Method of transmitting information using compressed noise-proof ternary codes and extensions based on them

Abstract

FIELD: telecommunication systems.SUBSTANCE: method for transmitting information using compressed noise-resistant ternary codes is proposed, which consists in the fact that a sequence of bits is subjected to the first stage of structural-algorithmic transformations (SAP-1), the results of which are presented in the form of a new sequence of bits, subjected to additional noise-resistant coding and randomization, then before recoding into a substitution ternary code, they are subjected to a scrambling operation, wherein the substitution ternary noise-resistant code is considered as the main ternary symbols, and the symbols represented by amplitude-pulse modulation, as duplicates, represented in the form of signals with pulse-width modulation (PWM), are converted at the second stage of modulation into phase manipulation with two opposite values of phase 0° and 180° frequencies that are used as a phase marker indicating the beginning and end of signals with a PWM signal, as a result of which the phase markers simultaneously become the carrier of the transmitted information.EFFECT: increasing the noise immunity index of transmitted information and in detecting errors.5 cl, 17 dwg

Description

[0001] This invention relates to telecommunications systems and can be used in data transmission systems over communication channels. Its use improves the reliability of information transmission without introducing structural redundancy into transmitted messages, and enables the detection of errors, both single and multiple, that occur during transmission. Its use will reduce redundancy in transmitted data, increase the speed of information transfer, and enhance its security against unauthorized access.

[0002] The following are known: “Methods for transmitting information and systems for their implementation” (patent RU 2480840 C1, published on 25.04.2013, bulletin No. 21 [1] and patent RU No. 2581774 with priority from 30.09.2014 [2]).

[0003] The ternary coding proposed in them, as well as considered in subsequent inventions [3-7], establishes as the basis of structural-algorithmic transformations (SAT) a direct logical correspondence between the binary symbols “1” and “0”, enclosed in angle brackets with index 2 (<>2), and their ternary equivalents (Fig. 1), which can be represented in the following form:

[0004]

[0005] where - ternary symbols duplicating each other.

[0006] Illustrations explaining the fundamental principles of the transition from the binary code traditionally used for transmitting information to the proposed ternary code with duplicate symbols are shown in Fig. 1. Fig. 1 also shows that, in addition to the direct correspondence (1), there is also its inverse form (1i):

[0007]

[0008] The following model is the basis for converting the original binary information encoding into the proposed ternary code. In the bit stream generated for transmission or storage, the first three bits are selected. If code constructions appear during direct encoding <101> 2or <001> 2, then they are assigned (↔) to the ternary symbols S2(T2) or S1(T1), respectively. If the first three bits represent other code constructions: <000> 2, <111> 2, <100> 2, <010> 2, <110> 2, the group of analyzed bit code structures is reduced to two bits each. The first bit in these structures becomes the last bit of the preceding conversion operation from binary code to the proposed ternary code, as shown in Fig. 1 (top illustration). As a result, the ternary code becomes recurrent: its adjacent ternary symbols are linked by the same preceding and following bit in the proposed two-level partitioning model.The upper partitioning level (R1) pertains to odd ternary symbols, and the lower one (R2) pertains to even ternary symbols, as shown in Fig. 1 (left). This partitioning allows for a better understanding of the essence of the proposed ternary coding. This allows for the emergence of initial uncertainty when converting binary code to ternary code. This uncertainty is related to the primary binary coding structure. <011> 2, since the bit preceding it becomes unknown <0011> 2or <1011> 2. This uncertainty is most easily resolved on the basis of service or synchronizing code words, which, according to their formation structure, should stand out against the background of the information sequence of bits and include as the last one after recoding into a ternary symbol S2(T2) ↔ <101> 2. Then, in addition to their main function, they simultaneously remove the uncertainty of decoding, which consists of the reverse transition from compressed ternary symbols. Concentrating a greater amount of transferable information load than the original binary code. This property forms the basis of a new direction in information theory called economical coding of data and messages.

[0009] Figure 2 shows, as an example, the results of transcoding a stream consisting of 16 bits. , into a sequence of ternary symbols represented only by index values As a result of such recoding, instead of 16 bits, it is necessary to transmit only 10 ternary symbols The compression ratio achieved in this way is equal to its theoretical value: In addition, from the illustration shown in Fig. 2, the meaning of the duplicate ternary symbols becomes clear. Symbols in primary pulse modulation they are represented as amplitude-pulse modulation (APM3) with three positions (i): i=0,1,2. At the same time, the symbols Ti , i=0,1,2 are displayed using pulse-width modulation (PWM3). They also have three values ​​(i=0,1,2) of duration: T0, T1=1.5T0 and T2=2T0. Significant differences between them appear only at the stage of secondary modulation of the carrier frequency of the transmitted signal, when, for example, PWM3, put in correspondence with duplicate ternary symbols are converted into three frequency values: - carrier frequency, and - its deviation, and PWM3 - in changes in the phase value of 0° and 180°, indicating the boundaries of the pulse change (Fig. 2). In this case, the phase changes (phase marks) determine the boundaries of the PWM pulses i . Also, the compression coefficients obtained during recoding may differ from its theoretical value Real values for a statistical sample equal to 1000 bits, are shown in Fig. 4. The volume of such samples was 180. They were obtained by modeling digital signal streams represented by binary code and including a significant number of series of identical bits of large length. The actual compression ratio obtained in this way was within the following range of values: from 1.3 to 1.38. Also, the achieved values ​​of the compression ratio can be significantly increased by using bit scrambling information technologies.

[0010] Methods for representing data using the transformation of the original binary coding into a quasi-ternary code are known [14,15]. In this case, two levels are traditional - they are used to represent the symbols "0" and "1" of the binary code. The third level of representation is used to change the code positions when long series of identical bits appear. In this case, the accuracy of the extraction of clock synchronizing pulses on the receiving side is increased due to a slight decrease in the noise immunity indicators caused by the transition from two to three coding positions. However, such a ternary code does not represent a ternary number system in the sense in which it is considered in number theory and in the algebraic theory of noise-correcting coding [14-16,19].Because of this, it is not possible to use the well-developed mathematical apparatus of the algebraic theory of error-correcting coding, oriented towards the traditional representation of data and messages by N-bit binary code

[16] , when synthesizing ternary codes.

[0011] Consequently, the essential characteristics of the invention lie in the fact that the proposed non-traditional data representation by ternary code is also a ternary number system in the sense used in various mathematical transformations. Therefore, all the rules of redundant error-correcting coding known in the existing theory

[16] are valid for it. The only exception is that comparison operations, which are performed modulo 2, when using ternary codes, should be performed modulo 3.

[0012] This provision can also form the basis for the formation of check ternary symbols PS3, which are information analogs of bits additionally introduced into the code words of messages and complementing them to ensure compliance with the parity rule of binary symbols <1> 2.

[0013] The simplest rule for generating ternary check symbols is when using the "3 / 2" error-correcting coding scheme. In relation to the proposed ternary coding, this means that one ternary check symbol (TS3) is allocated per code structure. consisting of two ternary information symbols Here, the distinctive feature of ternary coding will be that there can be several rules for forming optimal check ternary symbols (SC3), while with binary coding there will be only one.

[0014] One of such rules for forming check symbols of ternary code shown in Fig.3.

[0015] Fig. 3 shows that if we take as an example the sequence of indices (i) of the generated stream of ternary symbols

[0016]

[0017] then after the introduction of ternary check symbols (PCS), the following encoded stream of them will be transmitted:

[0018]

[0019] where the check symbols of PS3 are defined based on comparison operations modulo 3 (5).

[0020] In this case, the check ternary symbols (ПС3) are presented in brackets (.) i ;), formed on the transmitting side with excessive noise-immune coding

[16] .

[0021] The distinctive feature of the invention is as follows. The existing theory of redundant error-correcting coding, which has already become classical, uses data represented by binary code

[16] , and the proposed redundant code, synthesized according to the same rules, is oriented towards ternary symbols.

[0022] Another rule for forming ternary check symbols (TCS) is to establish the following correspondence:

[0023]

[0024] It is also shown in the illustration in Fig. 3 (left). The most preferred form of defining ternary check symbols (TCS) is associated with the use of the mathematical comparison operation modulo 3 (mod 3):

[0025]

[0026] where all possible two-digit code structures are listed on the left composed of two ternary symbols, and on the right, the corresponding values ​​of their sums modulo 3 (mod 3). They are used as formed ternary check symbols (FCC).

[0027] This mathematical form of defining ternary check symbols (TCS) was also used in the transition to redundant error-correcting coding, which involves adding it to the first two information ternary symbols in the illustration shown in Fig. 3 (on the right).

[0028] When representing the digital ternary stream of symbols <0,1,2>3, given under number (3) (sheet 5 of the description), the mathematical formula for forming ternary check symbols (PCS) (5) was also used.

[0029] Each of the above correspondences used to define ternary check characters (TCCs) has its own advantages and disadvantages.

[0030] Thus, the essential characteristics of the proposed method also include the fact that the proposed encoding using ternary symbols <0,1,2>3 has several options for generating check digits (SC3). This new property of using different rules for generating ternary check digits (SC3) corresponds to modern trends in "physically implemented security" (physical-layer security) and "resource-efficient cryptography."

[0031] Also, the essential characteristics include an increase in the information load of transmitted symbols while simultaneously improving the noise immunity of the transmitted information. These two metrics for assessing the effectiveness of data transmission systems with traditional message generation and transmission are antagonistic: if one improves, then with the existing approach, it only comes at the expense of the other. However, using the proposed method, both metrics improve. This situation also applies to many other performance metrics for information and telecommunications systems (ITS).

[0032] Simulation results

[0033] Let's test how this all works when transmitted over error-prone communication channels. We'll keep the error detection and correction rules the same as in the existing theory of redundant error-correcting coding: the check symbol (CS3) is not distorted by interference.

[0034] Let us consider the case of using the formation of ternary check symbols (TCS) based on the mathematical comparison operation modulo 3 (mod 3).

[0035] Let us assume that during the transmission of the generated stream of ternary symbols (3) over the communication channel, the following errors occurred (Fig. 3, bottom line):

[0036]

[0037] where the previously given sequence of ternary symbols (3) formed on the transmitting side was taken as the basis for the transmitted data, while erroneously received ternary symbols are marked with an *.

[0038] Analysis, detection and correction of transmission errors

[0039] Assume that the rule for generating a ternary check symbol (TCS) based on comparison (5) is selected. The first (i=1) code construction of the CC 31 21*(2). In accordance with the comparison-based coding rule (5), the check ternary symbol PS 31- is "0", and when transmitted it is represented by the ternary symbol "2". Therefore, there is an error. The check ternary symbol of the PS 31 "2" could only be with the following CC 31 : 11, 02 and 20. If we proceed from the assumption that in the transferred CC 31 If only one symbol is corrupted (there is one error), then only two cases need to be considered: 11 and 20. Next, the error detection principle used in binary coding can be used. An example is the Wagner code, which is used, for example, in shortwave communication lines (HF communication), in which the error is found in the parallel radio channel in which the minimum signal-to-noise ratio is observed: s / n → min). When using the proposed ternary coding, in contrast to the binary code, there are two error correction options - these are ternary code constructions: "20" and "22". But the ternary code construction (KK 31) "22" is not suitable, since it has a verification character PS 31 ("1"), which contradicts the adopted PS 31 ("2"). This means corrected (CC 31 ) - "20". The error has been corrected. It's easy to see that all other transmission errors will also be detected and corrected.

[0040] After the first stage of error detection and correction, it becomes possible to move to the next hierarchical level of control over the integrity and reliability of the information received.

[0041] Let's consider the sequence of ternary symbols restored after error correction:

[0042]

[0043] According to the ternary encoding rules, there must be only an even number of 1 characters between two adjacent "2" characters. Is this requirement met?

[0044] 1. In the first of the allocated groups KK 31 : "200110002" - this rule is executed.

[0045] 2. In the second of the selected groups KK 31: "202" is also observed. The same is observed in the third "2112", fourth "220112", and fifth "2112" groups.

[0046] This is the first manifestation of a new capability for monitoring the integrity and reliability of received information: between two adjacent "2" symbols, there must be only an even number of "1" symbols. This is similar to the property that is realized in the classical theory of redundant error-correcting coding

[16] by using the additional binary symbol "Bit Parity Check." The ability to detect and correct errors is also a distinctive feature of the proposed ternary coding.

[0047] Thus, additional essential characteristics of the claimed invention consist in the fact that with the proposed ternary coding, the possibility of detecting an error is achieved without introducing redundancy into the generated ternary code structures.

[0048] This scientific and methodological basis underlies a new capability for confirming the integrity and authenticity of received information. Its scientific and practical significance lies in the fact that error detection and correction was achieved with virtually no increase in the volume of transmitted data and messages. The introduction of redundancy in the form of PS3 check symbols increased the number of redundant ternary symbols by 33%, but this increase is offset by the achieved data compression ratio, which, even without scrambling, cannot be less than (Fig. 4).

[0049] For reference, Fig. 4 shows the compression ratio evaluation results. when using a real bit stream transmitted over a HF communication channel. The ordinate axis shows the compression ratio values and on the abscissa is the number of samples of 1000 bits each. There are 180 such samples, and the compression ratio is was determined by values ​​from 1.3 to 1.38.

[0050] Moreover, the proposed ternary code also has an additional possibility of controlling the integrity and reliability of the received data and messages. But it is associated with the use of the second (inverse) version of its representation of the bit sequence by the proposed ternary code (1i), which is inverse to the previously considered (direct) version (1) (Fig. 5).

[0051]

[0052] In this case, the result of the direct recoding of the original 18-bit code construction <1010100>0111100101><<END]]2, as shown in Fig. 5, will be represented by the following sequence of 12 ternary symbols <2,2,1,0,1,0,0,0,1,1,2,0>3. In this case, the inverse version of the recoding will have the form: <2i,2i,0i,0i,1i,0i,0i,1i,0i,2i,1i,0i>3 (Fig. 5). Its pulse form of display in the form of PWM3 will be shifted relative to the direct sequence of ternary symbols <2,2,1,0,1,0,0,0,1,1,2,0>3 by the duration of one bit T0 (Fig. 5, Fig. 6). If ternary code constructions (their direct and inverse forms) are written one under the other (5), then among s consecutive symbols <0> 3 and <0 and>3 will match (s - 1) (all except one of them):

[0053]

[0054] This property appears due to correspondences, the application of which does not have any special differences:

[0055]

[0056] The following rule for monitoring the integrity and reliability of information transmission is related to the fact that between two adjacent ternary symbols <2> 3There can only be an even number of ternary symbols <1> 3. A similar rule is also true for inverse ternary coding: between adjacent symbols <2 and >3 there must also be only an even number of ternary symbols <1 and >3. This rule for monitoring the integrity and reliability of information is similar to the technology known for transmitting information using a binary code, using an additional check symbol (CS) called "Bit parity check"

[16] . However, there are also significant differences: "Bit parity check" is an additionally introduced (redundant) symbol. With the proposed ternary coding, the ability to monitor the integrity and reliability of information is ensured without introducing redundant ternary symbols.

[0057] The need to use the inverse version of the proposed ternary coding (1i) also arises when it is necessary to use the technology of quadratic phase modulation (QPSK) by K. Feer

[17] .

[0058] Figure 6 shows the pulse forms of the representation of a ternary code with symbols T0, T1=1.5T0 and T2=2T0, expanded to 5 PWM5 positions. The expansion is performed by combining the durations of the following consecutive ternary symbols: 1) T0, T1=1.5T0 with the formation of a new fourth position corresponding to the duration T3=2.5T0 and 2) T0, T2=2T0 with the formation of a fifth position corresponding to the duration T4=3T0. The illustrations shown in Figure 9 are devoted to this operation. Figure 9(A) shows the pulse form of the original bit sequence, and Figure 9(B) shows it for a ternary code with symbols T0, T1=1.5T0 and T2=2T0. To obtain an extension of the ternary code represented by PWM3 to 5 positions of PWM5, the following consecutive ternary symbols 1) T0, T1=1.5T0 and 2) T0, T2=2T0, respectively, are combined into a single pulse with new durations T3=2.5T0 and T4=3T0.

[0059] The supporting illustrations (Fig. 7 and Fig. 8) show the basic operations of the existing technology for forming quadrature phase modulation (QPSK), which is oriented toward traditional coding of transmitted data values ​​and messages using natural binary code [14,15]. The essence of the operations performed in this case is as follows.

[0060] The original bit stream, each with a duration of T0, is divided into two half-streams. The first half-stream is represented by odd bits, and the second by even bits (Fig. 7). Therefore, their beginnings are shifted relative to each other by a time equal to the bit duration T0. With parallelization, the duration of each half-stream can be increased by a factor of 2 and becomes equal to 2T0. The first half-stream represents the in-phase component I(t), and the second half represents the quadrature component Q(t) (Fig. 7) [14,15]. In this case, the in-phase component I(t) is modulated by a harmonic oscillation changing in time according to the cosine law: 1 / √2 Cos(ω0t + π / 4), and the quadrature component Q(t) - according to the sine law: 1 / √2 Sin(ω0t + π / 4), (Fig. 7, Fig. 8 (upper graph)). When they are summed, a harmonic oscillation with a constant amplitude is again obtained, but taking on phase values ​​with respect to the clock time values, indicated on the graph of Fig. 8 (above) by vertical lines 4, the values ​​of which (Fig. 8 (below)):

[0061]

[0062] Then they are assigned the following transmitted code structures (KK i ), consisting of 2 bits:

[0063]

[0064] A similar picture is obtained by summing the pulse shapes of the direct and inverse ternary codes (Fig. 6). Only in this case, each value of the phases (9) will be assigned a greater number of bits in the decrypted code structures of the ternary code. All this also turns out to be true when expanding the ternary code to 5-position and 9-position codes. This position is confirmed by the illustrations using the expansion of the ternary code to 5 positions, shown in Fig. 6. Thus, in (Fig. 6(G)) the diagram (Fig. 9(B)) is repeated. In this case, the diagrams (Fig. 9(A-B)) explain how an expanded version of PWM5 up to 5 positions is obtained from the direct ternary code. Diagrams (Fig. 9(G) + )) and (Fig. 9(G -)) explain the new capabilities of the method related to increasing the accuracy of the formation of clock synchronization signals on the receiving side. They are formed in such a way that clock synchronization pulses appear that follow twice as often as in the existing practice of bit synchronization. As a result, it becomes possible to create a marker that defines not only the boundaries of the bit pulses in pulse-code modulation (PCM2), which is used in the transmission of binary codes, but also the expected location of the middle of the pulses (PCM2). This is necessary to ensure "soft" decoding of the transmitted distorted pulse forms of binary symbols (PCM2) based on the determination of the amplitude of the pulses at the moments in time that should fall on their middle

[16] . As a result of such "soft" decoding of distorted bit streams, it is determined whether the binary symbol "1" or the binary symbol "0" was transmitted.The same principle is maintained when providing “soft” decoding of transmitted PWMi pulses.

[0065] Also in Fig. 10 are presented the previously used correspondences between the durations of the symbols T i , i=0,1,2, which, in addition to integer values ​​T0, can also take on new fractional values ​​in the form of the value 0.5T0 (Fig. 9(B,C)). This makes it possible to generate clock pulses following at a time interval of 0.5T0, and more accurately tracking their actual temporal position when receiving information under conditions of interference and distortion.

[0066] Also shown in Fig. 10 is that the previously used pattern observed in the formation of ternary code positions (M=3) is also observed with the proposed expansion to 5 positions (M=5). Only in this case does the data representation system become quinary. The previously considered ternary codes are supplemented with two new symbols S i (T i), i=3,4, which are obtained with the proposed expansion of the ternary code for 5-position PWM5, and their decoding in the form of binary code constructions <110,0001>2i <1101> 2, respectively. Reduction of redundancy of transmitted symbols S i (T i ) when expanding the ternary code to a 5-position code, the designation of the PWM3 and PWM5 boundaries maintains the same noise immunity. For this, phase-shift keying (PSK) is again used, with two states: 0° and 180°. Phase-shift keying (PSK) is characterized by a minimum bit error probability (P б) among other types of digital modulation. In this case, as in binary coding, it designates the boundaries of the primary modulation pulses. Consequently, the noise immunity of 5-position (PWM5) and 9-position (PWM9) codes will be the same as when receiving binary codes. However, the number of positions (M) of the noise-resistant code is increased from M2 = 2 to M5 = 5 and M9 = 9, respectively. Fig. 10 shows that the efficiency of the ternary code will also be significantly increased by combining successive ternary symbols into a single PWM1 duration. <0> 3rd <1> 3, and also <0> 3rd <2> 3. This combination helps to reduce the likelihood of ternary symbols appearing <0> 3, having a minimum duration at PWMi. As a result, the frequency is equalized (empirical probability P i ) the appearance of various symbols T i , i=0,1,2.

[0067] Figure 11 shows illustrations explaining the subsequent processes of expanding the durations of the 5-position code (PWM5) to a 9-position code (PWM9), which is its information analogue. Figure 11(A) shows the proposed table for establishing correspondence between additional positions (i), i=5,6,7,8, which complement the 5-position code to obtain a new 9-position (M=9) extension of the original ternary code (M=3). The second column of the table shown in Figure 11 (A) shows which successive symbols of the ternary code, conventionally designated as: <1> 3, <0> 3rd <2> 3, must be combined at the PWM level to obtain an optimal 9-position code so that all the initial conditions for the synthesis of ternary codes are again satisfied. These could be the following ternary code constructions (KK 31 ), the corresponding PWM durations and decoding at the bit level:

[0068] Fig. 11 (B) shows how the 3rd and 4th positions are initially formed from the sequence of initial ternary symbols when expanding PWM3 to PWM5 (the following consecutive symbol durations are combined in this case <0> 3rd <1> 3s with duration T3=2.5T0, and also <0> 3rd <2> 3 seconds with duration T4=3T0 are circled in ovals with numbers underneath. <3> 5 and <4> 5, respectively). The minimum value of the compression ratio achieved in this case As the results of the experimental studies show, it increases by 1.8 times without using the operation of preliminary scrambling of the original binary code. In the same way, in Fig. 11 (B) the positions i=5,6,7,8 are designated, which complement the 5-position code (M=5) to obtain a new 9-position code (M=9). The original ternary symbols are outlined in ovals above them. <0> 3, <1> 3rd <2> 3, the durations of which are combined to obtain a new 9-position (M=9). The minimum value of the compression coefficient k achieved in this way сж9, as the results of the experimental studies show, increases by 2.2 times without using the operation of preliminary scrambling of the original binary code.

[0069] It should also be noted that the efficiency of the M-position code, including that obtained by ternary coding and expansion of the ternary code to 5 and 9 positions, is significantly affected by the uneven probability of occurrence of its various positions. Fig. 12 shows a variant of a 640-bit sequence generated by the local switch (LS) of the on-board radio telemetry system (ORTS). It represents the type of generated bit stream that is the worst in terms of information transmission. In it, long series of the same bits "0" and "1" are most often encountered. Moreover, a significant asymmetry is observed in the frequency of occurrence of the binary symbols "0" and "1": the symbol "0" appeared 499 times, and the symbol "1" 141 times. This situation is not typical for other information transmission systems.The pronounced asymmetry of the "1" and "0" bit series is primarily determined by the fact that the spaces in the digital group signal (DGS) allocated for the transmission of (N=2n=10)-bit words from telemetry sensors installed, for example, on the first stage of a rocket and which ceased operation due to its separation, are also filled with binary "0" symbols. These symbols, therefore, serve only to indicate the end of operation of the corresponding telemetry sensor and carry no additional information. In this case, the structure of the telemetry frame does not change, and therefore the operating mode of the BRTS remains the same. Therefore, such deliberate distortion of the transmitted DGS is most widespread in existing telemetry systems.

[0070] By directly converting the original sequence of such a distorted bit stream into a ternary code, the minimum compression ratio is obtained In other cases of information transmission, for example, in HF communication, it is not less (Fig. 4).

[0071] A number of inventions are known [8-13], in which, in order to increase the efficiency of transmitting message values ​​X j , represented by a natural (N=2n=10)-bit binary code, are recoded into its error-correcting binary non-redundant analogue composed of residual images Where - optimally selected comparison modules. This not only ensures the detection and correction of transmission errors but also improves the efficiency, accuracy, and reliability of the information processing results.

[0072] In the proposed invention, the use of this model of randomization of bit streams before recoding the binary code into the proposed ternary code in the worst case, associated with the transmission of telemetry information (TMI) (Fig. 12) with additional distortion of the structure of the transmitted digital signal, made it possible to obtain a compression ratio of: Thus, the use of an additional CTS transformation associated with the redundant coding of data and messages X before recoding the binary code into the proposed ternary code j images-remnants And provides the possibility of further increasing the compression ratio by 1.28 times. Similar structural-algorithmic transformations of the first stage (SAP-1), aimed at representing data and messages in binary code, form the basis of inventions [8 - 13]. Their use leads to the emergence of a complex technical effect that helps resolve not one, but several contradictions related to the transmission of information. One of them is, for example, providing the ability to detect and correct errors in the transmission of data and messages without introducing additional redundancy of binary code symbols. From the point of view of the classical theory of error-correcting coding

[16] , this cannot be. And this is true when a binary number system represented by a natural positional binary code is used as a digital representation of data and messages. In similar inventions [8 - 13], when representing data and messages X j images-remnants They are guided by a more economical mixed number system, which is the system of residual classes (SRC). In its minimal representation, it is formed by two remainder images collected together in newly formed data C, redundancy-free coding But the very meanings of the images-residues create additional internal redundancy compared to the traditional data representation using positional (N=2n)-bit binary code: within certain limits, their values ​​duplicate each other, but this property is not a simple repetition. The newly introduced system of additional coding in the residual class system (RCS) is mixed. Positional binary code is used only to represent the values ​​of residual images. n-bit binary positional code. In this case, the residual images in new code words can be swapped in position: This replacement results in two invariant code words And Their decoding provides the ability to restore the original values ​​of data and messages. when using different values ​​of minimum code distances: - optimally selected comparison modules. Consequently, the essential characteristics of the proposed invention are also related to the additional effect that arises from the non-traditional representation of data and messages in the RNS:

[0073] It is known [20, 21] that comparison operations also exhibit a significant new effect, which is associated with the highest degree of randomization of bits during their implementation. Therefore, they are actively used in the development of methods and algorithms for protecting information from unauthorized access (UA)

[20] .

[0074] However, the new representation of converted message values While providing a high level of bit randomization, it does not reduce the length of runs of identical "1" and "0" bits. This is the purpose of an information technology called bitstream scrambling.

[0075] Therefore, in addition to increasing the effect of bit randomization, in order to increase the efficiency of the generated ternary code and its extensions, it is also necessary to use the scrambling operation of the stream formed by them.

[0076] The essence of the proposed technical solution for scrambling a bit stream formed by the results of a non-traditional representation of message values is as follows (Fig. 13):

[0077] - message data is subject to scrambling presented as a bit stream;

[0078] - when subsequently recoded into the proposed ternary code with symbols and its expansion to 5-position PWM5, every 4 bit of the digital stream (k=4), composed of messages, is subjected to forced inversion (Fig. 13).

[0079] Figure 13(A) shows the bit numbering in the generated digital stream in tabular form. The next row of the table (Figure 13(B)) represents the bits by which information is transmitted. Figure 13(B) shows that scrambling of the transmitted symbol stream is implemented by replacing every fourth bit (k=4) with its inverse copy.

[0080] The following illustrations (Fig. 13(G)) and (Fig. 13(D)) are devoted to the additional increase in the data compression coefficient that occurs when converting the binary code into the proposed ternary code.

[0081] In this case, in Fig. 13(A *) the numbering of the bits of the original binary stream of transmitted data is repeated, shown in Fig. 13(A). Fig. 13(G) shows the results of recoding the bit stream without scrambling it (Fig. 13(B)) into a ternary code with symbols T0, T1=1.5T0, T2=2T0. The following technical effect was obtained: a stream of binary symbols, consisting of 20 bits, was represented as a result of recoding by 15 ternary symbols T i , i=0,1,2 (Fig. 13(G)). The data of a similar structural-algorithmic transformation, but using the operation of scrambling the original bit stream, are presented in Fig. 13(D). The number of ternary symbols T i , i=0,1,2 (Fig. 13(D)) was reduced to 13. A pertinent question arises: is the value k=4 chosen for scrambling (Fig. 13(B)) optimal?

[0082] The results of selecting the optimal values ​​(k*) for which the binary symbol of the original binary sequence is changed to the opposite bit are shown in the form of tables in Fig. 14. The simulation data were obtained with a statistical sample size of 10,000 bits of the original bit stream. The samples contained 68% of the generated long series S ms(from 8 to 14 bits). In this case, the efficiency evaluation was initially carried out for the case of using a ternary code and its extension to a 5-position PWM5 (Fig. 14(A), table). To obtain the initial bit arrays of 10,000 bits each, real streams of generated digital information were used. The simulation of the use of ternary codes and their extensions to 5-position PWM5 was carried out based on the simulation of the operation of a HF radio channel taking into account Rayleigh fading under pulsed interference. The implementation of "Rayleigh fading" in the simulation was ensured by multiplying the signal amplitude by a random variable (RV) generated by a random number generator (RNG). The normalized root mean square deviation (a) of the signal amplitude during "Rayleigh fading" was determined to be 0.7. The studies were then repeated for the case where subsequent expansion of the original PWM3 symbols of the ternary code (M=3) to 9 PWM9 positions (M=9) was used. The results of the studies are presented in Fig.14(B) in the form of a table.

[0083] Thus, the tables shown in Fig. 14(A) and Fig. 14(B) differ in that they relate to:

[0084] 1) Fig. 14(A) to the ternary code (M=3) obtained as a result of the structural-algorithmic transformations of the second stage (SAP-2) and its expansion to 5-positions (M=5);

[0085] 2) Fig. 14(B) to the subsequent expansion of the ternary code (M=3) to 9-positions (M=9).

[0086] The experimental studies were conducted at various signal-to-noise ratios (SNR). In the first case, when the object of study was a ternary code and its extension to 5 PWM5 positions, it was 10 dB: SNR = 10 dB. In this case, the original value of the bit error probability was equal to: In the second case, when the proposed technology for expanding the ternary code to 9 PWM positions was considered, the signal-to-noise ratio (SNR) was determined to be SNR=8 dB. Then the initial bit error probability was equal to the value

[0087] The following values ​​of the parameter (k) of the proposed bit scrambling method were used in the simulation: k=3,4,5,6,7,8, which corresponded to the forced inversion of each 3,4,5,6,7 and 8 bits, respectively. The second column of the tables (Fig. 14(A), Fig. 14(E)) showed how much the lengths (S ms ) series of identical bits with values ​​of k successively taking the values ​​3,4,5,6,7,8. (Recall that 68% of the generated long series S were present in the original samples. ms (from 8 to 14 bits)).

[0088] So, for the case of a ternary code (M=3) and its extension to 5-positions (M=5) with k=3, the maximum length S ms series no longer exceeded 6 bits. At k=4 it was reduced to 5 bits. With each successive increase in the value of k: 5, 6, 7 and 8, the remaining maximum series length (S ms) of the same bits increased by one and became equal to: 6,7,8,9. The third column of the tables (Fig. 14(A), Fig. 14(B)) shows the results of calculating the bit error values obtained as a result of experimental studies. As noted earlier, in the absence of the scrambling operation, the original value when using the ternary code (M=3) and its expansion to 5-positions (M=5) it was equal to: When using the scrambling operation, the empirical probability of bit error P бэ1 took the following values ​​from 0.021 at k=3 to 0.032 at k=8. Moreover, at k=4 it is equal to the minimum value: Thus, it has been established that the value k*=4, chosen for the illustrations shown in Fig. 13, is optimal. Considering that the original value of the bit error which was obtained before using the proposed scrambling operation was equal to: received the following technical effect:

[0089] The fourth column of the tables (Fig. 14(A), Fig. 14(B)) determines the value of the uniformity of the probability of occurrence of different (i) positions of the ternary code when it is expanded to 5-positions (M=5) (Fig. 14(A)) and to 9-positions (M=9) (Fig. 14(B)).

[0090] The uniformity index (R) of the appearance of various symbols (i) of the code was calculated using the formula:

[0091]

[0092] where - the frequencies of occurrence of the i-th symbol of the ternary code (i=0,1,2) and its extensions to 5 (i=0,1,2,3,4), as well as to the 9-position code (i=0,1,2,3,4,5,6,7,8), which are considered as empirical probabilities (e.v.) of occurrence of the i-th symbol of the ternary code and its extensions, and CP is the designation of the average value.

[0093] As a result of the conducted research, the optimal value of k* was obtained for expanding the ternary PWM3 code (M=3) to 5-position PWM5 (M=5): k*=4. In this case, the maximum series of identical bits after scrambling is equal to: S ms =5 (Fig. 14(A)). The estimate of the bit error probability after decoding the ternary code and its extensions to the 5-position 1DIM5 was reduced to the value: P б * =0.018. The uniformity index of the appearance of symbols T0, T1, T2, T3 and T4 (equalization of probabilities (P0, P1, P2, P3 and P4) in the formed sequence of their following was also high, tending to the value R*=0.89. This representation turns out to be preferable due to the fact that the uniformity index can be considered as a probability value. Let us recall that the value of the bit error probability when using the existing information transmission technology was equal to: (8.2 bits per 100 received symbols of binary code). For comparison, it should be noted that the performance threshold of known noise-resistant codes is determined by the value (2 out of 100 bits). A case was chosen for the simulation where it exceeded this limit by 4.1 times. In this case, known error-correcting codes do not correct errors; they merely amplify them. This is the main drawback of existing redundant error-correcting codes. Research has shown that it can only be eliminated by implementing the following new information technologies. This is achieved in the first stage of structural-algorithmic transformations (SAT-1) through the use of irredundant additional coding of data and messages using residual images. In the second stage of structural-algorithmic transformations (SAT-2), associated with the use of the developed compressed error-correcting coding, the proposed ternary codes and their extensions to 5- and 9-position PWM values ​​are proposed.It should also be noted that the decrease in the probability of bit error in the first experiment associated with the expansion of the ternary code to 5 positions (M=5), initially taking the value. (8.2 out of 100 bits) in p1≈ 4.5 times the apparent value (1.8 out of 100 bits) satisfies the performance condition of existing redundant error-correcting codes Therefore, they can also be used to further reduce the probability of bit error. but already at an additional stage of decoding the transmitted messages.

[0094] The table shown in Fig. 14(B) presents the results of the search for the optimal value of k and the evaluation of the efficiency of using the next extension of the ternary code to 9-position PWM9. From the presented data it follows that the optimal choice for the scrambling operation is k = 5. This means that every fifth bit of the binary code sequence formed by replacing the original representation of messages X must be subject to forced inversion. j , represented by (N=2n) - bit binary code, the results of irredundant complement coding C j using residual images [8-13]. The optimality of choosing the parameter k=5, which is one unit greater than the previously found value (k*): k*=4 for expanding the ternary code to a 5-position code, is confirmed by the following data given in the second, third and fourth columns of the table shown in Fig. 14(B). Thus, the maximum length of series (S ms ) identical bits equal to: S ms =6, is achieved with k values ​​equal to: k1=5 and k2=6. However, the bit error probability (with its initial value P би2 =0.115) becomes minimal with the new value of the scrambling parameter k: k1 * =5. So, when k2=6, it already increases to the value The gain in this key performance indicator of information and telecommunication systems (ITCS) is determined by the value In this case, the uniformity index R i the occurrence of the i-th symbols of the code compared to the expansion of the ternary code to a 5-position code (PWM5) decreased slightly, from R5=0.89 to the value R9=0.87 at PWM9.

[0095] The data presented in the table placed in Fig. 14(B) allow us to more clearly imagine how the R indicator has changed i when using the expansion of the ternary code to its 9-position information analogue. The first line of the table (Fig. 14(B)) presents the indices (i) of the 9-position PWM9: i=0,1,2,3,4,5,6,7,8, and below it, in the form of the second line, the empirical probabilities are given occurrence of the i -th code symbols without using the scrambling operation. The initial significant unevenness of the probabilities is noteworthy. related to the symbol number and to similar indicators the appearance of other symbols of PWM9: i=1,2,3,4,5,6,7,8. They take values ​​from 0.06 to 0.09. At the same time, when using the scrambling operation with the optimal value of the parameter (k*): k*=5 (the third row of the table shown in Fig. 14(B)), the empirical probabilities the appearance of the i-th symbols of the expansion of the ternary code to 9 positions (M=9) are aligned and become almost ideal, represented by the values from 0.1 to 0.12.

[0096] From the data presented, the following main conclusion can be drawn: the proposed options for implementing scrambling become especially important when using the proposed ternary code and its extensions to 5 and 9 positions, since their use allows for a reduction in the probability of a bit error from 4.5 to 4.1 times. Also, almost ideal probabilities are achieved the occurrence of the i -th symbols, resulting in maximum entropy and maximum noise immunity. In this case, the proposed consideration of the ternary code and its extensions, as oriented toward duplicate types of modulation S, acquires particular scientific and practical significance. i (T i). Thus, in a number of cases, the use of AIMi may be preferable. For example, when there is a need to represent ternary code symbols on the plane (IQ) (Fig. 3). This method of using ternary coding becomes especially relevant when the use of PWM requires certain adjustments to the existing hardware implementation of information transmission. In this case, the designation (I) refers to the in-phase component, and (Q) to the quadrature component of the transmitted signal.

[0097] At the same time, in contrast to the existing theory and practice of using quadrature modulation, the S symbols i acquire the same extended properties that characterize the representation T i in the form of PWMi. They are associated, for example, with the detection of errors at the syntactic level when representing symbols S iternary code in the plane (IQ) (Fig. 3), which did not exist before. A new possibility of monitoring the integrity and reliability of received information based on S symbols i ternary code represented on the plane (IQ) is related to the fact that between adjacent S2 symbols there can only be an even number of S1 symbols. This property applies to the representations of S symbols i on the plane (IQ) appeared due to the placement in one-to-one correspondence of duplicate ternary symbols S i (T i ), i=0,1,2. If this method of monitoring the integrity and reliability of the received information is carried out when representing the transmitted information with T symbols i , i=0,1,2, then it turns out to be operational at the level of ternary symbols S i (T i), i=0,1,2, represented on the plane (IQ). This is a new result, which was not present in the existing similar practice of representing signals on the plane (IQ). The conclusions that were associated with the use of scrambling of bit streams, the determination of the optimal parameter of the scrambling operation (k*) and the expansion of the ternary code to 5 and 9 positions also turn out to be valid. However, the gain from expanding the ternary code to 5 and 9 positions will not be as significant as with PWMi, which is associated with the need to use AIMi modulation in this case. Then the number of positions (M) when modulating a signal with a ternary code will increase: M=2 when using modulation of the transmitted signal based on phase manipulation and M=3, when AIM3 is converted into the corresponding 3 frequency values

[0098] Existing methods of quadrature modulation (Fig. 7, Fig. 8) suggest, as is known [14,15], the use of a four-position code (M=4) with phase values ​​(9) instead of a natural binary code (M=2):

[0099]

[0100] which define the corresponding transmitted code structures consisting of 2 bits (10):

[0101]

[0102] With the proposed ternary encoding, one symbol replaces the transmission of 2.5 bits, and for the transmission of T symbols i , represented as PWM3, only two phase values ​​are required, for example, 0° and 180°. In this case, even the data representation using duplicate ternary symbols i=0.1.2, also has significant advantages, since the phase distance between the different transmitted symbols was 90°(10), and with the new technical solution it increases to 120° (Fig. 3). In addition, a minimum compression ratio is also ensured (Fig. 4).

[0103] Also when using ternary code symbols T i , i=0,1,2 and its extensions to 5 and 9-position PWM i, the necessary simplest conditions for the implementation of quadrature modulation methods, which differ the least from known implementations (Fig. 7, Fig. 8) [14, 15], appear when using as an in-phase component (I) a pulse shape with the values ​​"-1" and "+1" of the direct ternary code (Fig. 5) and its extensions, for example, up to 5-position PWM5, which is shown in Fig. 6(G). Then, as a quadrature component (Q) a similar pulse shape of PWM5 with the values ​​"-1" and "+1" of the inverse ternary code and its corresponding extension (Fig. 6(D)) acts. As a result of summation of the pulse shapes of PWM5 of the in-phase (I) and quadrature (Q) components, four positions (M=4) are formed, to which the following values ​​of the carrier frequency phases correspond:

[0104]

[0105] Then the transmitted signal waveform shown in Fig. 8 (top) will be no different from its counterpart, which is based on natural binary data representation. Everything will be the same as when using existing quadrature modulation methods that use binary data and message representation as a basis.

[0106] The only difference will be that when receiving a signal based on four phase values ​​(12), not the binary coding pulse forms considered as in-phase (I) and quadrature (Q) components will be reconstructed, but the levels that are copies of their image, as shown in Fig. 6(E). As a result of the first decoding operation, as the inverse coding operation, two pulse forms of the ternary code expansion to 5 positions (M=5) will be reconstructed - direct and inverse. All this turns out to be true for the case of ternary code expansion to 9 positions (M=9).

[0107] The encoding and decoding operations of ternary codes and their extensions are inverse (oppositely symmetric). For the case of extension to 5 positions (M=5), the introduced additions to the original correspondence (1) are shown in Fig. 10.

[0108] The subsequent decoding operation will be associated with assigning to the i-positions of the restored PWM5 those new binary code constructions (i=3,4) that are determined by the correspondences presented in the fourth and fifth columns of the table shown in Fig.10.

[0109] A table similar to that shown in Fig. 10 is also shown in Fig. 11 (A). It also shows new binary code structures (i=5,6,7,8), which are defined by correspondences expanded to 9 PWM positions9. Fig. 11 (B) shows a sequence of ternary symbols S i (T i ), displayed by their indices 3=0,1,2. Ternary symbols <0> 3, <1> 3rd <0> 3, <2> 3, the durations of the corresponding PWMs of which are combined to transition to the 5-position code PWM5, are shown in Fig. 11(B) with the designation of additional (i=3,4) positions. Similarly, additional (i=5,6,7,8) positions of the next expansion of the ternary code to 9 positions (PWM9) are also designated. This significantly increases the data compression ratio k сж .

[0110] The procedure for the transition on the receiving side from the ternary code and its extensions to the original binary coding is presented as an illustration in Fig. 15. It is shown using the example of the ternary code and its extension to 5 positions (M=5): the matching last symbols of the previous and the corresponding first symbols of the binary code of the subsequent decodings, performed on the basis of the correspondence (1) and its complement, given in the tables in Fig. 10 and Fig. 11 (A), are combined and replaced by one bit.

[0111] As a result, the original binary bit sequence is restored. The procedure for decoding ternary codes (upper table, shown in Fig. 15) and expanding them to 5 positions (lower table) is fundamentally unchanged.

[0112] Similarly, the restored inverse pulse form of the expansion of the ternary code to its 9-position information analogue will be decoded.

[0113] A certain exception will appear only in those binary code constructions that are defined by correspondences (1i) (Fig. 1) for inverse ternary codes and their extensions. They are not only inverse with respect to correspondence (1) (Fig. 1), when the decoding bits of the ternary codes become opposite (correspondence (1i) (Fig. 1)), but also shifted relative to each other by the duration of one bit - T0 (Fig. 5). As a result, instead of one stream of recovered data (10), represented by the binary code, two of its versions are recovered, which are copies of the pulse sequences (Fig. 6(G) and Fig. 6(D)), respectively.

[0114] Also, they increase the noise immunity of the restoration of the original bit streams and provide higher cryptographic strength of the transmitted information [20,21].

[0115] The obtained results of modeling and experimental studies allow us to determine the following preferences when using extensions of ternary codes to 5 (PWM5) and 9 (PWM9) positions:

[0116] - expansion to 5 PWM5 positions with preliminary scrambling of the binary bit stream subjected to recoding into the proposed ternary code ensures a minimum bit error (P бэ * ) when restoring messages and, consequently, the highest indicators of noise immunity of information transmission;

[0117] - under similar conditions, expansion to 9 positions (PWM9) is slightly inferior in terms of noise immunity of message transmission to its information analogue - expansion to 5 positions (PWM5), but provides an additional increase in the compression ratio of transmitted data

[0118] Another feature of the expansion of the original ternary code (M=3) to a 5-position code (M=5), and then to a 9-position code (M=9) when introducing the check ternary symbols PS3 (3), is as follows.

[0119] The original ternary code (M=3) is expanded to a 5-position code (M=5) and then to a 9-position code (M=9) using ternary information symbols, for each pair of which a redundant check ternary symbol PS3 (3) is introduced. As a result, the noise immunity index is significantly increased due to the traditional approach of introducing additional check symbols (PS3). However, the fundamental difference from the existing practice of noise-immune coding, which manifests itself with the introduction of an additional 33% redundancy, is that it is introduced after approximately the same reduction during the transition from a binary code to the proposed ternary coding of the transmitted information. This possibility is taken into account in the developed structural diagram of the multi-stage ternary coding system and its expansion (Fig. 16 and Fig. 17), which implements the proposed method. In this case, the following adjustments are made to the procedure for decoding the received data.The encoding results for the ternary code extensions with M=9 and M=5 positions are converted back into the representations established for the ternary code M=3. The resulting stream of ternary symbols is then extracted, along with the following ternary check symbols (SCS). The SCS are determined. * , which are obtained by reconstructing the ternary code symbol stream. The PS3 check symbols generated on the transmitting side are compared with the PS3 data. * , which are obtained from ternary information symbols received against a background of interference. Their misalignment indicates the presence of errors. This makes it possible to detect and correct a single error.

[0120] Previously, the case (3, sheet 5 of the description) was considered, when the check symbols of the PS3 were determined on the basis of the operation of comparing the values ​​formed by the two preceding ternary symbols, modulo 3 (5).

[0121]

[0122] We will show the main features of error detection and correction when using the rule for forming ternary check symbols PS3 when using the second rule for their formation, determined by the correspondence (4).

[0123] In this case, the generated sequence of ternary symbols, taking into account the introduction of redundant PS3, will look like this:

[0124]

[0125] We will keep the distortion pattern of the sequence of ternary symbols, taking into account the introduction of redundant PS3 when using the second rule for their formation, the same as it was before (3 * , sheet 7 of the description):

[0126]

[0127] Under the same conditions, the following similarly distorted sequence of ternary information symbols will be received upon reception:

[0128]

[0129] Based on the first three ternary symbols 21*(0), where the first two are information symbols and the third is the check ternary symbol PS3, it can be concluded that an error has occurred. According to the accepted coding rules defined by the correspondence (4, Sheet 6 of the description), the code structure 21* must be matched with the check ternary symbol PS3 (1). However, on the transmitting side, PS3 was represented by the ternary symbol (0). This can only correspond to the information two-symbol code structure 20, which is correct. Thus, the single error is not only detected but also corrected.

[0130] The next three received symbols are represented by the following ternary code structure In accordance with the formation rule, the following information ternary code constructions (KK) can be associated with the check symbol PS3 (0) 3i ): <01> 3, <02> 3rd <20> 3. Considering that the detected error may be a single one, we come to the conclusion that the following information symbols were transmitted: <01> 3. The error has been fixed.

[0131] This analysis can be continued, but from the presented single case the following conclusion can be drawn: the ternary check symbol, unlike its binary counterpart, is capable of not only detecting the presence of an error, but also correcting it.

[0132] The developed structural diagram of the multi-stage ternary coding system and its extension consists of two subsystems related to the transmitting (Fig. 16) and receiving (Fig. 17) sides. It defines the main operations of the proposed method, the order of their use and the functions performed. On the transmitting side (Fig. 16) it contains: block 1 for generating a bit stream, the output of which is connected to the input of block 2 for generating a stream of ternary symbols the output of which is connected to the input of block 3 for generating check ternary symbols (PS3) and simultaneously to the first input of block 4 for generating a redundant ternary noise-immune code, to the second input of which the output of block 3 for generating check ternary symbols (PS3) is connected, the output of block 4 for generating a stream of redundant noise-immune ternary code is connected to the input of block 5 for expanding the redundant ternary code to 5 positions; the first output of which 125 is the first output of the transmitting subsystem, and the second output is connected to the input of block 6 for expanding the redundant ternary code to 9 positions, the output of which 129 is the second output of the transmitting subsystem.

[0133] The presence of two outputs 125 and 129 is associated with the following two possibilities of using the system:

[0134] 1) maximum increase in noise immunity of information transmission, which is ensured by expanding the ternary code to 5 positions (PWM5);

[0135] 2) Ensuring the highest data compression ratio when expanding the ternary code to 9 positions (PWM9).

[0136] On the receiving side, the subsystem (Fig. 17) comprises: a PWM9 pulse recovery unit 13, the input of which is the second input of the subsystem, and the output is connected to the second input of a PWM5 pulse recovery unit 14, the first input of which is the first input of the subsystem, and the output is connected to the input of a ternary code recovery unit 15, the output of which is connected to the first input of a ternary code error correction unit 16, the first output of which is connected to the input of an error detection and correction unit 17, the output of which is connected to the second input of an error correction unit 16 at the ternary code level, the second output of which is connected to a unit 18 for decoding corrected ternary codes, the output of which is connected to the input of a unit 19 for restoring the original bit stream, the output of which is connected to a unit 20 for registering the restored bit stream.

[0137] The description of the operation of the multi-stage ternary coding system and its extension explains the goals and technical results achieved by the operations that form the basis of the developed method. The first operation of the method is associated with the formation of a bit stream, which serves as the basis for subsequent multi-stage compressed error-correcting coding using ternary duplicate symbols. In the developed system (Fig. 16 and Fig. 17), it is implemented in block 1 for generating a bit stream. The stream of generated bits is a digital group signal (DGS) of the transmitted information, reflecting the adopted structure of the transmitted data and messages, which contains information and service bits, the reception of which ensures the restoration of the transmitted information in conditions of interference with its required quality. The general concept of quality is understood as indicators of integrity, availability, accuracy and reliability of the transmitted information, ensuring the required indicators of its protection from interference, unauthorized access (UA) and information technology influences (ITI). The next operation involves scrambling the binary symbols "1" and "0", in which each k bit of the generated stream is subjected to inversion. In this case, the optimal value of the scrambling parameter k is selected * If, in order to achieve the set goals and unconditionally fulfill the stated requirements, preference is given to increasing the noise immunity indicators based on the expansion of the ternary code to 5-position PWM1, i=0,1,2,3,4, then the optimal value of k * is chosen equal to: k*=4. In this case, the maximum length of the same series of bits can't be greater When is it necessary to ensure the highest lossless data compression ratio? then priority is given to expansion to a 9-position code and the optimal value of the scrambling parameter k* is set equal to k=5. Then the maximum length of the same series of bits can't be greater Then the generated bit stream, subjected to scrambling, is recoded into a sequence of ternary symbols This operation is implemented in block 2 for generating a ternary symbol stream. The initial ternary symbol stream generated in block 2 is fed to block 3 for generating check ternary symbols PS3 and to block 4 for generating a redundant ternary code. In this block, check ternary symbols PS3 are generated based on one of the selected methods (4) or (5), which are fed to the initial ternary symbol stream in block 4 for generating a redundant ternary code. Based on a specific rule, for example, 3 / 2 (two ternary information symbols - one check ternary symbol PS3). The redundant ternary code generated in block 4 is fed to block 5 for expanding the redundant ternary code to 5 positions. The entire sequence of generated ternary symbols is expanded therein, taking into account the inclusion of the check ternary symbols PS3. Another expansion of the redundant ternary code to 9 positions is also provided, which is implemented in block 6 for expanding the redundant ternary code to 9 positions. The corresponding outputs of blocks 5 (125) and blocks 6 (129) are the outputs of the subsystem used on the transmitting side. Due to this, it acquires adaptive properties, capable of changing its operating mode. Since the invention is devoted only to the encoding of transmitted data, the subsystem does not consider the subsequent information transmission path associated with the modulation of the transmitted signal.

[0138] The subsystem explaining the operation of the system implementing the proposed method at the receiving end is shown in the block diagram in Fig. 17. Its operation is as follows. The extended streams of the redundant ternary code 125 and 129, received under interference conditions, depending on the selected coding mode, are fed to the corresponding PWM9 pulse recovery unit 13 or the PWM5 pulse recovery unit 14. In them, based on the phase marks perceived as a change in the phase of the transmitted signals fed through input 129 to the PWM9 pulse recovery unit 13 by the opposite values ​​0° and 180°, the corresponding values ​​of the PWM9 pulse duration and their amplitudes are reproduced, which are obtained during demodulation of the frequency-modulated signals FM9. As a result of demodulation, 9 amplitude values ​​are obtained. Thus, the ternary symbols Si are restored. Similar operations are performed in block 14 for restoring PWM5 pulses, obtaining 5 amplitude values.In this case, the restored values ​​of the amplitudes AMMi, by means of which the values ​​of the ternary symbols S are displayed. i , where i=0,1,2,3,4 for the case of expansion of ternary codes by 5 positions and i=0,1,2,3,4,5,6,7,8 for the case of expansion of ternary codes by 9 positions, are used to duplicate the T symbols i , transmitted by signals with PWM.

[0139] The selection of one of the operating modes, when the input signal is fed to input 129 or to input 125, is carried out based on the preferences that are formed based on the need to best meet the basic requirements. If it is necessary to ensure the highest indicators of noise immunity of information transmission under interference conditions, then the transmitted signals are fed to input 125 and the initial recovery of the transmitted signals from PWM5 and their duplicate version from AIM5 is performed. When it is necessary to achieve higher indicators of compression of transmitted data and possible transmission rates with limited bandwidth of communication channels, the operation begins with the reception and recovery of PWM9 pulses and their duplicate version from AIM9 in block 13. In this case, an operation inverse to the expansion operations is implemented, which is completed in block 15 for restoring ternary symbols. The stream of ternary symbols being restored in this case is redundant, since it contains, in addition to information ternary symbols ternary check symbols PS3. In block 16 for correcting ternary codes, based on the determination of matches between ternary symbols PS3 that were not subject to distortion and their analogs, reconstructed on the receiving side taking into account errors caused by interference, the integrity and reliability of the transmitted information is monitored. In this case, the criterion for the presence of errors is the absence of a match between the transmitted PS3 and their analogs (corresponding to PS3 * ), obtained as a result of their formation during reception in the error detection block 17. If the data received in block 17 do not match, single errors are corrected, which is implemented in the ternary code error correction block 16. In the next block 18 for decoding the corrected ternary codes, their corrected values ​​are converted into a stream of binary bits, restored with increased reliability indicators of the received information. The illustration shown in the lower part of Fig. 17, in relation to the illustration shown in Fig. 15, demonstrates another algorithm for converting ternary symbols into binary code. It is shown using the example of duplicate ternary symbols S i , i=0,1,2 and is the inverse of the coding algorithm presented as an illustration in Fig. 1. In this case, two levels R1 and R2 of transformation of the reconstructed results of ternary symbols are also established in binary code constructions (KK 2i ) based on the correspondence (1) (Fig. 1). In this case, the first level R1 is allocated for recording the results of decoding odd ternary symbols, and the second R2 is for even ternary symbols In this case, the beginning of recording the last bit of the previous decoding of the odd symbol The start of the ternary code must coincide in time with the start of the recording of the first bit of the subsequent decryption, related to the next even symbol of the ternary code. In this case, the overlapping matching bits at two levels R1 and R2 are replaced by one corresponding binary symbol, thus completing the reverse conversion of the ternary code into its binary information analogue.

[0140] Next, in block 19, the bit stream is descrambled. For this purpose, each k bit of the recovered bit stream is inverted, resulting in the original bit stream, free of errors caused by interference and, therefore, possessing increased reliability. This is recorded in block 20 for recording the recovered bit stream. This enables its multiple playback, performed for processing and replenishment by repeating the transmission of missing time segments of its reception based on a request over the reverse communication channel.

[0141] The essential characteristics of the proposed invention also consist in the fact that the change of frequencies F i , i = 0,1,2, into which the results of primary amplitude-pulse modulation (APM) are converted at the stage of secondary (frequency) modulation i , i=0,1,2), are performed at moments in time that coincide with their maximum and minimum values ​​(peaks and troughs) of the harmonic signal itself, which is the result of frequency modulation with three frequency values ​​F i , i=0.1.2. This significantly reduces the spectral width of the signal transmitted over limited-bandwidth communication channels. This also increases the spectral-energy potential of the transmitted signal, which contributes to improved noise immunity.

[0142] The analysis of analogs and the research conducted allowed us to formulate the invention formula.

[0143] 1. A method for transmitting information using compressed error-correcting ternary codes and extensions based on them, which consists of recoding the original bit stream into a compressed error-correcting ternary code with duplicate ternary symbols based on the following direct coding rule: where in broken brackets with index 2 (<>2) are presented two-digit and three-digit binary code constructions, put in correspondence with the corresponding symbols of the ternary code in this case, the symbols of the ternary code represent amplitude-pulse modulation with the corresponding three amplitude values ​​(AIM3), and the symbols of the ternary code T that duplicate them i , i=0,1,2 are converted into pulse-width modulation (PWM3) with the corresponding three (M=3) duration values: T0, T1=1.5T0 and T2=2T0, where T0 is the duration of individual bits of the original binary code, characterized in that the generated sequence of bits used to transmit information is subjected to the first stage of structural-algorithmic transformations (SAP-1), for which it is converted into a sequence of transmitted messages the values ​​of which represent (N=2n)-bit binary code, then into new code words of the same bit depth composed of two residual images representing n-bit binary half-words, the values ​​of which are obtained on the basis of the operation of arithmetic division of values to the selected optimal comparison modules m1 and m2, equal to Accordingly, the results of the obtained structural-algorithmic transformations (SAP-1) are presented in the form of a new sequence of bits, subjected to additional noise-resistant coding and randomization at the level of binary representation of the values ​​of the transmitted data and messages, then before recoding it into a substitution ternary code with duplicate ternary symbols subjected to a scrambling operation with parameter (k), the essence of which is the forced inversion of each k bit of the new sequence obtained as a result of additional coding of the transmitted data and messages in the system of residual classes using residual images in this case, the substitution ternary error-correcting code with symbols presented in the form of primary pulse-width modulation PWM3 with three permitted states: T0, T1=1.5T0 and T2=2T0, where T0 is the duration of individual bits of the original binary code, are considered as the main ternary symbols, and the symbols S i , i=0,1,2, represented by amplitude-pulse modulation with the corresponding three amplitude values ​​(AIM3), as duplicates, subjected to frequency modulation errors before transmission to the communication channel based on the following correspondences: - symbols of the ternary code, assigned values ​​to the following frequencies of the transmitted signal: - carrier frequency, and - the value of its deviation, the primary modulation of ternary symbols presented in the form of signals with pulse width modulation (PWM3) is converted at the second stage of modulation into phase manipulation FM2 with two opposite phase values ​​of 0° and 180° frequencies which are used as a phase mark indicating the beginning and end of signals with PWM3, as a result of which the phase marks simultaneously become the carrier of the transmitted information and ensure an increase in the accuracy of formation when receiving clock synchronization pulses that coincide in time not only with the beginning and end of the transmission time of each symbol of the transmitted information, but also with its intermediate states, when the amplitude of the pulse-width modulation (PWM) when transmitting codes with ternary symbols used for the simultaneous transmission of duplicate ternary symbols S i , i=0,1,2 using the amplitude-pulse modulation (A&Pm) method turns out to be the least distorted as a result of interference.

[0144] 2. The method according to item 1, which consists in that the generated bit stream of transmitted information is subjected to a scrambling operation S(k), where (k - 1) is the number of bits in the generated information stream that remain unchanged, after which the k-th bit is inverted, and such an optimal value of it k is selected for use * , at which the probability of bit error (P б ) becomes the smallest while maintaining the same conditions of information transmission: k * =4 - for the ternary code and for its expansion to 5 positions and k * =5 - when expanding the ternary code to 9 positions.

[0145] 3. The method according to item 1, which consists in reducing the redundancy of transmitted symbols when switching from binary code to ternary coding with duplicate symbols S i (T i ), i=0,1,2, are used to introduce check ternary symbols (CS3), which are obtained on the basis of the correspondence: or comparison operations modulo 3 (mod 3):

[0146]

[0147] in this case, the choice of the algorithm for generating check ternary symbols (CS3) is made based on the need to ensure the required noise immunity indicators and ensure information protection when using practical resource-saving cryptography.

[0148] 4. The method according to item 1, consisting in that the obtained three-base code with symbols T0, T1 and T2 is expanded to a five-position code (M - 5) on the basis of combining in the formed sequence of the ternary code represented by PWM3, the following consecutive symbols of the ternary code with durations T0 and T1 = 1.5T0, as well as T0 and T2 = 2T0 into longer pulses with total time intervals T3 = 2.5T0 and T4 = 3T0, forming the fourth (T3) and fifth (T4) positions of the pulse sequence PWM5, respectively, leaving the other PWM3 signals in the same order of succession, formed as a result of the performed combinations, wherein the sequences of signals with additional durations of 2.5T0 and 3T0 are assigned the following enlarged binary code combinations:

[0149] 5. The method according to item 1, consisting in that the obtained three-base code with symbols T0, T1 and T2 is expanded to a nine-position code (M=9) based on the combination in the formed sequence of the ternary code, represented by PWM3, of the following consecutive symbols of the ternary code, forming the following ternary code constructions <100> 3, <22> 3, <111> 3rd <121> 3 with PWM pulse durations i T5=3.5T0, T6=4T0, T7=4.5T0 and T8=5T0, forming the sixth (T5), seventh (T6), eighth (T7) and ninth (T8) positions of the PWM pulse sequence 9, respectively, leaving the other signals PWM3 (i=0,1,2) and PWM5 (i=3,4,5) in the same order of formation and following, formed as a result of the performed combinations, while the signal sequences with additional durations the following enlarged binary code combinations are put into correspondence:

[0150]

[0151] 6. The method according to item 1, consisting in that the change of frequencies F i , i=0,1,2, into which the results of the primary amplitude-pulse modulation (APM) are converted at the stage of secondary (frequency) modulation i , i=0,1,2) are performed at moments in time that coincide with their maximum and minimum values ​​(peaks and troughs) of the harmonic signal itself, which is the result of frequency modulation with three frequency values ​​F i , i=0,1,2.

[0152] Thus, the proposed invention differs from known analogues by its significant novelty and allows for a significant increase in the key performance indicators of various information and telecommunication systems (ITS).

[0153] Additional essential characteristics are also manifested in the following:

[0154] - proposed ternary code with duplicate T i symbols S i , placed in strict accordance with them, has significant advantages over existing methods of data representation and signal modulation, since the signals S i , considered as belonging to the plane (IQ), where I is the in-phase and Q is the quadrature components, also acquire the unique properties of T signals i , presented in the form of ШИMi;

[0155] - its use allows achieving a new complex technical effect related to increasing the efficiency of information transfer with minimal implementation costs in existing and developed information and communication systems.

[0156] List of references

[0157] 1. "Method for transmitting information and device for its implementation", patent RU 2480840 C1, published 04 / 25 / 2013, bulletin No. 21.

[0158] 2. “Method for transmitting information and device for its implementation”, RU patent No. 2581774.

[0159] 3. "Method for transmitting information using a substitution logical ternary error-correcting code", RU patent No. 2724794, published June 25, 2020, Bulletin No. 36.

[0160] 4. "Method for transmitting information using a substitution logical ternary error-correcting code", RU patent No. 2735419, published 02.11.2020, bulletin No. 39.

[0161] 5. "Method for transmitting information using a substitution logical ternary error-correcting code", RU patent No. 2755640, published September 17, 2021, Bulletin No. 20.

[0162] 6. "Method of compressed noise-immune data coding for information transmission and storage", RU patent No. 2789785 with priority dated 13.12.2021.

[0163] 7. "Method for transmitting information using an extended logical ternary error-correcting code in narrowband and wideband communication modes", RU patent No. 2834404, published 7.02.25, Bulletin No. 7.

[0164] 8. Method for transmitting information and system for its implementation”, RU patent No. 2586605.

[0165] 9. “Method for transmitting information and a system for implementing it”, RU patent No. 2586833.

[0166] 10. “Method for transmitting information and a system for implementing it”, RU patent No. 2609747.

[0167] 11. “Method for economical coding of information and system for its implementation”, RU patent No. 2649291.

[0168] 12. "Method for primary information processing with detection and correction of transmission errors", RU patent No. 2658795.

[0169] 13. "Method for transmitting information using computer codes", patent No. 2820092, published 05 / 28 / 2025, bulletin No. 20.

[0170] 14. Levin L.S. Digital information transmission systems / L.S. Levin., M.A. Plotkin. - Moscow: Radio and Communications, 1982. - 216 p., pp. 133-143.

[0171] 15. Bylinski P. Digital transmission systems. Translation from English / P. Bylinski, D. Ingram: edited by A.A. Vizel. - Moscow: Svyaz, 1980. - 360 p.; - 242 p.; - 243 p.; P.336-342.

[0172] 16. Peterson W., Weldon E. Error-Correcting Codes. M.: Mir, 1976. - 600 p.

[0173] 17. Feer K. Wireless Digital Communications: Modulation and Spread Spectrum Applications / K. Feer. - Moscow: Radio i svyaz, 2000. - 552 p.

[0174] 18. "Method for synthesizing wideband signals based on the use of composite code structures", RU patent No. 2818227, published 04 / 26 / 24, bulletin No. 16.

[0175] 19. Kukushkin S.S. Finite field theory and computer science. In 2 volumes. Volume 1. Methods and algorithms, classical and non-traditional, based on the use of the constructive remainder theorem. - M.: Publishing House of the Ministry of Defense of the Russian Federation, 2003.-284 p.

[0176] 20. Romanets Yu.V., Timofeev P.A., Shan'gin V.F. Information security in computer systems and networks / Ed. V.F. Shan'gin. -M.: Radio and communication, 1999. - 328 p.

[0177] 21. Muzykansky A.I., Furin V.V. Lectures on cryptography. - M.: MCNMO, 2003. - 2nd ed., stereotype.- 68 p.

Claims

1. A method for transmitting information using compressed noise-resistant ternary codes, which consists of recoding the original bit stream into a compressed noise-resistant ternary code with duplicate ternary symbols S i (T i ), i = 0,1,2 based on the following direct coding rule: S0(T0)↔<11,00>2; S1(T1)↔<10,001>2and S2(T2)↔ <101> 2, where two-digit and three-digit binary code structures are presented, put in correspondence with the corresponding symbols of the ternary code S i (T i ), i = 0,1,2, while the symbols of the ternary code S i , i=0,1,2 represent amplitude-pulse modulation with the corresponding three amplitude values ​​(AIM3), and the symbols of the ternary code T duplicating them i, i=0,1,2 are converted into pulse-width modulation (PWM3) with the corresponding three (M=3) duration values: T0, T1=1.5T0 and T2=2T0, where T0 is the duration of individual bits of the original binary code, characterized in that the generated sequence of bits used to transmit information is subjected to the first stage of structural-algorithmic transformations (SAP-1), for which it is converted into a sequence of transmitted messages X j , the values ​​of which represent (N=2n)-bit binary code, then into new code words of the same bit depth C j , composed of two residual images b 1j (mod m1) and b 2j (mod m2), which are n-bit binary half-words whose values ​​are obtained based on the operation of arithmetic division of the values ​​of X j for the selected optimal comparison modules m1 and m2, equal to 2 n -1 and 2 n+1, accordingly, the results of the obtained structural-algorithmic transformations (SAP-1) are presented in the form of a new sequence of bits, subjected to additional noise-resistant coding and randomization at the level of binary representation of the values ​​of the transmitted data and messages, then before recoding it into a substitution ternary code with duplicate ternary symbols S i (T i ), i = 0,1,2, are subjected to a scrambling operation with parameter (k), the essence of which lies in the forced inversion of each k bit of the new sequence obtained as a result of additional coding of the transmitted data and messages in the system of residual classes using residual images b 1j (mod m1) and b 2j (mod m2), while the substitution ternary error-correcting code with symbols T i, i = 0,1,2, presented in the form of primary pulse-width modulation PWM3 with its three permitted states: T0, T1 = 1.5T0 and T2 = 2T0, where T0 is the duration of individual bits of the original binary code, are considered as the main ternary symbols, and the symbols Si, i = 0,1,2, presented by amplitude-pulse modulation with the corresponding three amplitude values ​​(AIM3), as duplicates, subjected before transmission to the communication channel with frequency modulation errors based on the following correspondences: S2↔F2=ƒ0-Δƒ ∂ ; S1↔F1= ƒ0and S0↔F0=ƒ0+Δƒ ∂ , where F i = 0,1,2 - symbols of the ternary code, assigned to the following values ​​of the frequencies of the transmitted signal: F2= ƒ0-Δƒ ∂, F1=ƒ0and F0=ƒ0+Δƒ ∂ , where ƒ0 is the carrier frequency, and Δƒ ∂- the value of its deviation, the primary modulation of ternary symbols T0↔{ <00> 2, <11> 2}, T1↔{ <10> 2, <001> 2} andT2↔ <101> 2, presented in the form of signals with pulse-width modulation (PWM3), is converted at the second stage of modulation into phase manipulation FM2 with two opposite phase values ​​0° and 180° of frequencies F i , i=0,1,2, which are used as a phase mark indicating the beginning and end of signals with PWM3, as a result of which the phase marks simultaneously become the carrier of the transmitted information and provide an increase in the accuracy of formation when receiving clock synchronization pulses that coincide in time not only with the beginning and end of the transmission time of each symbol of the transmitted information, but also with its intermediate states, when the amplitude of pulse-width modulation (PWM) when transmitting codes with ternary symbols T i , i=0,1,2, used for simultaneous transmission of duplicate ternary symbols S i, i=0,1,2 using the amplitude-pulse modulation (A&Pm) method, turns out to be the least distorted as a result of interference.

2. The method according to paragraph 1, which consists in that the generated bit stream of transmitted information is subjected to a scrambling operation S(k), where (k-1) is the number of bits in the generated information stream that remain unchanged, after which the k-th bit is inverted, and for use, such an optimal value k* is selected for it, at which the probability of a bit error (P б ) becomes the smallest while maintaining the same conditions for transmitting information: k* = 4 - for the ternary code and for its expansion to 5 positions and k* = 5 - when expanding the ternary code to 9 positions.

3. The method according to paragraph 1, which consists in reducing the redundancy of transmitted symbols when switching from binary code to ternary coding with duplicate symbols S i (T i), i = 0,1,2, are used to introduce check ternary symbols (CS3), which are obtained on the basis of the correspondence: <01,02,20,10,12,21,00,11,22>3↔ <0,0,0,1,1,1,2,2,2>3= CS3 or the comparison operation modulo 3 (mod 3): <00,12,21,01,10,22,02,20,11>3≡ <0,0,0,1,1,1,2,2,2>3(mod 3) = PS3, In this case, the choice of the algorithm for generating check ternary symbols (CTS) is made based on the need to ensure the required noise immunity indicators and ensure information protection when using practical resource-saving cryptography.

4. The method according to paragraph 1, consisting in that the obtained three-base code with symbols T0, T1 and T2 is expanded to a five-position code (M=5) based on the combination in the formed sequence of the ternary code represented by PWM3 of the following consecutive symbols of the ternary code with durations T0 and T1=1.5T0, as well as T0 and T2=2T0 into longer pulses with total time intervals T3=2.5T0 and T4=3T0, forming the fourth (T3) and fifth (T4) positions of the pulse sequence PWM5, respectively, leaving the other signals of PWM3 in the same order of succession, formed as a result of the performed combinations, while the sequences of signals with additional durations of 2.5T0 and 3T0 are assigned the following enlarged binary code combinations: T3↔{ <110> 2,<0001 >2} and T2↔ <1101> 2.

5. The method according to paragraph 1, which consists in that the obtained three-base code with symbols T0, T1 and T2 is expanded to a nine-position code (M = 9) based on the combination in the formed sequence of the ternary code, represented by PWM3, of the following consecutive symbols of the ternary code, forming the following ternary code structures (KK 3i ): <100> 3, <22> 3, <111> 3rd <121> 3 with PWM pulse durations: T5=3.5 T0, T6=4T о , T7= 4.5T0 and T8=5T0, forming the sixth (T5), seventh (T6), eighth (T7) and ninth (T8) positions of the pulse sequence PWM9, respectively, leaving the other signals PWM3 (i = 0,1,2) and PWM5 (i = 3,4,5) in the same order of formation and sequence, formed as a result of the performed combinations, while the sequences of signals with additional durations T5= 3.5T0, T6= 4T0, T7= 4.5T0 and T8= 5T0 are associated with the following enlarged binary code combinations: T5↔<1000.00111>2, T6↔ <10101> 2, T7↔<10010.001001>2and T8↔ <001010> 2.

6. The method according to paragraph 1, which consists in changing the frequencies F i , i = 0,1,2, into which the results of the primary amplitude-pulse modulation (APM) are converted at the stage of secondary (frequency) modulation i , i = 0,1,2) are performed at moments in time that coincide with their maximum and minimum values ​​(peaks and troughs) of the harmonic signal itself, which is the result of frequency modulation with three frequency values ​​F i , i = 0,1,2.

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