage area n.
(Step St220) The input vector t is regarded as a bit string, and the number of bit strings that are "1" is counted.
(Step St230) Both the input vector t and the vertical vector component h _l are regarded as a bit string, and the parity of the logical product of the input vector t and the vertical vector component h _l is calculated by the equation (70). When the parity is "1" (step St230; YES), the variable j is incremented.
(Step St240) It is determined whether or not the variable l has reached (n-1). If the variable l has not reached (n-1) (step St240; NO), the variable l is incremented (step St260) and the process is returned to step St230. When the variable l has reached (n-1) (step St240; YES), the process proceeds to step St270.
(Step St270) Increment list b [j] (increment the value of the element in list b by 1).
(Step St280) It is determined whether or not all the components of the input vector t have been calculated. If not calculated for all the components of the input vector t (step St280; NO), the process returns to step St220. When all the components of the input vector t are calculated (step St280; YES), the process proceeds to step St290.

(Step St290) Initialize the bit inversion probability α and the variable j.
(Step St300) Initialize the variable temp1.
(Step St310) Processing is switched according to the value of the bit inversion probability α. Specifically, when the bit inversion probability α = 0, the process proceeds to step St230. When the bit inversion probability α = 0.5, the process ends. When the bit inversion probability α> 0 and <0.5, the process proceeds to step St340.
(Step St320) When the bit inversion probability α = 0, (2 ^m -1) is assigned to the variable emp1 to increment the bit inversion probability α (step St330), and the process is returned to step St300.
(Step St340) Initialize the variable temp4.
(Step St350) It is determined whether or not the variable j = 1. When the variable j = 1, the variable temp3 = 2 * log (-2α + 1) is obtained (step St360), and the obtained variable temp3 is assigned to the variable temp4 (step St370). If the variable j = 1, the sum of the variable temp3 and the variable temp4 is assigned to the variable temp4 (step St380).
(Step St390) It is determined whether or not the list b [j] ≠ 0. If the list b [j] ≠ 0 (that is, the list b [j] = 0), the variable j is incremented (step St440), and the process is returned to step St350. If the list b [j] ≠ 0, the process proceeds to step St400.
(Step St400) List b [j] * exp [temp4] is obtained, and the obtained value is assigned to the variable temp2.
(Step St410) The sum of the variable temp1 and the variable temp2 is assigned to the variable temp1.
(Step St420) It is determined whether or not the variable j has reached n. If the variable j has not reached n, the variable j is incremented (step St440) and the process returns to step St350. If the variable j has reached n, the process proceeds to step St430.
(Step St430) Root (temp1) / Root (2 ^m ) is calculated, and the calculated result is output as an evaluation value F for the bit inversion probability α.

In the above, the division of K was considered, but theoretically, it is the division of F ^m ₂ rather than the division of K. Here, K is divided into n from f (t) = 0 ⇔ t = 0 and 0 ≠ ∈ K (where the symbol 0 ≠ ∈ K indicates that 0 (zero) is not an element of K). did. When considering the division of F ^m ₂ , it is necessary to consider the n + 1 division of F ^m ₂ from 0 ∈ F ^m ₂ (this F ^m ₂ indicates a bit string). Therefore, it can be seen that most of the calculation of the evaluation value F of 2-norm results in the problem of counting the number of elements of the set in which F ^m ₂ is divided. Using the numerical experiment algorithm of the above-mentioned modification, plot the horizontal axis as the bit inversion probability α of the binary symmetric communication path BSC and the vertical axis as the evaluation value F of 2-norm for (n, k) = (60,20). The results are shown in FIG.

FIG. 13 is a diagram showing an example of an experimental result of the evaluation value F by the algorithm of the modified example of the present embodiment. With the above parameters, the evaluation value F near the theoretical value α _BSC is F = || PS-PSe || ₂ ≈ 3.636 × ^10-5 , so that the above-mentioned criteria are satisfied for the evaluation of 2-norm. Here, the expression || A || ₂ indicates 2-norm of A. Regarding the evaluation of 1-norm, by multiplying both sides by Rot (240), Rot ( ²⁴⁰ ) · ^F≈38.131 , so that the evaluation of 1-norm is an inappropriate parameter.
The algorithm after the improvement (modification example) has a shorter calculation time than the algorithm before the improvement. In the above-mentioned (n, k) = (60,20) (that is, m = nk = 40), in the case of the algorithm before improvement, the calculation was not completed even after about one week in the experimental environment. In the case of the improved algorithm, the calculation was completed in about four and a half hours in the same experimental environment as before the improvement. Furthermore, in the case of (n, k) = (400,370), the calculation that takes about two and a half days with the algorithm before the improvement, but after the improvement, takes about four and a half minutes in the same experimental environment as before the improvement. I was able to calculate.

As described above, the evaluation device 10 of the present embodiment uses the multivariable discrete Fourier series shown in the equation (30) in the calculation of the noise characteristic function φSe (t). Here, regarding the operation of the exponential part of the equation ₍ 30), the modulo operation is performed as the operation of the field F2. By adopting this procedure, the noise characteristic function φSe (t) can be obtained by calculating only 2 ^m of discrete points of the input vector t. That is, according to the evaluation device 10 of the present embodiment, the evaluation value of the coding rate in the wiretapping communication path coding can be obtained by a practical procedure.

Further, the evaluation device 10 of the present embodiment does not obtain the probability distribution by, for example, the inverse transformation from the z-transform of one variable. The evaluation device 10 of the present embodiment has a uniform characteristic function φU (t) and a noise characteristic function φSe (t) by directly calculating 2 ^m discrete points in the Fourier transform region without performing the inverse transform. Find 2 norms directly.

Further, the evaluation device 10 of the present embodiment evaluates the random variable Se of the eavesdropper Eve and the 1 norm of the uniform distribution U by using the relational expression of 1 norm and 2 norm shown in the equation (36). Is performed via the above-mentioned calculation by 2 norms. That is, the evaluation device 10 of the present embodiment obtains two norms of the uniform characteristic function φU (t) and the noise characteristic function φSe (t), and then uses the relation of the equation (36) to obtain the uniform distribution U. Evaluate one norm with the noise random variable Se. Further, the entropy of the random variable Se possessed by the eavesdropper Eve is evaluated by using the Juanes-type inequality shown in the equation (35).

Further, the evaluation device 10 of the present embodiment aims to speed up the calculation by calculating the number of 1s in the vector by the popcnt (formula (57)) which is a general-purpose function.

Further, in the evaluation of the inspection matrix H, the evaluation value F is calculated by variously changing the bit inversion probability α in the range of 0.0 to 0.5. Here, when the evaluation value F is calculated by changing the bit inversion probability α in various ways, there is a calculation portion in which the calculation order is O (2 ^m ). In the evaluation device 10 of the present embodiment, even when the bit inversion probability α is changed from 0.0 to 0.5, the calculation order becomes O (2 ^m ) (that is, the calculation load is large). The evaluation value F is calculated by an algorithm that requires only one calculation (calculation part).
Therefore, the evaluation device 10 of the present embodiment can speed up the calculation as compared with the conventional method.

Although the embodiments of the present invention have been described in detail with reference to the drawings, the specific configuration is not limited to this embodiment and can be appropriately modified without departing from the spirit of the present invention. .. The configurations described in each of the above-described embodiments may be combined.

It should be noted that each part included in each device in the above embodiment may be realized by dedicated hardware, or may be realized by a memory and a microprocessor.

Each part of each device is composed of a memory and a CPU (Central Processing Unit), and the function is realized by loading and executing a program for realizing the function of each part of each device in the memory. May be.

Further, the control unit can record a program for realizing the functions of each part of each device on a computer-readable recording medium, read the program recorded on the recording medium into the computer system, and execute the program. Processing by each provided part may be performed. The term "computer system" as used herein includes hardware such as an OS and peripheral devices.

Further, the "computer system" includes the homepage providing environment (or display environment) if the WWW system is used.
Further, the "computer-readable recording medium" refers to a portable medium such as a flexible disk, a magneto-optical disk, a ROM, or a CD-ROM, and a storage device such as a hard disk built in a computer system. Further, a "computer-readable recording medium" is a communication line for transmitting a program via a network such as the Internet or a communication line such as a telephone line, and dynamically holds the program for a short period of time. In that case, it also includes those that hold the program for a certain period of time, such as the volatile memory inside the computer system that is the server or client. Further, the above-mentioned program may be for realizing a part of the above-mentioned functions, and may be further realized by combining the above-mentioned functions with a program already recorded in the computer system.

10 ... Evaluation device, 20 ... Vertical vector component calculation unit of input vector / inspection matrix, 110 ... Uniform characteristic function calculation unit, 120 ... Noise characteristic function calculation unit, 130 ... Evaluation value calculation unit, F ... Evaluation value

Claims (5)

The eavesdropper estimation message obtained from the inspection matrix which is a public parameter in the eavesdropping channel coding method, the bit inversion probability of the eavesdropping channel, the eavesdropper reception bit string acquired via the eavesdropping channel, and the inspection matrix. The acquisition unit for acquiring the input vector of the function obtained by multivariate discrete Fourier transform of the probability distribution of the noise vector, which is a bit string indicating the noise based on the bit inversion probability, which is included in
A noise characteristic function that is a characteristic function of the probability distribution of the noise vector based on the input vector acquired by the acquisition unit, the vector component of either the vertical vector or the horizontal vector of the inspection matrix, and the bit inversion probability. Noise characteristic function calculation unit that calculates
An evaluation value calculation unit that calculates the evaluation value of the inspection matrix for each bit inversion probability based on the noise characteristic function calculated by the noise characteristic function calculation unit and the bit inversion probability.
An evaluation device equipped with. A uniform characteristic function calculation unit for calculating a uniform characteristic function, which is a characteristic function of uniform distribution, is further provided based on the input vector acquired by the acquisition unit.
The evaluation value calculation unit
The evaluation device according to claim 1, wherein the norm of the noise characteristic function and the uniform characteristic function calculated by the uniform characteristic function calculation unit is calculated as an evaluation value of the inspection matrix for each bit inversion probability. The evaluation value calculation unit
The evaluation device according to claim 2, wherein the evaluation value is calculated by calculating 2 norms of the noise characteristic function and the uniform characteristic function and converting the calculated 2 norms into 1 norm. The noise characteristic function is indicated by the inner product of the input vector and the vector component of the inspection matrix.
The evaluation value calculation unit
The evaluation device according to any one of claims 1 to 3, wherein the evaluation value is calculated based on the value of the inner product. The evaluation value calculation unit
The first step of calculating the count value of the input vector whose inner product values match each other among the plurality of input vectors for each evaluation value, and
Using the count value calculated by the first procedure, the second procedure of obtaining the total sum of the input vectors whose inner product value is 1 among the input vectors for each bit inversion probability.
Calculate the evaluation value by
The evaluation device according to claim 4 .

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