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Cybernetics and Systems Analysis, Vol. 50, No. 2, March, 2014

NEW MEANS OF CYBERNETICS, INFORMATICS, COMPUTER ENGINEERING, AND SYSTEMS ANALYSIS THEORY OF RELIABLE AND SECURE DATA TRANSMISSION IN SENSORY AND LOCAL AREA NETWORKS Y. M. Nykolaychuk,a† B. M. Shevchyuk,b A. R. Voronych,c† T. O. Zavediuk,c‡ and V. M. Gladyuka‡

UDC 004.416.2:004.67

Abstract. A systematic analysis of data transmission in sensor and local area networks is performed. Characteristics of a new class of signal correcting Galois field codes are described that provide error detection and correction at the physical level of computer networks without additionally generating and transmitting cyclic redundancy-check (CRC) codes. Methods are presented for processing harmonic signals by a digital processor with neurocomponents. Keywords: wireless sensor network, processor with neurocomponents, signal correcting code, number-theoretic basis, linear and spiral Galois code. INTRODUCTION Modern trends of development of electronic element bases and technologies of packet data transmission in wireless networks, adoption of new frequency ranges, and development of efficient protocols of functioning of decentralized networks with self-organization of data transmission provide conditions for the large-scale penetration of radio technologies into the area of construction of promising industrial, medical, and household systems and networks of personal, local-regional, and global communication. General-purpose packet-radio networks are most dynamically developed in the direction of construction of mesh networks (cellular networks) with complete decentralization of functions of control over packet transmission routes. Examples of such networks are wireless sensory and local-regional networks [1–5]. Wireless sensor networks (WSNs) allow one to efficiently solve many applied problems among which are remote gathering, processing, and transmission of monitored data from different remote monitored and control objects and also transmission of control commands using radiocommunication. The construction of a WSN is based on the use of information technologies in the following three different directions: sensory perception, communications, and computer data processing. Structurally and functionally, a WSN is a mesh network whose abonent systems are small-sized and consist of devices characterized by ultralow power consumption since they mostly operate in sleep mode. At the present time, the most widespread standard of construction of sensory networks in the field of WSNs is the standard Zigbee whose specifications are constantly updated [2–4]. ANALYSIS OF DATA PROTECTION METHODS IN WIRELESS NETWORKS A Zigbee network allows one to organize data transmission with the topology “each to all others;” and, in this case, data can be transmitted from one node of the network to another through different routes, which makes it possible to construct distributed networks with secure long-distance data delivery. In addition to the standard technologies Zigbee and a Ternopil National b V. M. Glushkov Institute c Ivano-Frankivsk National ‡

Economic University, Ternopil, Ukraine, †[email protected]; ‡[email protected]. of Cybernetics, National Academy of Sciences of Ukraine, Kyiv, Ukraine, [email protected]. Technical University of Oil And Gas, Ivano-Frankivsk, Ukraine, †[email protected]; [email protected]. Translated from Kibernetika i Sistemnyi Analiz, No. 2, pp. 161–174, March–April, 2014. Original article submitted April 29, 2013. 304

1060-0396/14/5002-0304

©

2014 Springer Science+Business Media New York

Wireless HART, partial solutions of companies such as Sensicast (www.sensicast.com), Millennial Net (www.millen-nial.net), Dust Networks (www.dustnetworks.com), Crossbow (www.xbow.com), and the Russian platform Meshlogic (www.meshlogic.ru) can also be used for the creation of WSNs. The wireless data transmission technology DASH7 (www.dash7.org) with ultralow power consumption and the wireless communication standard ISA SP100.11a for industrial automation are developed. A distinctive feature of the technology Meshlogic is the presence of its own stacks of network protocols that provide the following advantages: the full mesh topology of a network, all nodes operate on equal terms and are routers, self-organization and automatic search for routes, high scalability and reliability of data delivery, and the possibility of operation of all nodes from independent supply sources. A further development of Zigbee is the standard 6loWPAN of interaction of low-power WSNs made to the standard IEEE 802.15.4 according to the protocol IPv6. The standard 6loWPAN is oriented toward applications that require wireless connection to the Internet with a low data transmission rate for devices with bounded performance and power capability. Local-regional mesh networks are characterized by an enhanced fault tolerance. They connect their nodes even in the case of a failure of the majority of them. Modern WiFi systems that operate in two spectrum bands, namely, 2.4 GHz and 5 GHz and provide high-speed packet data transmission in constructing ad hoc and mesh networks with alternative routes of data delivery between nodes. Accordingly, transmission rates at primary levels of computer systems of a radio network compete with those of fiber-optical communication networks. In deploying a WSN, positive and negative properties of data protection mechanisms in wireless local networks (Wireless Local Area Network; WLAN) should be taken into account. Distinctive features of such mechanisms are presented in Table 1 [2–4]. In wireless networks with the Zigbee standard technology, mechanisms of access to transmission channels are used that support 128-bit AES encryption. For information protection in wireless local area networks (WLANs) at the MAC level, a data protection mechanism is provided that includes authentication of abonent stations and encryption of transmitted data according to WEP (Wired Equivalent Privacy), WPA (Wi-Fi Protected Access), and WPA2 algorithms. Their key features are presented in Table 1. In other wireless technologies such as Cellular Digital Packet Data (CDPD) transmission for mobile phones and pocket computers and also the third generation global system for mobile communications (3GSM) and time division multiple access (TDMA) for cellular telephones and pocket computers, their own (often closed) wireless communication and information protection protocols are specified. In digital broadcasting systems based on the standard Eureka-147 oriented toward terrestrial, cable, and satellite broadcasting, the protection of information is provided as a result of its multiplication by some pseudorandom sequence whose generation key is an 8 byte control word which is periodically changed. Then all data are encrypted with a view to smoothing signal energy to provide maximally smooth noise-like form of its spectrum. In WiMAX (IEEE 802.16) [2], the dataflow to be transmitted is scrambled, i.e., is subjected to randomization by multiplying by a pseudorandom sequence obtained in a 15-bit shift register. In generally accessible wireless local networks (even if data protection mechanisms are involved at access points), an essential threat is posed by a possibility of unauthorized connection to a rogue access point [4]. Such an access point is an authorized point that is included in the network and at which, as a rule, the encryption system is not activated. Any user located within the communication radius of the network can get access to the resources of a corporate network. Regular tests for the presence of rogue access points in a network are also urgent for Ethernet wire networks. To counteract unauthorized accesses, mutual authentication between remote abonents (devices) and an access point is used in prevalent local networks. In such networks, methods are used owing to which a base station can make sure of the identity of an abonent. This allows it to make certain that a user (abonent) is “legal” and that he has established connection with a legitimate access point. At the same time, access points must be authenticated in routers and gates, which eliminates the presence of rogue access points in a network. The use of encryption and authentication considerably increases computer network security. However, in wireless networks, a definite danger is represented by the following “man-in the middle attacks” [4]: an unauthorized user of a network (a hacker) introduces a device between a legitimate abonent (user) and a wireless network. In this case, during the realization of such an attack, the address resolution protocol (ARP) is used in all networks with TCP/IP. The essence of the problem connected with the ARP protocol is that it is a danger to protection systems of a network because of the possibility of spoofing, i.e., the imitation of a connection as follows: a hacker sends a fixed ARP answer containing the IP-address of a legitimate network device and the MAC address of the rogue device to an abonent (station) through a rogue network device and thereby misleads the station. As a result, all legitimate stations of the network update their ARP tables by importing false data into them. Thus, these stations will transmit packets to the rogue device rather than to a legitimate access point or a router. As a result of these actions, the hacker can control communication sessions of the user, he will obtain passwords and data, and he also can interact with corporate servers. 305

TABLE 1. Data Transmission Algorithms in WLANs WEP, standard IEEE 802.11 The RC4 stream cipher is applied, and CRC32 is used for calculating control sums. Keys are static, and their lengths equal 40 bits and 104 bits for WEP-40 and WEP-104, respectively.

WPA, standard IEEE 802.11i

WPA2, standard IEEE 802.11i-2004

The advanced encryption scheme RC4 (Advanced Encryption Standard (AES)) includes mandatory authentication using EAP (Extensible Authentication Protocol). MIC (Message Integrity Check) is used to prevent the interception of data packets whose content can be changed and then the modified packet can be transmitted again along the network. TKIP (Temporal Key Integrity Protocol) generates dynamic keys of length 128 bits that are automatically generated and broadcasted by the authentication server, a special hierarchy of keys, and a key control method.

CCMP (Counter Mode with Cipher Block Chaining Message Authentication Code Protocol) is the protocol of block encryption with a message-type identifier (MIC) and the mode of chaining blocks and the counter. In contrast to TKIP, keys and the integrity of messages are controlled by one component constructed on the basis of AES with the use of a 128-bit key.

Efficient defense against all sorts of attacks is information protection by abonents of a network using digital signatures, masking of the fact of transmission of data packets within radio channel noises by steganography methods [1, 6], a chaotic change in carrier frequencies (data communication monochannels), and directional antennas and also insecure optical channels. The main problem facing WSNs can be formulated as follows: information should be transmitted to maximal distances, with maximal transfer rates, and with detection and correction of errors with a given level of noise protection and defense against unauthorized accesses. These problems are solved at the physical and channel levels. At the physical level of modern networks, different signal processing methods are used [2–4]. A fundamental drawback of well-known signal processing methods is that they do not provide for detecting and correcting errors during receiving binary values of data being transmitted by standard modems. This is caused by the fact that each transmitted bit in well-known bit manipulation methods is statistically independent and does not possess definite Markov properties except for binary phase-shift keying (BPSK) [3] whose principle of operation is as follows: the previous bit is the etalon for the next bit but with mirror phase. The use of this method was caused by the problem of fluctuations of signal amplitudes in communication lines. However, BPSK has a major drawback, namely, a one-fold error implies the reception of the mirror code of an signal. An analysis of frames of basic protocols at the channel level of the ÎSI model (Fig. 1) [2] shows that they are characterized by the presence of service (redundant) information. The dependence of the service information volume on the total information volume is shown in Fig. 2. Here, the level of redundancy is rather high for small data volumes, which is very important for lower levels of computer networks, i.e., in creating WSNs. As is obvious from Fig. 1, the presented protocols do not provide for error detection and correction at the physical level. Here, the following denotations are used: PA (Preamble), SD (Start Delimiter), FC (Frame Control), DA (Destination Address), AC (Access Control), SA (Source Address), PDU (Packet Data Unit), FCS (Frame Check Sequence), CRC (Cyclic Redundancy Check), ED/FS (End Delimiter/Frame Status), FT (Frame Type), and F (Flag). Unsolved problems include the necessity of repeated transmissions, complicated algorithms for CRC encoding/decoding, vulnerability of the FCS codes, the decrease in the transmission rate at lower levels by 30–40% in practice, and impossibility of error correction at the physical level since a correction is possible only at the channel level after the reception of the whole data packet. There are many noise-immune correcting codes. Among them, the codes of Bose–Chaudhuri–Hocquenghem (BCH) and Reed–Solomon (RS) [7] should be singled out. 306

Ethernet

PA 56 bits SD 8 bits

Token Ring

AC 8 bits

PA 16 bits

FDDI

SD 8 bits

DA 48 bits

SA 48 bits

FT 16 bits

PDU 512–32 000 bits

FC DA SA PDU CRC 8 bits 48 bits 48 bits up to 18200 ´ 8 bits 32 bits

SD 8 bits

FC 8 bits

DA 48 bits

SA PDU 48 bits up to 4478 ´ 8 bits

ED 8 bits

FCS 32 bits

FS 8 bits ED/FS 16 bits

HDLC

F Address FC 8 bits 8 bits 8 or 16 bits

PPP

F Address FC Protocol 8 bits 8 bits 8 bits 8 or 16 bits

Information Variable length, 0 or more bits ´8 bits

FCS F 16 or 32 bits 8 bits

F 8 bits

Information Variable length, 0 or more bits ´8 bits

FCS 16 bits

Frame Relay

Information Variable length, 0 or more bits ´ 8 bits

FSC 32 bits

Address 8 or 16 bits

FCS F 16 or 32 bits 8 bits

F 8 bits

Fig. 1. Structure of frames of different protocols of the channel and physical levels. 32

V,%

Ethernet Token Ring

16

FDDI 8

HDLC

4

PPP Frame Relay

2 1

20 0

5

10

15

25

V , Kbits 30

0,5 0.25 0.13 0.06

Fig. 2. Dependence of the service information volume on the total information volume in different protocols. The analysis of frames of protocols that are used in computer networks at the channel level, estimation of the redundancy of service information, and also the authentication of distinctive features of extensively used correcting codes allows one to classify the following attributes of well-known methods: (1) at a transmitting station, information is protected against errors by computation of the CRC code that is added to data and, together with them, is transmitted along communication channels; (2) at a receiving station, an CRC code is computed from the transmitted data packet and is compared with the transmitted code; (3) after detection of a mismatch between these codes, an error correction algorithm is realized according to the correcting codes being used; (4) if error correction is impossible, then an inquiry is sent for the repeated transmission of the data packet. 307

A fundamental drawback of this error detection and correction method is the absence of error-checking procedures in transmitted data packets at the physical level of networks and error correction during data transmission. This drawback is caused by the fact that transmitted data are encoded only with a view to restricting the possibility of unauthorized access. The method does not provide for data encryption with capabilities of checking each data bit rather than the entire packet as a whole. In particular, the transmission of each bit with the help of noise-like signals leads to the increase in the number of signal bit-oriented codes and to the corresponding decrease in the transmission rate and performance characteristics of transceivers. The proposed solution of this problem with the zero redundancy of the correcting codes being used follows from the fundamentals of mathematics of number-theoretic bases that generate number systems. MATHEMATICAL FRAMEWORK OF ENCODING SYSTEMS IN DIFFERENT NUMBER-THEORETIC BASES Number-theoretic bases (NTBs) are fundamental theoretical grounds of number systems and data coding methods. A basis is generated by systems of orthogonal functions. The mathematical basis for number-theoretic bases consists of systems of orthogonal functions on some argument variation interval [8–10]. Modern computer and telecommunication systems extensively use NTBs based on piecewise-constant discrete functions that provide a simpler implementation of digital generators and also simplify algorithms of digital reception of signals. Representations of well-known bases are reflected in Table 2. In modern computer systems, well-known bases such as unitary, Haar, Craig, Rademacher, Krestenson, and Galois bases are extensively used. These bases generate number systems, which provides a considerable simplification of digital processing of basis functions on the basis of their representation in the form of logical code matrices [8–12]. Important characteristics of each basis are the size Vi of its code matrix M and the number of active elements (independent code values) N i (see Table 2), which determines the characteristics of redundancy of information representation based on the following analytical estimate: (1) Vi = n i × N i , where n i is the number length. An analysis shows that the unitary basis, Haar basis, and Craig basis that detect errors have a high level of redundancy in comparison with other bases whose use is inefficient and inexpedient. The Rademacher and Krestenson NTBs are non-redundant, however, for error protection, they require an additional service information. The code matrix of the Galois NTB is most densely packed and, owing to recurrent properties, provides the detection of all single errors and the correction of all errors in the case of absence of deletions and insertions of bits. The analysis of correcting properties of code matrices of NTBs presented in Table 2 shows that all the bases except for the Galois basis do not possess recurrent properties and, for data protection, require the formation of additional service information as, for example, the parity check method in the Rademacher NTB when the parity bit that makes it possible to detect a one-fold error is added to a seven-bit sequence. In the Krenstenson basis, error detection or correction is provided by an extension of the system of coprime moduli, which also increases data redundancy. A fundamental theoretical footing of code systems and Galois codes is the theory of Abelian groups and extended Galois fields [10]. According to a general classification, Galois field codes [9, 10, 12] pertain to the subclass of cyclic block codes that possess all basic properties of noise-immune codes. In block codes, a sequence of elementary messages is partitioned into blocks of symbols ( B1 , B 2 , B 3 , K , B n ) of fixed length with each of which a definite combination of symbols of a code word ( b1 , b2 , b3 , K , bn ) is associated. Advantages of the Galois basis can be most efficiently used in encoding integral values since integration increases each next value by 1. Each discrete value of the integral of a function x( t ) is fixed by one Galois bit rather than by an n-digit binary code in contrast to the Rademacher basis [9, 10].

308

TABLE 2. Code Matrices of Detection and Correction of Errors of the Bases Being Compared Orthogonal Functions of Bases

Characteristics of a Basis

1

2

Unitary Basis +1 0

Uni(0)

+1 0

Uni(1)

MUni

+1 0

Uni(2)

… … … … … … … … … … … … … … … … … ….

...

+1 0

0 0 0 K 0 1 0 0 K 0 = 1 1 0 K 0 , V = N 2, K K K K K 1 1 1 K 1

Uni (m , q , i ) = sign (sin (2 m p (q + i × 2 - n ))), the basis generates a unitary number system and detects N 2 - N errors

Uni(n)

Haar Basis +1 0 -1

H1(0)

+1 0 -1

H2(1)

………………………...

...

+1 0 -1

Hr(n)

0 1

K2 (0)

0

K2 (1)

0

……………………… ...

K2 (2) K2 (n)

0

K2 (n + 1)

0

……………………… ...

0

+1 0 -1 +1 0 -1

...

K2 (2n)

MÑrg

Rad (2)

……………………… ...

...

0 0 1

K K K K K 0 0 K 0 1 Crg (n , q ) = sign [ 2 n - 1 p , q ], the basis generates the Craig number system and detects ( N 2 - 4 N ) / 2 errors

Rad (0)

Rad (1)

0 0

K 0 0 K 0 0 K 0 0 K K K K K , V = N 2 / 2, = 1 1 K 1 0 1 1 K 1 1 0 1 0

Rademacher Basis

+1 0 -1 +1 0 -1

K2 (n + 2)

K K

Har (n , q , i ) = sign [sin(i 2 n p , q )], the basis generates the Haar number system and detects N 2 errors

...

0

0 0

M Har = 0 1 0 K 0 , V = N 2 , K K K K K 0 0 0 K 1

Craig Basis 0

0 0

M Rad

0 0 K 0 0 0 0 K 0 1 = 0 0 K 1 0 , V = N × log 2 N , K K K K K 1 1 K 1 1

Rad (n , q ) = sign [ 2 n p , q ], the basis generates the binary number system and binary codes and does not detect errors

Rad (n)

309

TABLE 2 continued 1

2

Krestenson Basis

P1 0 1

+1 0 -1

Kar(0)

+1 0 -1

Kar(1)

………………………...

...

P2 K Px 0 L 0 1 L 1

m

MGres = 2 2 L 2 , V = å log 2 (Pi ) , i =1 0 3 L 3 L L L L a1 a2 L ax n

+1 0 -1

Kar(n)

N i = res å (B i × bi ) mod P , i =1

the basis generates a system of residual classes and does not detect errors Galois Basis

+1 0 -1 +1 0 -1 +1 0 -1 +1 0 -1

G(0) G(1)

MG = | 0 0 K 0 1 1 1 |T , V = N , N i = f (C j - n - 1 , K , C j - 1 , C j ), Cj =

G(2)

………………………...

...

G(n -1)

n -1

å C j -1 × a (mod 2 ),

j=0

the Galois basis generates the Galois number system and Galois field codes and detects and corrects N errors

n To generate Galois field codes G æç ö÷ , the following primitive algebraic polynomials are used [10]: è 2ø

4 : x1 Å x 4 ; 5 : x 2 Å x 5 ; 6 : x1 Å x 6 ; 7 : x 3 Å x 7 ; 8 : x 2 Å x 3 Å x 4 Å x 8 ; 9 : x 4 Å x 9 ; 10 : x 3 Å x10 ; 11: x 2 Å x11 ; 12 : x1 Å x 4 Å x 6 Å x12 ; 13 : x1 Å x 3 Å x 4 Å x13 ; 14 : x1 Å x 6 Å x10 Å x14 ; 15 : x1 Å x15 ; 16 : x1 Å x 3 Å x12 Å x16 ; 17 : x 3 Å x17 ; 18 : x 7 Å x18 ; 19 : x1 Å x 2 Å x 5 Å x19 ; 20 : x 3 Å x 20 ; 21: x 2 Å x 21 ; 22 : x1 Å x 22 ; 23 : x 5 Å x 23 ; 24 : x1 Å x 3 Å x 4 Å x 24 ; 25 : x 3 Å x 25 ; 26 : x1 Å x 2 Å x 6 Å x 26 ; 27 : x1 Å x 2 Å x 5 Å x 27 ; 28 : x 3 Å x 28 , 29 : x 2 Å x 29 ; 30 : x1 Å x 4 Å x 6 Å x 30 ; 31: x 7 Å x 31 ; 32 : x 2 Å x 6 Å x 7 Å x 32 . ænö There also are primitive algebraic polynomials for higher order fields G ç ÷ , where ð is a prime number. è pø An important advantage of a Galois code sequence is simple generation of codes on the basis of a recurrence equation. The simplest keys of Galois field codes are described by the expression G i = G i -1 Å G i - m ; m £ n .

(2)

An important mathematical and practically expedient property of a Galois sequence is the presence of recurrent connections through levels [10] with high entropy characteristics.

310

Fig. 3. Signal correcting code packed in the form of a spiral. Áàéò Transmitted èñòî÷íèêà Byte

10001110

01100110

Å 011000110

Êîäîâàÿ

Galois Code ïîñëåäîâàSequence

Code Communication Êîä in â Channels êàíàëàõ ñâÿçè

11101000

Å 10001110 11101000

Êîä ïðèåìà Received Code

òåëüíîñòü Ãàëóà

Fig. 4. Data encoding based on a Galois code sequence. æ4ö Let the following Galois field code with a key Gi = Gi -1 Å Gi - 4 be specified G ç ÷ : è2ø æ4ö G ç ÷ = 1111 01011 0010 0011 1101 0110 0100 0111 1010 1100 1000 1111 0101K . è2ø This code can be packed into a spiral (Fig. 3), and, for each of the four generatrices, a recurrent sequence having corresponding recurrent properties of a code in the Galois basis is formed [9]. After unrolling the spiral that is encoded by a recurrent Galois field code, a recurrent sequence is formed through levels according to the expression (3) Gi , j = Gi - 4 , j Å Gi -16 , j , j = 1, 4, or, in the general case, Gi = Gi - 4 u Å Gi - 4 u+ 1 , u = 0, 1, 2, 3 ... .

(4)

In view of properties of a spiral, a signal recurrent code can be used for the detection and correction of error packets since errors are first found and corrected according to expression (2) and then according to expression (3) along the spiral generatrices [11].

DATA FORMATION AND PROCESSING PRINCIPLES PROVIDING ERROR CORRECTION BASED ON SIGNAL CORRECTING GALOIS FIELD CODES Galois field codes are widely used for information protection from unauthorized access [8–10]. Data encoding based on a Galois code sequence is shown in Fig. 4. In [5, 10, 12, 13], a method is proposed for non-redundant error protection of information dataflows on the basis of a new class of signal correcting codes in which recurrent properties of linear and spiral Galois field codes are used. In information transmission and reception based on the proposed codes, manipulated signals are formed on the basis of four signs (­, ¯, + , -) that are associated with elements of an information message according to Galois field codes [9, 10, 12]. The principle of formation of a signal correcting Galois field code is as follows: bits equal to 1 are numbered in a data packet ænö by a recurrent Galois field code G ç ÷ [12]. In this case, for 1s in the data packet, a Galois bit equal to 1 is transmitted by the è2ø rising edge (­ ) and a Galois bit equal to 0 is transmitted by the falling edge (¯ ) . Bits equal to zeros in the data packet are ænö also numbered by a recurrent Galois field code G ç ÷ . For zeros in the data packet, a Galois bit equal to 1 is transmitted by è2ø 311

G1i

a)

Gi0

G1i

b) c)

F

d) c') Gi0

b')

F

e)

Fig. 5. Structure of formation of code-manipulated signals on the basis of Galois field codes.

N Bits

1

2

3

4

5

6

7

8

9

10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

...

1

0

0* /1

...

ÑãÊ SgC G24 (1)

1

G24 (0)

D Ä

1

1 1

1

0

0

1 0* /1

1 1

0

1

0

0

1

0 1

1

1

0

1

0

1 1

1

0

1

0

0

1* /0

1

1

1

1

1* /0

1

1

0

0 1 0

1

1

...

0

...

Fig. 6. Scheme of realization of error detection and correction in code-manipulated signals. a positive potential +, and a Galois bit equal to 0 is transmitted by a negative potential -. In the capacity of these four signs of manipulation at the physical level, collections consisting of four phases, frequencies, M-sequences, Barker codes, noise-like signals, and their other combinations can be used. The structure of formation of code-manipulated signals on the basis of Galois field codes is presented in Fig. 5, where 1 Gi and Gi0 are generators of Galois bits for the symbols 1 and 0, respectively, and F is the former of output manipulated signals; here, (a) partition of the input information flow into 0 and 1; (b, b¢) encoding of flows of 1s and 0s by Galois field codes; (c, c¢) representation of Galois bits by the symbolic signs; (d) multiplexing of the symbolic signs 1 and 0; (e) high-entropy manipulation of the output signal at the physical level. Thus, an efficient symmetric encoding is provided in the form of Galois field codes by a sequence of 0s and 1s of a data block with unique determination of their number N 0 + N 1 = N D used for error detection and correction, i.e., the detection of deletions and insertions of individual bits or their packs after data transmission [12]. Figure 6 show the scheme of realization of error detection and correction in code-manipulated signals at the physical level, where N is the number of a bit position in an information message, D are information bits of received data with the detected and corrected errors, SgC is a signal code, G24 (1) and G24 ( 0) are, respectively, bits of the Galois G24 for the information bits 1 and 0 with error detection and correction, and 0* and 1* are erroneous bits. The following two cases of identification of Galois bits are possible: inverting the Galois sign of a bit equal to 1 or 0 and replacement of signal signs ­ and ¯ by + or - or vice versa. In all cases, an error is detected and corrected by a hardware-software Galois decoder. Modern systems of digital communication at the physical level mostly use amplitude-frequency-phase harmonic signals. In this case, special processors with neurocomponents are rather efficiently used as digital receivers. The analysis of scientific publications in the field of neural networks and neurocybernetics demonstrates important scientific results of modeling and theoretical formalization of functions of a neuron, a perceptron, and neural networks [13, 14]. 312

x 1 sin(t ) 0.5 sin 2 (t ) t 0

sin(2t ) sin(2t + p )

- 0.5 -1

2p

a

Z

t a

b

c

d

f

e

g

h

b Fig. 7. Plot of a model of the harmonic signal y( x ) = sin 2 ( x ) and its derivative (a) and impulse response of a neuron (b). To solve a wide class of problems in the field of intelligent data processing and signal identification, hybrid neuro-fuzzy systems and wavelet-neuro-fuzzy systems are increasingly used. They have improved approximating properties and, at the same time, do not lose the ability to function in real time. Among such systems are the architectures of the Wang–Mendel type, adaptive neuro-fuzzy Takagi–Sugeno–Kanga systems, wavelet-neuro-fuzzy networks, and adaptive wavelet-neuro-fuzzy systems with W-neurons [15]. The architecture of a wavelet neuron, which was used to solve the problem of on-line prediction of nonstationary signals, is rather close to that of a formal neuron with n inputs. After arriving a vector signal x( k ) ( k = 0, 1, 2, ¼ is the current discrete time) at the input of a wavelet neuron, a signal is formed at its output whose value can be determined from the expression n n hj (5) y( k ) = å f i ( x( k )) = å å w ji ( k ) jji ( x i ( k )) , i =1

i =1 j =1

where w ji ( k ) are synaptic weights and jji ( x i ( k )) are wavelet functions. In the general case, the response of a formal neuron to an analog input signal x( t ) can be rather adequately described by the following model of an extended operator of a PID controller [16]: Z ( t ) = a 0 x ( t ) + a1

d 2x dx + a 2 ò xdx + a 3 + K + a i ò x( t )x( t + t )dx + ... , dt dt 2

where a 0 , a1 , a 2 K are weight coefficients and

ò

(6)

x( t ) x ( t + t )dx is the autocorrelation function of the input signal.

A drawback of this description of such a model is the absence of correlation components in the equation; they are taken into account in the Kolmogorov formula for predicting the value of a stationary function [17], which is used to implement the Kolmogorov–Gabor predicting filter n

n

n

n

n

n

0

0

0

0

0

0

g[ x( t )] = r0 + å r0 x n + å å x n1 x n2 rn1n2 + å å å x n1 x n2 x n3 rn1n2n3 + ... ,

(8)

where g[ x( t )] is the predicted value of the function, x n1 , x n2 ,... are previous values of this function, and rni are influence coefficients (weights) of each term.

313

xi

x( t ) ADC

[ xi ] 2

F a ai

xi b xi-1

a i-1

p

h xi - n

Hi

å

ai- n

Fig. 8. Structure of a correlation neuroprocessor for identifying harmonic signals on the basis of a dynamic neuron model. Hi 6 4 2 i-n

0 -2 0

15

10

5

20

a

30

25

a1

- 0.9014

a5

0.5010

a9

0.6061

a13

0.2040

a2

0.1421

a6

0.4800

a10

0.8909

a14

- 0.4929

a3

0.4017

a7

- 0.1363

a11

- 0.8322

a15

0.7469

a4

0.9246

a8

0.2685

a12

0.8319

a16

0.0268

b Fig. 9. Signal impulse code obtained at the output of a correlation neuroprocessor (a) on the basis of weight coefficients (b). It has been established as a result of investigations that an impulse frequency-modulated signal is formed at the output of a neuron and this signal is realized on the basis of a threshold function. As is mentioned in [18], at the level of neural structures, a harmonic sinusoidal signal at the input of a neuron is transformed into a quadratic space at the level of excitatory and inhibitory inputs. Figure 7a shows the plot of a model of the harmonic signal y( x ) = sin 2 ( x ) and its derivative, and Figure 7b demonstrate the response of the neuron to this signal by identifying the points a - h according to the expressions x( t ) = 0 (for a and e), x( t ) = ( dx( t )) / dt (for b, d , f , and h), and x( t ) = max (for c and g) and the formation of the corresponding output impulse sequence. Figure 8 shows the structure of a correlation neuroprocessor based on the model of a dynamic neuron for harmonic signal ì 1, Z i ³ p, identification [19], where F is the former of pulses presented in Fig. 7b. The output signal is of the form H i = í î 0, Z i < p. n

The function of the neuron response to an input signal x i is described by the expression Z i = å a i × x i , where a i is a i =1

weight coefficient and ð is a threshold value. As a result of processing a signal impulse flow (see Fig. 7b) by the processor with the structure of the dynamic neuron (Fig. 8), the signal impulse code presented in Fig. 9 is obtained that corresponds to the correlation folding of Barker codes well-known and widely used in communication engineering. The performed investigations of the efficiency of application of linear and spiral signal correcting codes in the Galois basis made it possible to establish the possibility of correction of all one-fold errors in information flows due to linear signal correcting codes in the Galois basis and also error packets with simultaneous application of linear and spiral signal correcting codes in the basis. 314

CONCLUSIONS

Promising solutions of the problem of improving system characteristics of WSNs with allowance for the implementation of a maximal transmission range of information flows with error detection and correction and also protection against unauthorized access are considered. New methods are proposed for efficient message encoding and manipulation in the code system over the Galois NTB using a new class of signal correcting codes providing detection and correction of errors at the physical level of computer networks in online mode. The developed technology of coded manipulation of signals at the physical level of computer networks is compatible with well-known standard protocols. Its application together with the harmonic signal identification technology using correlation neuroprocessors considerably increases the information rate at lower levels under high-intensity noise conditions.

REFERENCES

1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18.

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B. N. Shevchuk, V. K. Zadiraka, L. O. Gnativ, and S. V. Frayer, Technology for Multifunctional Processing and Information Transmission in Monitoring Networks [in Russian], Naukova Dumka, Kyiv (2010). N. V. Shakhnovich, Modern Wireless Communications Technologies [in Russian], 2nd Edition, Tekhnosfera, Moscow (2006). B. Sklar, Digital Communications: Fundamentals and Applications, 2nd Edition, Prentice Hall, New Jersey (2001). J. Geier, Wireless Networks First-Step, Cisco Press, Indianapolis (2005). Ya. M. Nykolaychuk, A. R. Voronich, and V. M. Gladyuk, Wireless Sensor Network, Ukrainian Patent 73756, MPK (2012.01) H04W 4/00, Publ. 10.10.2012, Bul. No. 19. B. N. Shevchyuk, “Data processing, encryption, and transmission by means of abonent systems of informationallyefficient radio networks,” Computer Means, Networks, and Systems, No. 9, 130–139 (2010). W. Peterson and E. J. Weldon Jr., Error-Correcting Codes, 2nd Edition, MIT Press, Cambridge (Mass.) (1972). Ya. M. Nykolaychuk, Theory of Information Sources [in Russian], 2nd Edition, OOO “Terno-Graph,” Ternopil (2010). Ya. M. Nykolaychuk, Galois Field Codes: Theory and Application [in Russian], OOO “Terno-Graph,” Ternopil (2010). E. Artin, Galois Theory [Russian translation], MTsNMO, Moscow (2004). Ya. M. Nykolaychuk and A. R. Voronich, Multi-Channel Method of Information Transmission and Reception, Ukrainian Patent 63648, MPK (2011.01) H04J13/00, Publ. 10.10.2011, Bul. No. 19. Ya. M. Nykolaychuk and A. R. Voronych, “Entropic methods of signal processing with protection from errors in Galois base,” J. Qafqaz Univ. of Baku (Azerbaijan), No. 30, 69–77 (2010). Ya. M. Nykolaychuk and T. O. Zavedyuk, “Structure and functions of a recurrent bioneuron for pattern recognition in Hamming space,” Postup v Nauku, No. 6, 37–39 (2010). T. O. Zavedjuk, Ya. M. Nykolaychuk, and A. R. Voronich, “Self-reconstructed system of transmission of signals of a bioneuron fiber in the Krestenson basis,” Visn. Khmel’n. Nath. Un-tu, No. 4 (191), 137–142 (2012). Ye. Bodyanskiy, I. Pliss, and O. Vynokurova, “Hybrid wavelet-neuro-fuzzy system using adaptive W-neurons,” Wissenschaftliche Berichte, FH Zittau/Goerlitz, 106, Nos. 2454–2490, 301–308 (2010). A. A. Voronov (ed.), Automatic Control Theory [in Russian], Vyssh. Shk., Pt. I (1977). O. G. Ivakhnenko and V. G. Lapa, Prediction of Random Processes [in Ukrainian], Naukova Dumka, Kyiv (1969). T. O. Zavedyuk, “Specifics of recognition of signals are on the basis of correlation neuronlike processor,” in: Proc. Xth Intern. Conf. TCSET’2010 “Modern problems of radioelectronics, telecommunication, and computer engineering,” Slavske (2010). T. Zavedyuk and N. Shyrmovska, “Specialized data neuroprocessors and diagnostics quasisteady objects based on cluster models,” in: XIth Intern. Conf. “The Experience of Designing and Application of CAD Systems in Microelectronics (CADSM 2011),” Lviv Polytech. Nat. Univ., Lviv (2011). 315