WO2014126504A1

WO2014126504A1 - Method for transmitting and receiving information

Info

Publication number: WO2014126504A1
Application number: PCT/RU2013/000693
Authority: WO
Inventors: Владимир Петрович ПАНОВ
Original assignee: Panov Vladimir Petrovich
Priority date: 2013-02-12
Filing date: 2013-08-08
Publication date: 2014-08-21
Also published as: RU2530289C1

Abstract

The present method makes it possible to increase the efficiency of systems for transmitting and receiving information between first and second transmit and receive sides, taking into account all factors that impact on the cost and technical characteristics of such systems, including confidentiality. For this purpose, initial information, or a part thereof having a specific volume, which is to be transmitted by a first side and is represented as a corresponding sequentially and consecutively numbered set of whole numbers is transformed using the proposed method with transform elements which are known only on the first side, and is transmitted to the second side. On the second side, the set of numbers is received, transformed using the proposed method with transform elements which are known only on the second side, and transmitted to the first side. On the first side, the set of numbers is received, retransformed using the proposed method with transform elements which are known only on the first side, and transmitted back to the second side. On the second side, the set of numbers is received and transformed using the proposed method with transform elements which are known only on the second side, and the initial information, or a part thereof having a specific volume, is recovered using the proposed method.

Description

Title of invention:

Method for transmitting and receiving information

Technical field

The invention relates to communication technology, and more specifically, to methods for transmitting and receiving information (SPPI) in a digital communication system. The problem of increasing the technical and economic efficiency of information transmission and reception systems, taking into account all the components that affect their cost and technical indicators, including confidentiality, is relevant, which, in turn, requires the development and improvement of SPS.

State of the art

Known SPPI [Radio Engineering: Encyclopedia / Ed. Yu.L. Mazora et al. - M.: Dodeka-XXI Publishing House, 2002, pp. 63-64], the features of which are implemented, essentially, in all relevant methods and which is an analogue of the proposed technical solution. In this method, the source information is sequentially converted into a message in the physicoelectric information converter, encoded in an encoder, in the radio transmitter, the carrier frequency is encoded by the encoded message and the signal is sent via the communication channel, the signal is received in the radio receiver, demodulated , decode and perform the inverse electrophysical conversion of the information message in a convenient form for the consumer.

The closest analogue is the method of transmitting and receiving information [Sklyar Bernard. Digital communication. Theoretical foundations and practical application. Ed. 2nd rev .: trans. from English - M.: Williams Publishing House, 2004. - 1 104 p. 32-36], in which on the transmitting side form by known methods, a digital bitstream, codes of stream bits are identified from a given set of codes, the latter are converted into signals compatible with the communication channel, and transmitted. On the receiving side, in the reverse order, the signal stream is converted into a digital bit stream, it is formed in the opposite way to the aforementioned known methods, and is conveniently supplied to consumers, and if necessary, stored on information carriers.

Disclosure of invention

The objective of the proposed method is to increase the technical and economic efficiency of the SPPI between the first and second transceiving parties due to the fact that the original information or its part of a given volume transmitted by the first side and represented by the corresponding orderly sequentially numbered set of integers is transformed by the proposed method with transformation elements known only on the first side and are transmitted to the second side. It is received on the second side, converted by the proposed method with transformation elements known only on the second side, and transmitted to the first side. It is received on the first side, converted again by the proposed method with transformation elements known only on the first side, and transferred back to the second side. It is received on the second side, converted by the proposed method with transformation elements known only on the second side, and the original information or part of the given volume is restored by the proposed method.

In order to achieve the indicated technical result in the method of transmitting and receiving information between the first and second transceiver parties, on the first side, predominantly integer elements are formed

with dimension x defined in such a way that its determinant det [ol. ] is not equal to zero, and formed elements bl _{v of the} transposed matrix of algebraic complements of the elements α \ _ϋ in the determinant of the matrix [αΐ. ], and on the second side, elements a2 _{and a} square matrix [a2. ] with dimension Νχ Ν defined in such a way that its determinant det [a2 _{i; /} ] is not equal to zero, and the elements b2 _{and the} transposed matrix of algebraic complements of the elements a2 _{0 are formed} in the mentioned determinant of the matrix [ı2 _y ], while in the indicated and in the following matrices, the index corresponds to the row number, the index j corresponds to the column number, M and N are the given natural numbers known on the first and second sides, and the initial information or its part of the given volume transmitted by the first side, using one of the known methods submitted by and the corresponding ordering is a sequentially numbered set of integers x \ _k , where the values of the index k vary from 1 to a given value of K ₀ , and the numbers x \ _k take values from a given set of numbers, the elements y \ _{of a} rectangular matrix formed from these numbers with dimension Μ ^χ Ν for each value of the index k, varying from 1 to Κ ₀ <Μ ^χ при, and if necessary, when Μ = Ν, for each value of the index k, varying from 1 to K ₀ <Ν ² - 2Ν, in accordance with the expression = x \ _k , and the values of the indices / and j are predominantly determined sequentially in accordance with the expressions i = (k - \) divN + l, where A divB is the integer part when dividing the integer A by the integer B, and j = k - (il) N, and in case of incomplete matrix filling

[ _y ] in the indicated way, for each of the missing elements, for example, an integer x0 given and known also on the second side, not included in the set of numbers used for the numbers x \ _k , is also used through the generated elements zl _{v of the} matrix [ zl ,. ] with dimension Μχ Ν in and

in accordance with the expression ζΐ, - = o1 ₍₍ . _. the corresponding orderly sequentially numbered set of integers x2 _k is determined in accordance with the expression x2 _k = z \ _y , where the values of the index k are determined in accordance with the expression k = {i - \) N + j by interruption for each index value / from 1 to M of index values j from 1 to N, the specified set of numbers x2 _{k is} converted by one of the known methods and transmitted, including, if necessary, by signals compatible with a communication channel, to the second side and a joint venture known on it sobom inverse of said reduced ordered set of numbers x2 _k, where the index value to vary from 1 to Κ _ι = Μ ^χ Ν, formed elements of these numbers y2 _n rectangular matrix

with dimension Μ ^χ Ν for each value of the index k, varying from 1 to AT _j , are determined in accordance with the expression y2 _tJ = x2 _k , while the values of the indices / and j are determined sequentially in accordance with the expressions i = (k - \) divN + \ and j = k - (i -l) N, also through the generated elements z2 _{y of the} matrix [ ^z2 v] ^with dimension Μ ^χ Ν in accordance with the expression

Ν

z2 = ^ y2 _lr a2 _{rJ the} corresponding _{food order} is determined

a carefully numbered set of integers x3 _k in accordance with the expression xb _k = z2 _fJ , where the values of the index k are determined in accordance with the expression k = (i-l) N + j by enumerating for each index i from 1 to M values index j from 1 to N, the specified set of numbers x3 _{k is} transformed by one of the known methods and transmitted, including, if necessary, by signals compatible with the communication channel, to the first side and the method known to it inverse to that restored pour an ordered set of numbers x _k , where s the beginnings of the index k vary from 1 to K _{ , the elements 3 _y formed directly from these numbers coal matrix [^ 3,] with dimension Μχ Ν for each value of the index k, varying from 1 to A, are determined in accordance with the expression уЗ = хЗ _к , while the values of the indices and j are determined sequentially in accordance with the expressions i = ( k - \) divN + \ and j = k - (i - l) N, also through the generated elements z3 _{y of the} matrix [* 3 _{| y} ] with dimension Μ ^χ Ν, respectively

According to the expression z3 = ^ b \ _{! r} 3 _rJ provided that the above det [al _iy ] is equal to one, otherwise, in accordance with the expression ^z ^ ij ~ Σ * ¹ _"· ^ / det [α1 _ι;, J , the corresponding order is determined

K r = \)

a sequentially numbered set of integers x4 _k in accordance with the expression x4 _k = z3 _tJ , where the values of the index k are determined in accordance with the expression k = (i - \) N + j by enumerating for each index value / from 1 to M values index j from 1 to N, the indicated set of numbers x4 _{k is} transformed by one of the known methods and transmitted, including, if necessary, by signals compatible with the communication channel, to the second side and the reverse method known on it, mentioned restore an ordered set of numbers x _k, where the index value to vary from 1 to A ^'formed of the numbers of the rectangular matrix elements 4y

with dimension Μ ^χ Ν for each value of the index k, varying from 1 to Κ _γ , are determined in accordance with the expression 4 ₀ = x4 _k , while the values of the indices and j are determined sequentially in accordance with the expressions i = (k - \) divN + l and j = k - (i - \) N, also through the generated elements z4 _{i} of the} matrix [z4 ₍ .] with dimension

N

Μχ Ν in accordance with the expression z4 _v ^ '_ _l y _ir b2 _rj provided that the aforementioned det [o2 _& .] Is equal to unity; otherwise, in accordance with the expression \

by z4 ... / 'd ^et [ ^a2 ,], the corresponding

a sequentially numbered set of integers x5 _k in accordance with the expression x5 _k = z4 .., where the values of the index k are determined in accordance with the expression k = (i - l) N + j by enumerating for each index value from 1 to M values index j from 1 to N, and after the exclusion of the indicated numbers x from the set of integers x5 _k , the indicated set of integers x \ _{k is} restored, where the values of the index k vary from 1 to the given value K ₀ , and from the resulting set x \ _{to the} known method on the second side, reflux the aforementioned method for presenting information, restore the original information or its said portion, and if necessary subsequent transmission information pieces all these steps are repeated for each of them, as the information transmission if necessary from the second side to the first drive proiz- appropriate actions similar thereto.

In the current level of technology, no sources of information have been identified that would contain information about objects of the same purpose with the indicated set of distinctive features, which allows us to consider the SPPI of the present invention as new and having an inventive step.

The implementation of the invention

. SPSI of the present invention can be embodied in a digital communication system with the appropriate organization of its work and well-known methods of signal processing. The invention is described in more detail below.

The essence of the method is as follows. Previously, on the first side, elements l _{(of a} square matrix [αΐ.] With dimension Мх М, defined in such a way that its determinant det [ol,] are not equal to zero, are predominantly formed from integers. Also, elements b \ _{and a} transposed matrix of algebraic complements of the elements a \ _(j in the mentioned matrix determinant [al,] (G. Korn, T. Korn. Handbook of mathematics for scientists and engineers, ed. 5, Moscow, Nauka, GRFML, 1984, p. 393). On the second side, the elements a2 _{and the} square matrix [a2 _ff ] with dimension Νχ Ν are predominantly formed from integers, defined in such a way that its determinant det [a2, _y ] is not equal to zero.

Also formed elements L2 _have transposed matrix algebraic additions α2 _ν elements in said matrix determinant

[a2. ]. In this case, in the indicated and subsequent matrices, the index / corresponds to the row number, the index j corresponds to the column number, M and N are the given natural numbers known on the first and second sides.

The initial information or its part of a given volume, transmitted by the first side, is represented by one of the known methods by the corresponding orderly sequentially numbered set of integers x \ _k , where the index values k vary from 1 to the given value K ₀ , and the numbers xl _k take values from a given set of numbers. The elements y \ _{tj of the} rectangular matrix _yl _y ^~ with dimension Μχ Ν formed for these numbers for each value of the index k varying from 1 to K ₀ <Μ ^χ Ν, and if necessary, for Μ = Ν for each value of the index k , varying from 1 to K ₀ <Ν ² - 2Ν, are determined in accordance with the expression y = x \ _k . Moreover, the values of the indices f and j are mainly determined sequentially in accordance with the expressions i = (k - \) divN + \, where A divB is the integer part when dividing the integer A by the integer B, and j = k - (i - \) N. In the case of incomplete filling of the matrix [] with the indicated method, each of the missing elements is used, for example, an integer O given and known also on the second side, not included in the set of numbers used for numbers

. Also, through the generated elements z \ _{y of the} matrix [zl _/ ] with dimension

Μχ Ν in accordance with the expression zl. = ^ a \ _1r y \ ^ the corresponding orderly sequentially numbered set of integers x2 _k is determined in accordance with the expression x2 _k = z \ _jj , where the values of the index k are determined in accordance with the expression k = (i - \) N + j by enumerating for each index value from 1 to M index values j from 1 to N. The set of numbers x2 _{k is} transformed by one of the known methods and transmitted, including, if necessary, by signals compatible with the communication channel, to the second side and by a method known inverse to the aforementioned one, the ordered set of numbers x2 _{k is} restored, where the index values to vary from 1 to Κ ^ Μ Ν. Formed from these numbers, the elements y2 _{0 of a} rectangular matrix [.Y2,.,] With dimension Μχ Ν for each value of the index k, varying from 1 to K _x , are determined in accordance with the expression y2 _q = x2 _k , and the values of the indices / and j are determined sequentially in accordance with the expressions i = (k - \) divN + \ and y ^' = £ - (z ^' -l) N. Also, through the formed elements z _{i} of the} matrix ^z2 _y ] ^with dimension Μ ^χ Ν in accordance with the expression

Ν

z2 _tJ = ^ y2 ₁ T a2 _g; . the corresponding orderly subsequently numbered set of integers xb _k is determined in accordance with the expression x _k = 2, where the values of the index k are determined in accordance with the expression k = (i - \) N + j by enumerating for each index value / from 1 to M index values j from 1 to N. The set of numbers x3 _{k is} transformed by one of the known methods and transmitted, including, if necessary, by signals compatible with the communication channel, to the first side and the method known on it, opposite to the one mentioned above, the ordered set of numbers x3 _{k is} restored, where the values of the index k change from 1 to K _x . The elements y3 formed from these numbers. of a rectangular matrix [З ₍ ] with dimension Μ ^χ Ν for each value of the index k, varying from 1 d, oK _{1} are} determined in accordance with the expression у3 ₀ = хЗ _к . Moreover, the values of the indices and j are determined sequentially in accordance with with the expressions = k-) divN + \ and j = k- {i - \) N. Also, through the formed elements of gZ _{and the} matrix [ζ3 _ι; ] with dimension Μ ^χ Ν in accordance

in accordance with the expression z3 _y = ^ bl _ir y3 _rJ provided that the above det [al,] is equal to one, otherwise, in accordance with the expression b \ _ir y3 _rj / det [al, _y ], the corresponding order is determined sequentially sequentially a numbered set of integers x4 _k in accordance with the expression xA _k = rZ _c , where the values of the index k are determined in accordance with the expression k = (i - \) N + j by enumerating for each index value from 1 to M the values of index j from 1 to N. The set of numbers x4 _{k is} transformed by one of the known methods and transmitted, including, if necessary, by signals compatible with the communication channel, to the second side and the method known inverse to it mentioned above, the ordered set of numbers x4 _{k is} restored, where the index values k vary from 1 to The elements y4 _{0 of the} rectangular matrix formed from these numbers [_y ^~ with dimension x ^ for each value of the index k, varying from 1 to K, are determined in accordance with the expression _y = x4 _k , for this index values and j define yayutsya sequentially in accordance with the expressions i = (kl) divN + l and j = k- (ii) N. Also formed through the matrix elements z4 _jJ [z4 ..] with dimension Μ ^χ Ν in accor- with the expression g4u = y4 _1d b2 _g] provided that said det [o2, _y ] is equal to one, otherwise, in accordance with the expression z4 _y = ^ y ^ _ir b2 _rJ / det [o2 _(y ], the corresponding orderly, sequentially numbered set of integers x5 _k is determined in accordance with by the expression x5 _k = z4 _y , where the values of the index k are determined in accordance with the expression k = (i -l) N + j by enumerating for each index value from 1 to M the values of the index j from 1 to N. After the exception the indicated numbers JO from the set of integers x5 _k restore the specified set of integers x \ _k , where the values of the index and k vary from 1 to a predetermined value of K _0. Based on the obtained set x \ _k , the original information or its specified part is restored in a manner that is opposite to the above method of presenting information, which is known on the second side. each of them.Also, when it is necessary to transfer information from the second side to the first, the corresponding similar actions are performed.

We illustrate the implementation of the proposed method on two examples of transmission-reception of a text message - the word PANOV. In the first example, we use a 6-bit ASCII encoding [Sklar Bernard. Cit. p. 90]: P - 000010, A - 100000, N - 011100, O - 111100, V - 011010. The initial information transmitted by the first party is represented by the corresponding orderly sequentially numbered collection consisting of 30 integers; 1 ^ from a set of numbers 0 and 1 (index k varies from 1 to ₀ = 30): 000010100000011100111100011010. From these numbers, elements of a rectangular matrix with dimension Μχ Ν are formed, where M and Ν are given natural numbers known on the first and second - on the four sides (in this example, M = 8, Ν = 4) for each value of the index k, defined in correspondence with the expression y \ _v = xl _k , and the values indices / and j are determined sequentially in accordance with the expression

0 0 0 0

1 0 1 0

0 0 0 0

mi i = (Jt-l + l and 0 1 1 1

) ifcV4 j = k - (i - \) A \ [yl _v ] = 0 0 1 1 Number of elements of mat- 1 1 0 0

0 1 1 0 of the matrix is 32, and the number of numbers xl _k is 30. Therefore, the last row of the matrix is supplemented by two missing elements, for which we use the number x = 2, also known on the second side and not included in the set of numbers 0 and 1 used for x \ _k numbers. On the first side, elements a \ _{h of a} square matrix with dimension 8x8 are formed from integers, det [al. ] which is equal to unity, and the elements Ы _{0 of the} transposed matrix of algebraic complements of the elements al of the determinant of the matrix [al _y ], which in the case of the diagonal matrix coincides with the inverse. In the example, this was done quite simply using the lower and upper triangular matrices whose diagonal elements are equal to unity. The determinants of such matrices, as well as products of an arbitrary number of them, are equal to unity. Their inverse matrices are simply determined. The determinant of the inverse matrix is also equal to unity. The given lower A \ 1 and upper A \ 2 triangular matrices and the defined inverse matrices A \ ¹ and Α \ 2 ^'γ corresponding to them have the form:

1 0 0 1 0 0 0 1 1 about -1

0 1 0 1 0 0 0 o 1 o o

0 0 0 o o o o o

0 1 o o o -1 o o

2 = A ¹ = A12-

0 0 1 0 o o 0 o o

0 0 0 1 o o 1 o o

0 0 0 0 1 o 0 1 o

0 0 0 0 o o o 1 J The matrices al _(y ] formed from them have the form:

On the second side, the lower and upper triangular matrices are formed in the same way and they are inverse and the matrices d2, _y ] and [b2, _y ], which have the form:

e in accordance with

by the expression zl ₀ = ^ a \ _1y y \ ^ the elements zl _{y of the} matrix are formed

and the corresponding order is defined

sequentially numbered set of integers x2 _k in accordance with the expression x2 _k =

, where the values of the index k are determined in accordance with the expression £ = (? ^' - 1) 4 + y by enumerating for each index value / from 1 to 8 index values from 1 to 4: 113322541121121112221 11123432343.

The set of integers x2 _{k is} transformed by one of the known methods and transmitted, including, if necessary, by signals compatible with the communication channel, to the second side and the method opposite to the one known thereon, the ordered set of integers x2 _{k is} restored, where the index values k vary from 1 to K _{ = 32. Elements of y2 formed from these numbers _{for a} rectangular matrix [2,] with dimension 8 x 4 for each value of the index k, varying from 1 to 32, are determined in accordance with the expression y2 _q = x2 _k , while the values of the indices / and j are determined sequentially in accordance with the expressions i = (k-l) div4 + [*! _/; ])· On

form

determine the corresponding orderly sequentially numbered set of integers xb _k in accordance with the expression x _k = z2y, where the values of the index k are determined in accordance with the expression k = (r - 1) 4 + j by enumerating for each index value / from 1 to 8 values of the index j from 1 to 4 -. 8 9 11 11 13 15 18 17 5 6 7 6 5 7 6 6 7 9 9 9 4 5 5 5 12 15 16 15 12 15 16 15. The specified set of integers x b _{k is} transformed by one of the known methods and transmitted, including if necessary, by signals compatible with the communication channel, to the first side and using the method opposite to the one mentioned on it, the ordered set of integers x b _{k is} restored, where the index values k vary from 1 to K _{ = 32. Elements of the matrix are formed similarly [d ^] with a dimension of 8x 4 for each value of the index k, varying from 1 to 32, determined in accordance with the expression y3 ₀ . = x3 _k , and the indices / and j are determined sequentially in accordance with the expressions r = (k - 1) divA + 1 and j = k - (r - 1) 4 (this matrix will have the form of the matrix [z2. ]).

On the first side, in accordance with the expression z3, _v = ^ b \ _lr y3 _rJ form 2 2 3 2

0 0 0 0

elements z3 _v matrices 3 4 4 4

2 2 3 3 with dimension 8x 4 and determine 2 3 2 2

2 3 3 2

5 5 7 7

the corresponding orderly sequentially numbered set of integers x4 _k in accordance with the expression x4 _k = r3 _y , where the values of the index k are determined in accordance with the expression k = (/ - 1) 4 + j by enumerating for each index value / from 1 to 8 the values of the index y are from 1 to 4: 00002232000034442233232223325577. The indicated set of integers x4 _{k is} converted by one of the known methods and transmitted, including if necessary by signals compatible with the communication channel, to the second side and the method known on it in reverse After that, restore an ordered set of integers x4 _k , where the values of the index k vary from 1 to K _x = 32. Similarly, elements of the matrix [ _(y ] with a dimension of 8x4 are formed for each value of the index k varying from 1 to 32, determined in accordance with with the expression y4 .. = x4 _k , and the values of the indices r and j are determined sequentially in accordance with the expressions i = {k - \) div4 + \ and y = A: - (/ - 1) 4 (this matrix will have the form of a matrix gZ,]). On the second side in accordance with the expression

z4 _fJ =

dimension 8 4. This matrix completely coincides with the matrix [^ _j ,] - From it determine the corresponding orderly sequentially numbered set of integers x5 _k in accordance with the expression _x 5 _k = z \ ,. _} where the values of the index k are determined in accordance with the expression k = (g - 1) 4 + j by enumerating for each index value from 1 up to 8 values of the index y from 1 to 4: 000010100000011100111 10001101022. After excluding the numbers x0 = 2 from the specified set of integers x5 _k , the set of numbers x \ _{k is} restored

(00001010000001110011 110001 1010) and, according to the obtained combination x \ _k, known in the second side, in the opposite way to the information presentation method, restore the original information (PANOV). Note that all operations in the example are integer and there is no division operation.

We also consider the second example with the same initial information transmitted by the first side as in the first example, and use the aforementioned representation of it as an ordered sequentially numbered collection consisting of 30 integers from the set of numbers 0 and 1 (000010100000011100 1 11 100011010 000010100000011100111100011010). Imagine this collection as another orderly collection of x \ _k ten integers 0240347432 from the set of numbers 0, 1,2, ..., 7, obtained by splitting the first population into groups of three numbers and considering each group as 8- decimal number, which corresponds to an integer from a set of numbers 0,1,2, ..., 7. Further, from these numbers, elements of a rectangular matrix with dimension Л xN are formed, where M and N are given natural numbers known on the first and second sides (in this example, M = 4, N = 3) for each index value k, determined in accordance with the expression y \ _ij = x \ _k , while the values of the indices \ and j are determined sequentially in accordance

0 2 4

with the expressions i = (k - \) divi + \ and y = £ - (/ - 1) 3: [,] = 0 3 4

7 4 3. In the last

2 8 8

the line as the missing two elements uses the number xO = 8, not included in the set of numbers used for the numbers x! _to . On the first and second 1 0 3 1 sides also form matrices 1 1 1 1 respectively

1 2 1 2, where 1 0 0 1 det [al ,,.] = 3, and [α2 _ν ] = v ι i, where det [2, _y ] = 4, the elements of _{и and the} transposed matrix of algebraic complements of the elements a \ _and matrix determinant

-1 6 -3 1

form -1 3 0 -2

[ol ..] in [S ₉ = 1 0 0 -1 and elements Z> 2. transposed matrix

1 -6 3 2

algebraic complements of the elements a2 _{and the} determinant of the matrix in the form [b2 _y - form an ele-

which he orderly sequentially numbered a set of integers x2 _k in accordance with the expression x2 _k = zl _y , where the values of the index k are determined in accordance with the expression £ = (/ -1) 3 + / by enumerating for each index value / from 1 up to 4 values of the index j from 1 to 3: 2322219171911283121012. The set of integers x2 _k is converted by one of the known methods and transmitted, including if necessary, by signals compatible with the communication channel, to the second side and the method known on it, reverse to the above, restore order a given set of integers x2 _k , where the values of the index k vary from 1 to K _x = 12. Elements of y2 formed from these numbers _{in the} rectangular matrix

with a dimension of 4x3 for each value of the index k, varying from 1 to 12, are determined in accordance with the expression y2 _y = x2 _k , while the values of the indices i and j are determined sequentially in accordance with the expressions i = (£ -ΐ) ώ ^' ν3 + 1 and j = k - (g -1) 3 (i.e., the matrix

[2, _y ] will have the form of the matrix [r1 ₍ ]). On the second side in accordance with by the expression z2 = ^ y _ir a2 _rj the elements z2 _{y are formed} . matrices and determine the corresponding orderly sequence

a thoroughly numbered set of integers x3 _k in accordance with the expression x3 _k = z2 _jj , where the values of the index k are determined in accordance with the expression k = (/ - 1) 3 + 7 by enumerating for each index value / 'from 1 to 4 index values j from 1 to 3: 108 110 134 83 73 80 132 112 120 48 38 38. The set of integers x3 _{k is} transformed by one of the known methods and transmitted, including, if necessary, by signals compatible with the communication channel, to the first side and the method known to it inverse to the above, restore the ordered set of integers x3 _k , where the values of the index k vary from 1 to A ^" , = 12.

Formed from these numbers, the elements З _{of a} rectangular matrix уЗ ..] with a dimension of 4 x 3 for each value of the index k, varying from 1 to 12, are determined in accordance with the expression у ₀ = хЗ _к . Moreover, the values of the indices i and j are determined sequentially in accordance with the expressions i = (k -l) div3 + \ and j = k - (i -1) 3 (this matrix will have the form of the matrix [z2, _y ]). On the first side matching the expression

14 10 8 ^ζ3 _{! /} ⁼ [Σ ^έ1 <^ ³ 1

/ det [al _j,. ] form elements 15 11 10

gZ _c matrix [z3. ] ^: 20 24 32 AND

34 28 30 determine the corresponding orderly sequentially numbered set of integers x4 _k in accordance with the expression x4 _k = z3 _tJ , where the values of the index k are determined in accordance with the expression k = (/ -1) 3 + j by enumerating for each index value from 1 to 4 index values j from 1 to 3: 14 10 8 15 11 10 20 24 32 34 28 30. The set of numbers x _{k is} converted using one of the known methods and transmitted to including, if necessary, signals that are compatible with the communication channel, to the second side and using the opposite method mentioned on it, restore an ordered set of numbers x4 _k , where the values of the index k vary from 1 to 12. Elements of y4 _c formed from these numbers - matrix

with a dimension of 4 x 3 for each index k, varying from 1 to 12, are determined in accordance with the expression y4 ₀ = x4 _k , while the values of the indices and j are determined sequentially in accordance with the expressions i = (k - l) div3 + l and / = £ - (/ - 1) 3. On the second

(h

on the other side according to the expression z4. = [Σ ^ y ^^ ^ ^ / det [o2,]

0 2 4

form elements ζ4 _{ν of the} matrix 0 3 4

7 4 3 with a dimension of 4 x 3. This mat

2 8 8

the matrix fully coincides with the matrix [ _y ] - From it, the corresponding orderly sequentially numbered set of integers x5 _k is determined in accordance with the expression x5 _k = z4 _ij , where the values of the index k are determined in accordance with the expression k = (g -1) 3 + j by means of a search for each index value / from 1 to 4 index values j from 1 to 3: 0 2 4 0 3 4 7 4 3 2 8 8.

After exclusion of numbers x0 = 8 out of said plurality of integers x5 is reduced _to the set of numbers x \ _k (0 2 4 0 3 4 7 4 3 2) and semi- chennoy aggregate x \ _a known manner on a second side, said method of inverse representation information, restore the original information (PANOV). Note that all operations in the example, despite the presence of division operations, are integer and are performed on integers.

Industrial applicability Thus, a more efficient transmission of information is proposed, the method is simple to implement using a modern elemental base.

The present invention can be applied to the development and improvement of existing and future communication systems. The analysis made it possible to establish: analogues with a set of features identical to all the features of the claimed technical solution are absent, which indicates the conformity of the claimed method to the “novelty” condition. The results of the search for well-known solutions in the field of API for the purpose of identifying features that match the distinguishing features of the claimed method from the prototype have shown that they do not follow explicitly from the technical level.

Claims

Claim

A method of transmitting and receiving information between the first and second transceiving parties, in which the elements a \ _{ij of a} square matrix [al,] with dimension M M, defined in such a way that its determinant det [al, _y ] is not equal to zero, and the elements M of the transposed matrix of algebraic complements of the elements are formed

determinant in said matrix _[y o1], and on a second side formed mainly of integers ₀ a2 elements of the square matrix _[a2; ] with dimension Ν ^χ Ν defined in such a way that its determinant det [o2 _i; ] is not equal to zero, and the elements b2 _{and the} transposed matrix of algebraic complements of the elements a2 are formed. in the determinant of the matrix [a2,], while in the indicated and subsequent matrices the index / ^' corresponds to the line number, the index j corresponds to the column number, M and N are the given natural numbers known on the first and second sides, and the initial information or a part of a predetermined volume transmitted first side, one of the known methods is represented by its corresponding ordered sequentially numbered set of integers ^ χΐ, where the values of their scores to vary from 1 to a predetermined value K _0, and the number of the received xl ^ added value from a given set of numbers formed from these numbers element cops

with dimension Μ ^χ Ν for each value of the index k, varying from 1 to K ₀ < ^{χ χ} при, and if necessary, when Μ = Ν for each value of the index k, varying from 1 to K ₀ <Ν ² - 2Ν, are determined in accordance with the expression yl _y = x \ _k , while the values of the indices and j are mainly determined sequentially in accordance with the expressions i = (k - l) divN + l, where A divB is the integer part at dividing the integer A by the integer B, and j = k - (i - \) N, and if the matrix [j> l _fy ] is incomplete in the indicated way, for each of the missing elements, for example, the given and the integer xO, which is also known on the second side, is not included in the set of numbers used for the numbers x \ _k , also through the generated elements z \ _{tJ of the} matrix [zl _tf ] with

and

dimension Μχ Ν in accordance with the expression zl, _y = a1, - _. the corresponding orderly sequentially numbered set of integers x2 _k is determined in accordance with the expression x2 _k = z \ _i} , where the values of the index k are determined in accordance with the expression k = (i - \) N + j by enumerating for each index value / from 1 to

M index values j from 1 to N, the specified set of numbers x2 _{k is} transformed by one of the known methods and transmitted, including, if necessary, by signals compatible with the communication channel, to the second side and the method opposite to the one known on it, restore the ordered set of numbers x2 _k , where the values of the index k vary from

1 to K = Μ ^χ Ν, the elements y2 formed from these numbers _{in a} rectangular matrix with dimension Μ Ν for each value of the index k varying from 1 to K _x are determined in accordance with the expression y2 _v = x2 _k , and the values indices / and j are determined sequentially in accordance with the expressions r = (k - \) divN + 1 and j = k - (i - 1) N, also through the generated elements z2 _{v of the} matrix [z2. ] with dimension Μ Ν in

Ν

According to the expression z2 _ij = y2 _ir a2 _rj , the corresponding orderly sequentially numbered set of integers q; 3 ^ is determined in accordance with the expression xb _k = ζ2 _ν , where the values of the index k are determined in accordance with the expression k = (i -l) N + by enumerating for each index value / from 1 to M index values j from 1 to N, the specified set of numbers x3 _{k is} transformed by one of the known methods and transmitted, including, if necessary, by signals compatible with the communication channel, to the first side and the reverse method mentioned in the way known on it, restore the ordered set of numbers x3 _k , where the values of the index k vary from 1 to K _x , the elements formed from these numbers are ultrasound elements _{c of a} rectangular matrix [З, _у ] with dimension Μχ Ν for each value of the index k, varying from 1 to Κ, are determined in accordance with the expression уЗ _and = хЗ _k , while the indices i and j are determined sequentially in accordance with the expressions = {k - \) divN + \ and j = k - {i - \) N, also through the generated elements z3 _{tJ of the} matrix [^] with

m

Μχ Ν dimension in accordance with an expression _q eb _{_{= ^ b \ ir y3 r]}} . provided that

equal to unity, otherwise, in accordance with the expression z3 _tJ = ^^ b \ _ir y3 _rj , j / det [al ₍ ,.], the corresponding orderly sequentially numbered set of integers x4 _k is determined in accordance with with the expression x4 _k = ζ3 _ν , where the values of the index k are determined in accordance with the expression k = (i-l) N + j by means of a selector for each index value from 1 to M the values of the index j from 1 to N, the indicated set x4 numbers _to convert one of the known methods and are transmitted, including signals, if necessary, compatible parable with kana ohm connection, and on a second side a known manner thereon, the reciprocal of said ordered set of numbers is reduced _to x4, where the index value to vary from 1 to Κ _λ, formed elements of these numbers y4 _n rectangular matrix [y4 _y] with dimension x N for each value of the index k, varying from 1 to K, are determined in accordance with the expression y4 _y = x4 _k , while the values of the indices and j are determined sequentially in accordance with the expressions

J = (k - \) divN + \ and j = k - (i - \) N, also through the formed elements ζ4. matrices [ ^z4 , _j ] ^with dimension Μ ^χ Ν in accordance with the expression z4, = ^ y ^, _r b2 _g] . provided that the above det a2 _{i; /} J is equal to unity, otherwise, in accordance with the expression

the corresponding ordering is divided into a sequentially numbered set of integers x5 _k in accordance with the expression x5 _k ^' V where the values of the index k are determined in accordance with the expression k = (i - \) N + j by enumerating for each index value / from 1 to M, the values of the index j are from 1 to N, and after the exclusion of the indicated numbers xO from the set of integers x5 _k , the indicated set of integers x \ _{k is} restored, where the values of the index k vary from 1 to the given value K ₀ , n from the resulting set x \ _{to the} famous Tue On the other side, in the opposite way to the method of presenting information, the original information or its specified part is restored, and if it is necessary to transmit subsequent parts of the information, all these steps are repeated for each of them, also if it is necessary to transfer information from the second side to the first perform appropriate actions similar to those indicated.