RU2513725C2 - Method of providing integrity of transmitted information - Google Patents

Abstract

FIELD: radio engineering, communication.

SUBSTANCE: invention relates to error correction at the receiving side in communication systems. The method of providing integrity of transmitted information involves receiving information over n parallel channels at the receiving side; calculating a value

, where P(S₁) and P(S₂) are a priori probabilities of transmitted symbols (S₁=1; S₂=-1) of information from a source; x₁, …, x_i, …, x_n are values received symbols over each of the n channels; $$P_M^{(i)}$$

is the probability of unauthorised third party action over the transmitted symbols from the source in each of the i-th of the n channels; comparing the calculated value with zero; if the calculated value is greater than zero, the symbol S₁ was transmitted, otherwise the symbol S₂ was transmitted.

EFFECT: high efficiency of receiving transmitted information while taking into account the probability of modification of the transmitted information.

9 dwg, 1 tbl

Description

The invention relates to the field of computer technology and can be used in multiservice communication systems (for high-speed applications) to correct errors on the receiving side without using requests for retransmission along the feedback lines or introducing redundancy in the transmitted signal.

Known methods for ensuring error-free reception of transmitted information [1] use mechanisms of interleaving, hopping, adding redundancy to the transmitted signal, and using feedback. In this case, only the integrity of the information is monitored, and if it was changed unauthorized during the transfer, the data will need to be retransmitted.

The main disadvantage of the known methods is the increase in the delay time of information transmission due to the use of interleaving, hopping, the use of feedback for retransmission of information in case of high indicators of the probability of information change during transmission over communication lines by third parties. Thus, the amount of delay in the transmission of information can be significantly higher than the normative indicators for the provision of multimedia high-speed services, as a result of which the known methods can be limitedly used for applications operating in real time (critical to time delays).

When applying the methods of interleaving, it is first necessary to evaluate the depth of interleaving with these channel parameters in order to achieve the highest relative information transfer rate. Thus, channel information is transmitted with a delay depending on the method of interleaving used on the transmitting side, it is also worth considering the need for deinterleaving on the receiving side, which also causes a time delay due to the need to obtain characters to restore the original sequence.

In turn, the use of hopping is necessary to combat fading and does not always give a gain in speed. For this method, you must have at least one channel in reserve for the implementation of hopping. Thus, it is possible that the backup channels will be idle and used only at the moments when errors appear in the main information transmission channel, which in turn is not effective in terms of resource use.

Using the feedback method also introduces the time delay required for interrogation by the receiver in case of accepting a combination with errors. In addition, for the organization of feedback, a reverse channel is needed to be able to send a signal to the transmitter about the need to re-send the code combination. Thus, the transmission time of information due to its retransmission is doubled.

The closest technical solution in relation to the claimed invention are methods for the parallel transmission of information in communication networks [2, prototype].

The disadvantage of the known prototype [2] is that it does not take into account the likelihood of modification of the transmitted information by third parties (unauthorized actors) throughout the transmission from the sender to the recipient via parallel channels.

The aim of the invention is to ensure error-free reception of transmitted information while reducing the delay time of information transmission and taking into account the likelihood of modification of the transmitted information due to work on the receiving side of the proposed decision circuit.

This goal is achieved by the fact that information symbols (conventionally “0” and “1”) are transmitted simultaneously to non-parallel channels, on the receiving side they enter a decisive scheme in which, based on the received information symbols, knowledge about the magnitudes of the probabilities of modification of the transmitted information by third parties ( at each parallel connection), a priori probabilities of the transmitted symbols, a certain value is calculated, if it is greater than zero, one symbol was transmitted (conditionally “0”), otherwise ugoy (conditionally "1").

Thus, even at high probabilities of character modification by third parties during transmission over communication lines, the delay time for transmitting information consists only of the transmission time over the communication lines and the time taken to make a decision about the transmitted character at the receiving point, without requests for retransmission and without using other methods that increase error-free reception of information.

The invention is illustrated by the following description and the accompanying drawings, in which Fig. 1 shows a functional diagram of the proposed method for ensuring the integrity of the transmitted information, Figs. 2-5 show an algorithm that implements the proposed method for ensuring the integrity of the transmitted information, Figs. 6-9 graphs obtained using simulation modeling, confirming the efficiency of the claimed method of ensuring the integrity of the transmitted information.

, на каждом i-м соединении из совокупности $$\left(i=\overline{\mathrm{0,}n}\right)$$

.The information stream from the source consists of the symbols S ₁ or S ₂ , with a priori probabilities of occurrence of P (S ₁ ) and P (S ₂ ), respectively. Such a stream is transmitted simultaneously through a set of parallel n channels, where symbols transmitted through communication lines can be unauthorized by third parties with a probability $$P_M^i$$

, on each i-th connection from the set $$\left(i=\overline{0n}\right)$$

.

On the receiving side, the received symbols x = (x ₁ , ..., x _i ..., x _n ) enter the proposed decision circuit, respectively, along parallel n inputs.

Thus, the conditional probability that a decision at the output of a decision circuit with n inputs will be made in favor of S ₁ or S ₂ will be determined by the formulas:

$$P\left(S_{\mathrm{one}}/\left(x_i;i=\overline{0n}\right)\right)=\frac{P\left(S_{\mathrm{one}}\right)\left\{\underset{i\in x_i=S_{\mathrm{one}}}{P}\left(\mathrm{one}-P_M^{\left(i\right)}\right)\underset{i\in x_i=S_2}{P}{P}_M^{\left(i\right)}\right\}}{P\left(x_i;i=\overline{0n}\right)};$$

$$P\left({\mathrm{<figure-callout\; id="2"\; label="S"\; filenames="00000035.png,00000036.png"\; state="\{\{state\}\}">S</figure-callout>}}_2/\left(x_i;i=\overline{0n}\right)\right)=\frac{P\left(S_2\right)\left\{\underset{i\in x_i=S_{\mathrm{one}}}{P}{P}_M^{\left(i\right)}\underset{i\in x_i=S_2}{P}\left(\mathrm{one}-P_M^{\left(i\right)}\right)\right\}}{P\left(x_i;i=\overline{0n}\right)};$$

However, since the probability value in the denominator is unknown, we take the probability ratio, and if the result is greater than unity, the decision will be made in favor of S ₁ , otherwise S ₂ :

$$\frac{P\left(S_{\mathrm{one}}/\left(x_i;i=\overline{0n}\right)\right)}{P\left(S_2/\left(x_i;i=\overline{0n}\right)\right)}=\frac{P\left(S_{\mathrm{one}}\right)}{P\left(S_2\right)}\times \frac{\underset{i\in x_i=S_{\mathrm{one}}}{P}\left(\mathrm{one}-P_M^{\left(i\right)}\right)}{\underset{i\in x_i=S_{\mathrm{one}}}{P}P\left({}_M^{\left(i\right)}\right)}\times \frac{\underset{i\in x_i=S_2}{P}{P}_M^{\left(i\right)}}{\underset{i\in x_i=S_2}{P}\left(\mathrm{one}-P_M^{\left(i\right)}\right)},$$

Having logarithmized both parts of the expression, we get:

$$ln\frac{P\left(S_{\mathrm{one}}/\left(x_i;i=\overline{0n}\right)\right)}{P\left({\mathrm{<figure-callout\; id="2"\; label="S"\; filenames="00000035.png,00000036.png"\; state="\{\{state\}\}">S</figure-callout>}}_2/\left(x_i;i=\overline{0n}\right)\right)}=ln\frac{P\left(S_{\mathrm{one}}\right)}{P\left(S_2\right)}+{\displaystyle \sum _{i\in x_i=S_{\mathrm{one}}}ln\frac{\left(\mathrm{one}-P_M^{\left(i\right)}\right)}{P_M^{\left(i\right)}}+{\displaystyle \sum _{i\in x_i=S_2}\frac{P_M^{\left(i\right)}}{\left(\mathrm{one}-P_M^{\left(i\right)}\right)}}}.$$

We introduce the following notation:

$$a_0=ln\frac{P\left(S_{\mathrm{one}}\right)}{P\left(S_2\right)};\left(\text{one}\right)$$

$$a_i=ln\frac{\left(\mathrm{one}-P_M^{\left(i\right)}\right)}{P_M^{\left(i\right)}};\left(\text{2}\right)$$

Conditionally S ₁ = + 1, S ₁ = -1, as a result of the conversion received:

$$ln\frac{P\left(S_{\mathrm{one}}/\left(x_i;i=\overline{0n}\right)\right)}{P\left({\mathrm{<figure-callout\; id="2"\; label="S"\; filenames="00000035.png,00000036.png"\; state="\{\{state\}\}">S</figure-callout>}}_2/\left(x_i;i=\overline{0n}\right)\right)}=a_0+{\displaystyle \sum _{i=0}^n{x}_i{a}_i}.$$

Thus, it can be argued that for a decision circuit with n parallel inputs, simultaneously received messages x = (x ₁ , ..., x _i , ..., x _n ) and one output, the following relation holds:

$$a_0+{\displaystyle \sum _{i=0}^n{x}_i{a}_i}=\{\begin{array}{l}>0t\mathrm{about}{\text{S}}^{\text{*}}=S_{\mathrm{one}},\hfill \\ <0t\mathrm{about}{\text{S}}^{\text{*}}={\mathrm{<figure-callout\; id="2"\; label="S"\; filenames="00000035.png,00000036.png"\; state="\{\{state\}\}">S</figure-callout>}}_2.\hfill \end{array}\left(\text{3}\right)$$

When applying the proposed decision scheme, there is no need to use, for example, requests for retransmission, interleaving methods, hopping.

The invention is illustrated by a specific implementation example in the form of the device shown in Fig.1.

The device contains:

1 - parallel inputs of the device,

2 - block summation of works,

3 - block calculating the coefficients a _i , (in accordance with formula (2)),

4 - adder block,

5 - block calculating the coefficients a ₀ (in accordance with formula (1)),

6 - device output.

The device operates as follows.

Block 2 receives:

, принятый по i-му параллельному каналу,- out of 1 for each parallel input, the signal x = (x ₁ , ..., x _i , ..., x _n ), changed by an unauthorized person with a probability $$P_M^{\left(i\right)}\left(i=\overline{0n}\right)$$

received on the i-th parallel channel

- the value of ai calculated in block 2.

Then, in block 2, the received quantities from the inputs and the values from block 3 are multiplied and then added together in accordance with the right term of the left side of equality (3).

In block 3, the values of the coefficients a _i are calculated in accordance with formula (2).

In block 5, the values of the coefficients a ₀ are calculated (in accordance with formula (1)).

Next, in block 4, the values received in it are summed up and compared with the resulting zero. In the event that the value is greater than zero, the decision on the transmitted symbol is made in favor of the symbol S ₁ , otherwise S ₂ .

At the output of the device (block 6), the symbol transmitted by the source.

Thus, the use of new techniques (the operation of the deciding circuit at the reception) reduces the time of information transmission due to the lack of requests for retransmission and the use of interleaving and hoping methods, and also takes into account the likelihood of third-party information changing during transmission via parallel channels.

To verify the invention, a simulation of the functioning of the decision circuit (PC) was carried out.

Given that the results will be stochastic in nature, the Monte Carlo method was used [3].

The following assumptions were made for the expected results:

- accuracy ε = 0.01,

- reliability α = 0.999.

To determine a sufficient number of tests N, in statistical modeling, the expression from [3] was used:

$$N=t_{\alpha }^2\frac{p\left(\mathrm{one}-p\right)}{{\mathrm{<figure-callout\; id="2"\; label="\epsilon "\; filenames="00000035.png,00000036.png"\; state="\{\{state\}\}">\epsilon </figure-callout>}}^2},\left(\text{four}\right)$$

where t _α ^{is the} function inverse to the normal distribution (for α = 0.999 t _α = 3.29), p is the desired probability of ensuring the integrity of the information.

From (4) it is clear that the maximum value of N will reach at p = 0.5, we finally got:

. $$N={3.29}^2\left(\frac{0.5\left(\mathrm{one}-0.5\right)}{{0.01}^2}\right)=27061$$

.

Thus, assuming the total number of tests N = 30000 for the given parameters, an absolute error of the results of at least 1% will be ensured.

The stages of the algorithm (Figure 2-5).

1. Input data input (block 1-2):

( $$j=\overline{\mathrm{1,}n}$$

, где n - количество параллельных соединений),- probability of modification $$R_m=R_m^{\left(j\right)}$$

( $$j=\overline{\mathrm{one,}n}$$

where n is the number of parallel connections),

- a priori probability P (S ₁ ) the appearance of the symbol S ₁ ,

- the number of tests N = 30000,

- the maximum number of parallel connections n = 15.

2. Modeling of the transmitted message flow S is carried out according to the rule (block 4-8):

, $$S=\{\begin{array}{l}{S}_i=+\mathrm{one,}\text{if z}\le \text{P}\left({\text{S}}_{\text{one}}\right)\hfill \\ S_i=-\mathrm{one,}\text{if z}>\text{P}\left({\text{S}}_{\text{one}}\right)\hfill \end{array}$$

,

.where z is a random number generated using a random number sensor in accordance with the uniform distribution law (0≤z≤1), $$i=\overline{\mathrm{one,}N}$$

.

3. The formation of the stream x _ij , consisting of N changed (under the action of P _m ) symbols of the stream S _i transmitted over n parallel connections, is performed according to the rule (block 10-15):

, $$x_{ij}=\{\begin{array}{c}e\mathrm{from}l\mathrm{and}\text{z}\le {\text{P}}_{\text{m}},t\mathrm{about}\mathrm{and}smenen\mathrm{and}ee\mathrm{from}tb{\text{, x}}_{\text{ij}}=S_i\times \left(-\mathrm{one}\right)\\ e\mathrm{from}l\mathrm{and}\text{z}>{\text{P}}_{\text{m}},t\mathrm{about}\mathrm{and}smenen\mathrm{and}\mathrm{I\; am}net,{\text{x}}_{\text{ij}}=S_i\end{array}$$

,

, $$j=\overline{\mathrm{1,}n}$$

.where z is a random number generated using a random number sensor in accordance with the uniform distribution law (0≤z≤1), $$i=\overline{\mathrm{one,}N}$$

, $$j=\overline{\mathrm{one,}n}$$

.

4. The calculation of the coefficients a ₀ and a _j respectively (block 16-18):

$$a_0=ln\frac{P\left(S_{\mathrm{one}}\right)}{\mathrm{one}-P\left(S_{\mathrm{one}}\right)},$$

$$a_j=ln\frac{\left(\mathrm{one}-P_m\right)}{P_m},$$

.Where $$j=\overline{\mathrm{one,}n}$$

.

5. The calculation of the ratio (3) for the i-th character transmitted via j-connections (block 20-26):

, $$X_{ij}=a_0+{\displaystyle \sum _{j=\mathrm{one}}^n{x}_{ij}{a}_j}$$

,

, j=3,5,…,n.Where $$i=\overline{\mathrm{one,}N}$$

, j = 3,5, ..., n.

6. The formation of the stream of received symbols S ^* = y _ij (block 27-29):

, $$y_{ij}=\{\begin{array}{l}{y}_{ij}=+\mathrm{one,}{\text{if X}}_{\text{ij}}>0\hfill \\ y_{ij}=-\mathrm{one,}{\text{if X}}_{\text{ij}}<0\hfill \end{array}$$

,

, j=3,5,…,n.Where $$i=\overline{\mathrm{one,}N}$$

, j = 3,5, ..., n.

7. Counting correctly received characters and calculating the probability of information integrity at the output of the decision circuit R _{C RS} (block 33-38):

, $$P_{c\text{RU i}}=\frac{N_{al}}{N}$$

,

where N _al is the number of correctly received symbols during transmission over i-connections, i = 3,5, ..., n.

8. Counting correctly received characters and calculating the probability of information integrity without using a combination of parallel connections (block 40-43):

, $$P^c=\frac{N_p}{N}$$

,

where N _p is the number of correctly received symbols during transmission over one connection (n = 1).

Software implementation of the invention was carried out in a MatLab environment. The simulation results are presented in Fig.6 and table 1, where n is the number of parallel connections for transmitting information (or the number of inputs of the decision circuit), R _m is the probability of message modification, R _{c RS} is the probability of ensuring the integrity of the message at the output of the RS.

Table 1 - the Dependence R _tsRS = ƒ (P _m ) with a different number of inputs of the RS n P _m R _{c RS} 3 5 7 9 eleven 13 fifteen 0.05 0,9922 0,9988 0,9996 0,9999 one one one 0.1 0.9720 0,9920 0,9976 0,9992 0,9997 0,9999 one 0.15 0.9390 0.9729 0.9889 0.9945 0,9974 0,9990 0,9996 0.2 0.8944 0.9412 0.9655 0.9793 0.9866 0,9919 0,9955 0.25 0.8421 0.8965 0.9298 0.9507 0.9652 0.9762 0.9825 0.3 0.7836 0.8366 0.8735 0.9020 0.9217 0.9374 0.9509 0.35 0.7159 0.7673 0.8026 0.8297 0.8530 0.8716 0.8894 0.4 0.6515 0.6866 0.7114 0.7329 0.7523 0.7886 0.7853 0.45 0.5765 0.5952 0.6125 0.6254 0.6380 0.6476 0.6577 0.5 0.4959 0.4959 0.4959 0.4959 0.4959 0.4959 0.4959 0.55 0.5722 0.5935 0.6105 0.6246 0.6376 0.6494 0.6539 0.6 0.6512 0.6845 0.7073 0.7323 0.7517 0.7692 0.7852 0.65 0.7125 0.7615 0.7950 0.8252 0.8474 0.8666 0.8841 0.7 0.7817 0.8359 0.8734 0,9005 0.9222 0.9386 0.9507 0.75 0.8414 0.8952 0.9297 0.9518 0.9670 0.9770 0.9835 0.8 0.8969 0.9427 0.9689 0.9810 0.9887 0,9936 0,9962 0.85 0.9416 0.9739 0.9880 0,9943 0.9970 0.9987 0,9994 0.9 0.9736 0,9916 0,9973 0,9993 0,9998 0,9999 one 0.95 0,9932 0,9986 0,9998 one one one one one one one one one one one one

Figure 6 shows the nature of the dependence R _{c RS} = ƒ (P _m ) at n = 3,7, 11, 15.

Based on the results of simulation, the following conclusions can be drawn:

- theoretical results obtained using (3) coincide with the simulation results,

- the efficiency of the decision-making algorithm for restoring the modified transmitted symbol is confirmed,

- with an increase in the probability of modification P _{m, the} algorithm allows to increase the probability of ensuring the integrity of the information P _res ^c due to the coefficients a, with a break point in R _m = R _{c RS} = 0.5.

Since the expression for calculating a _i includes the probability of modifying the message P _m , which is random in nature, it can be assumed that the accuracy of its determination will affect the simulation results as a whole. In this regard, an analysis of the influence of the accuracy P _m on the decision on the transmitted symbol was carried out using statistical modeling.

The simulation results are presented in Fig.7-9 with n = 5 and P (S ₁ ) = P (S ₂ ) = 0.5.

List of sources used

1. Melentyev O.G. Theoretical aspects of data transmission over channels with grouping errors / Edited by Professor Shuvalov V.P. - M .: Hot line - Telecom, 2007 .-- 232 p.

2. Andronov I. S. Transfer of discrete messages on parallel channels / I. S. Andronov, L. M. Fink / - M.: Sov. Radio, 1971. - 408 pp. (prototype).

3. Buslenko N.P. Modeling of complex systems / N.P. Buslenko / - M .: Nauka, 1968. - 356 p.

Claims (1)

A method of ensuring the integrity of the transmitted information, characterized in that on the receiving side receive information on n parallel channels, calculate the value

where P (S ₁ ) and P (S ₂ ) are the a priori probabilities of the transmitted symbols (S ₁ = 1; S ₂ = -1) information from the source; x ₁ , ..., x _i , ..., x _n are the values of the received symbols for each of n channels;

the likelihood of unauthorized exposure by a third party to transmitted characters from the source in each i-th of n channels; comparing the calculated value with zero; if the calculated value is greater than zero, then decide that the symbol S _{1 was} transmitted, otherwise the symbol S _{2 was} transmitted.

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