This paper considers an integrated method of information protection against channel interference, imitation and familiarization based on ensembles of domestic stochastic codes. In comparison with the use of a single protection algorithm and a single introduction of redundancy, the proposed method reduces the number of code and hardware tools used when problems are to be solved separately. The possibilities of stochastic codes for the implementation of a given guaranteed probability of error-free decoding in channels with various error models, including short-wave ones, are presented.

The article “New Opportunities for Short-Wave Radio Communications in Solving Aerospace Defence Tasks by Combat Aviation” published in No. 2, 2017 of this journal, addressed new information capabilities of combat aircraft beyond the radio horizon based on adaptive short-wave radio communication technologies that realize radio communications of a quality comparable to line of sight.

This work continues the topic as relates to one of the key aspects of the radio communication quality, not covered in the previous article, namely, the possibility of providing integrated information protection against all possible interferences during transmission in channels with unpredictable characteristics, primarily short-wave. The topic of the article concerns the questions of information integrity and secrecy preservation in the conditions of jamming and electronic countermeasures by domestic innovative technology of integrated information protection against jamming, imitation, and unauthorized familiarization, realized by stochastic codes with singleentry redundancy.

The possibility of wide application of the given technology was the result of long-standing research in the field of data transmission and information protection theory by the following Russian scientists: Dr. Sci., Eng. L. M. Fink, Dr. Sci., Eng. V. I. Korzhik, Cand. Sci., Eng. S. A. Osmolovsky, Dr. Sci., Eng. G. A. Kabatyansky, Dr. Sci., Eng. I. Yu. Zhukov, Dr. Sci., Eng. M. A. Ivanov, and others [1–49]. S. A. Osmolovsky (1946–2018), a student of one of the communication theorists Dr. Sci., Eng. L. M. Fink, played a significant role in the application of universal properties of anti-jamming stochastic codes, creating a scientific basis and implementation of integrated information protection via stochastic transformations.

The author would like to pay tribute to the long-standing work of his companion and fellow student with this article.

The main factor of information distortion has always been and still remains constant presence of jamming in communication channels, particularly in radio channels. Anti-jamming is traditionally conducted with the use of error detecting and/or correcting anti-jamming codes, regularly implemented in data communication equipment (DCE). The prevailing DCE in the air communication networks is R-098 (Pereval) type, which has been in operation over the latest several decades.

Electronic countermeasures are able to fully or partially suppress information exchange and/or alter and impose false information. Protection against such interferences is provided by special imitation protection codes, implemented in individual devices. Neutralizing the suppression of concentrated noise exchange can be achieved by frequency hopping spread spectrum (FHSS), changing the direction and width of antennas radiation patterns, etc.

Confidentiality of information, i.e. protection against unauthorized familiarization, is usually provided by special encryption hardware with the use of cryptographic codes. In some cases such hardware resolves the tasks of confidentiality preservation and imitation protection simultaneously.

All mentioned protection functions are traditionally implemented independently of one another by similar code structures in different types of hardware, but all of them have one final goal of information integrity preservation. Meanwhile, a breach of confidentiality can also be viewed, to a certain extent, as a breach of its integrity and privacy.

All protection functions are provided by codes with a certain degree of quantitative redundancy, due to which arrays of the so called “prohibited” code combinations are formed. As a result of jamming, the “permitted” information carrier combinations can also transfer into the “prohibited” ones. The formation of secrecy preservation cryptographic codes is somewhat different: the main distinguishing factor of their design is statistically equally probable sequence of signals transmitted to a channel and independent on the statistics of individual letters appearance in the original encrypted sequence.

The influence of redundant coding, as a tool of credibility enhancement, on the fidelity of received discrete data can be compared with the course of a confidential conversation between two subscribers over a telephone channel with strong noise. In this process of “data exchange,” unintelligible words and even separate letters have to be repeated several times as requested by the receiving party. The more clarifications and repetitions are requested, i.e. the longer “the code structure – information block” is, the closer to the original the received phrase is, which marks higher credibility of information.

It can be assumed that if a subscriber is able to receive anything meaningful in noisy conditions, in the end it would be possible to achieve 100 % credibility of perception regardless of phrasal complexity even in the hardest noisy conditions.

A similar meaning of this phrase for a discrete channel is contained in one of C. Shannon’s main theorems on information stating that it is feasible to obtain the highest possible credibility of received information as long as its transmission rate in a channel is lower than its bandwidth (i.e. the worst state of audibility – “bandwidth” in the example above, at which there is still a possibility to receive words meaningfully while upon its decrease the communication becomes useless due to complete loss of understanding of what is being said).

Continuing the analogy with a telephone conversation, let us assume that someone wants to record the overheard conversation from an adjacent room with employment of technical means. Keeping such a risk in mind and intending to prevent unauthorized recording, the subscriber turns on running water, the “stochastic” (random) noise of which makes it impossible to preserve the meaning of the conversation when recording. The given comparison is similar to the influence of random signals on data secrecy as the notion of a q-ary symmetric channel is further investigated in the article.

The most important parameter for data exchange effectiveness estimation is the credibility of received information largely dependant on the probability of error undetectable by a specific protection code (рно). In its essence, the undetected error is a loss of information, caused by “permitted” combination transfer into another “permitted” combination yet equivalent to another symbol under the influence of jamming. For the purposes of reducing the probability of such transfer, it is preferable to select a code with high percentage of prohibited code combinations. It is possible only under the condition of increased number of redundant symbols and a resulting increase in the code combination length.

Only a small part of the existing set of error-detecting and correcting redundant codes are put to practice: Hamming codes, BCH codes, Reed – Solomon codes, convolution and recently developed turbo codes [26]. First of all, it is explained by the fact that distribution of errors in real communication channels is such that none of this set of codes ensures the provision of a predetermined or guaranteed probability of correct information reception within a specific communication channel (for the purposes of increasing the accuracy of a specific information process realization).

Their creation was intended for mathematical models of channels, which roughly describe the properties of actual communication channels [5][8].

When calculating the parameters of antijamming code, a model of some idealized channel called binary symmetric channel (BSC) is most widely used, where errors have equal distortion probabilities, 0 or 1.

The most prominent examples of non-stationary channels are short-wave channels. The instability of their characteristics, as well as the presence of constant grouping jamming has not allowed to create their mathematical model of acceptable accuracy until today.

The search for such a model, preferably universal, has started. This model would make it possible to create a code that would provide a certain guaranteed рно value in any communication channels at the set values of n and k (where n – length of a code combination with redundancy in bits and k – length of information bits in a code combination). At the same time it is preferred that the consumer would get almost no false information at small values of рно (approx. 10–9–10–8) and the decrease in speed of information transfer (n/k) shall be a signal for transition to different quality of the communication channel.

The method of creating such a code has been developed by the team of specialists from the Military Academy of Communications headed by D. Sc., Eng. L. M. Fink [1] in the 1970s.

The method of obtaining a given probability of undetected error by random coding with the use of stochastic transformations was mathematically substantiated in the article “Universal Stochastic Coding in Systems with Decisive Feedback”.

Random coding, suggested to be considered for jam-proof coding by C. Shannon, is understood as a random choice of code words from a set of possible combinations with the length equal to the code length.

Formula (1) of undetected error probability in any channel, derived within this work, is so simple that the necessity of engineering extensively long codes with high redundancy for obtaining small рно becomes evident

pно < 1/2n-k. (1)

Creation of a new universal code was inseparably connected to the practical realization of a new channel model, so called q-ary symmetric channel, without which the new code had no feasible use for they are in fact two sides of the same coin. The new model brought in the necessity of revisiting some traditional views on the rules of engineering, coding, and decoding of jam-proof codes.

Strictly speaking, the concept of a q-ary symmetric channel has already existed, but only as a mathematical abstraction. The contribution of S. A. Osmolovsky consists in transformation of the abstraction into a real model and creation of jam proof random redundant codes fit for the model; the codes are further named stochastic and possess a number of original features in the q-ary symmetric channel. The author came to the conclusion that none of the classical codes is feasible for use in the framework of the new model, because of the loss of their properties related to the detection, localization, and correction of errors. It is necessary to create a new code employing the presence of a transformed discrete channel. In the implemented diagram (Fig. 1), the binary consecutive transformation offered in [1] is applied as follows: the transformation of coding operations (K coder) and direct stochastic transformation employing a pseudorandom sequence on the transmitting side (R) and operations of reverse stochastic transformation and decoding on the receiving side. A set of two stochastic converters R and R-1, connected via a discrete communication channel DC, forms a q-ary symmetric channel.

The binary message is divided into L-bit binary sets of q-ary symbols. Total number of such symbols is q = 2L. The nL-bit code sequence is viewed as an n-bit code block, consisting of q-ary symbols, where k are information symbols and n–k are redundant ones.

In the coding block K, the information I is converted into a binary n,k-code and further formed into code blocks of q-ary symbols of n length, where k symbols are information ones. The information is further supplied to the block of direct stochastic transformation R, performing the function of randomization (Random) of data in a binary discrete channel (DC) at random tables with double-stochastic matrix transitions, a reverse stochastic transformation block performing the function R1, a decoding block, where error detection and correction as well as issue to consumer I1 occurs [2]. Randomization of binary sequences serves as a means of increasing accuracy of decoding outcomes description. Blocks R and R1carry out transformation of each q-ary symbol, thus the result of transformation has no statistical dependence on the results of other symbols transformation within a code sequence, which is inherent in cryptographic algorithms.

The property, which the transformed channel now possesses, consists in equal probability of all situations where decoding errors occur.

Thus, the discrete channel of the new model has been practically created where each error of L-bit q-ary symbol is equal to the error probability for the overall remaining (q – 1) symbols. At the same time, the probability of occurrence of each situation leading to a decoding error can be easily calculated, thus ensuring the pre-set probability of correct information reception [2]. The author has justified the length of the q-ary symbol L equal to 32 bits at which pно is guaranteed to be no worse than 10–9.

The modern tendency of increasing accuracy of information flows processing truly exists, thus demanding the requirements to the guaranteed probability of errors in the received data upon decoding to be revisited so that it is reduced from 10–6, predominantly common today, to 10–9.

Nowadays, the increased information credibility is necessary for the control systems during target coordinate data transmission to the precision-guided means of destruction, during processing and storage of large volumes of data (big data), commands on application of special weapons, UAV management, for information protection during transfer of open keys in the general network environment, friend-or-foe identification, decametric information transfer, etc.

Stochastic error-correcting codes engineering is based on the principle of correctly received sequence localization, employing, among other, some provisions of the modern theory of linear binary codes [7].

The rate of errors corrected by stochastic codes has the form: t = d – 2 (where d – code distance) [3]. For most anti-jamming codes t = d – 1/2.

The optimal parameters of (n,k,q)-codes ensuring the maximum transmission rate n/k are related to the channel quality (by the probability of q-ary symbol pq distortion), maximum rate of corrected errors d – 2 and code length n expressed by npq = d – 2.

Stochastic codes have a close relationship between the properties of interference immunity and information secrecy, which, if implemented appropriately, allows to provide secrecy and control over the integrity of transmitted information simultaneously.

The practical method of such implementation is proposed by D. Sc., Eng. M. A. Ivanov, a specialist in the field of information protection. Given that the procedures of creating the secrecyensuring means are strictly regulated in our country and new methods of ensuring secrecy need to be specified as per the established order, it is suggested to resolve these issues in accordance with GOST R 34.12-2015 “Information technology. Cryptographic information protection. Block ciphers,” providing the requirements to block cipher sizes easily adaptable to stochastic codes.

For the purposes of obtaining the necessary additional functions, it is suggested to implement multiround stochastic transformations as blocks R and R-1 (Fig. 1), and to use a multi-exit pseudorandom sequence generator (PRSG) having a two stage design and specified to implement additive stream encryption by GOST R 34.12-2015 to generate the parameters of the stochastic transformation.

The implementation of the proposed data transmission diagram allows to provide universal protection of transmitted data by a single algorithm with a single redundancy introduction. At the same time, the problem of anti jamming is solved by the elements of stochastic jamproof coding, while the secrecy and integrity of information are provided at the expense of other diagrams of direct and reverse stochastic transformation, cryptographic in nature, and by the requirements to PRSG, specified in GOST R 34.12-2015 [5].

The error-correcting capability of stochastic codes was tested within the framework of design and development work “Argo” performed by Air and Space Defence Corporation (where the author was acting as Chief Designer) on an ensemble of four stochastic codes of various length (8.2; 8.4; 16.7; 16.11), which provided the possibility of using adaptation to its states in the short-wave channel with increasing error-correcting capability of various lengths simultaneously with signal-code structures of employed SW modems.

In aviation control, often requiring only the unidirectional transmission mode with the required guaranteed probability, the application of stochastic error-correcting codes may be very promising. Error correction generally contributes to qualitative improvement of network technologies, primarily in terms of their productivity improvement, since the rejection of algorithmic methods of information protection by the method of interrogation upon error detection and the transition to code-based methods of correction significantly increases the productivity of expensive network resources. In addition, the elimination of time losses for re-interrogation increases the speed of data exchange in radio networks.

Besides, the possibility of implementing two additional vital functions of information protection (imitation resistance and secrecy) within one code structure is absolutely unique as per efficiency-to-cost criterion as of now.

The practical application of stochastic codes operation in a short-wave channel were presented in the development of special equipment Vesna-4M.

The application of stochastic transformations in the field of integrated information protection is unprecedented.

The creation of a new q-ary channel model and ensembles of random stochastic codes can be considered an outstanding achievement of national science, well recognized abroad [4][49]. Their presence allowed to obtain high guaranteed credibility values with exchange rates optimal for a particular channel state in a wide class of channels with unpredictable parameters, in particular within the short-wave range.

In the course of entire communication session with characteristics of such channels capable of changing multiple times, the use of code ensembles ensures stable exchange due to the selection of the code length optimal for each channel state from the ensemble.

The use of a q-ary symmetric channel within this range might become a better – and free – alternative to the special interleaving procedure widely applied in short-wave modems. This procedure is undertaken to convert group errors (error packets) into single errors, since error packets are highly likely to scatter into single errors.

The same code structures ensure the secrecy of information, if necessary.

Stochastic codes can be of use at minimal costs for universal information protection in promising control systems of Russian Aerospace Forces, civil aviation, including radio control channels of manned and particularly unmanned aircraft, where high level of protection from all interferences is required without the application of encryption equipment [6][50].

They are effective for information protection in any channels of data exchange, for computer memory storage, for protection against traffic capture and decryption in local computing networks [50], as well as for circulation of information on different types of carriers.