Physical layer security and energy efficiency over different error correcting codes in wireless sensor networks

ABSTRACT


INTRODUCTION
The open nature of the wireless communication technologies makes the wireless medium subject to many threats. Due to the increase in the number of attacks against the wireless communication system, a growing interest has developed in securing the information over wireless transmission system [1]. In the TCP/IP model, security algorithms are applied in the upper layers. However, physical layer security (PLS) does not contain any type of security even though it contains features that could provide security from information theory point of view [2].
In PLS, the transmitter and receiver are assumed to be aware of the techniques used for transmission. PLS is achieved when the parties of the communication system aware of the information about the used techniques for transmission yet there is a variation in the quality between wiretap channel and the main channel [3][4][5][6][7]. In addition, it is assumed that the wiretapped channel (eavesdropper channel) is a degraded version of the main channel, this helps the legitimate receiver using the main channel to get back the transmitted data but the eavesdropper node is not able to get back the transmitted data and this is how PLS is achieved. There are several metrics for security performance. In this paper, the selected security performance metric is the security gap ( ) because it is practical to be implemented, depends on the bit error rate (BER) and the signal to noise ratio (SNR), and it is simple. Security gap is defined as the difference between the SNR of the intended receiver and the SNR of the eavesdropper [8,9].
Wireless sensor network (WSN) helps in analyzing and collecting the information. Security is the major challenge to deploy for the WSN. The main reason is the vulnerability of the WSN to several attacks such as wormhole attacks, Hello flood attacks, black hole attack, Sybil attack, attacks the data in transit, and denial of services [10]. Cryptography is an approach to avoid these attacks. However, the algorithms of cryptography are computationally expensive. Researchers proposed several strategies to calculate the quality of the transmitted data, such as bose-chaudhuri-hocquenghem (BCH), reed solomon (RS), and low-density parity check (LDPC). The challenging part is to identify the suitable strategy in terms of power efficiency for error correction [11,12]. This open research question makes this topic to be the interest of many researchers.
The threats that are facing the WSN leads to implement several works to prevent WSN from some of the attacks. Typically, the energy and computation abilities of WSN are not enough to manage the conventional security methods (sensor network method). To avoid the attacks with less computational energy and power, physical layer security for WSN is an excellent approach to be selected. In [13] demonstrate that the PLS techniques could be applied to WSN to ensure perfect secrecy. The authors of [14][15][16] claim that the ancryption techniques such as channel aware encryption, and stochastic encryption achive security and realibality. Yet, high computational energy and ability are required.
To the best of the authors' knowledge, the error correction codes benefits in WSN has not been adequately well investigated in terms of PLS. This paper studies the affects of various error correction codes on the security of WSN. In this paper, the metric is used unlike the previous literature works where the maximum equivocation is used as the metric for security. In this paper, a brief explanation on the security and the energy efficiency of the WSNs is presented as well since many previous works only focus on the energy efficiency or the security aspects. Nontheless, there are a few investigations suggesting that the various channel codes affect the energy consumption differently for WSNs [17,18]. The efficiencies of the code's energy are evaluated with an analytical radio model. The authors of [4] shows that the energy efficiency is changing with the variation of the codes based on the quality of the channel. In otherwords, there are small differences between the codes in terms of energy efficiency in a good quality channel. Since the processing power consumption for the coding technique is high [19], selecting the less complex coding technique is essential mainly with the WSN applications due to the processing and memory constraints [20].
This paper analyzes the PLS by investigating several error corrections codes such as RS t-error correction codes. Moreover, the focus is to study the affect of the t-error correction codes on the PLS. The BCH codes acchives high compared with LDPC codes. Thus, BCH is introduced with additional techniques such as scrambling [21]. Scrambling the data bits is employed as an additional strategy to improve the security by decreasing the gap between the eavesdropper node and legitimate receiver. By scrambling the data bits, the probability of bit error is maintained close to 0.5 with the increasing of SNR [22]. The organization of this paper is as follows. Section 2 presents the system model. Section 3 provides some introduction regarding the scrambled t-error correction codes, RS correcting codes, and BCH code. Section 4 discusses the results of the comparison between scrambled t-error correction codes and the (RS). Finally, section 5 concludes this paper.
The main contributions of this paper are summarized as follow:  The analysis of error correction codes such as scrambled error correction codes, BCH, and RS are illustrated in terms of .  The comparison in terms of is investigated between the scrambled error correction codes and the RS.  The comparison is done in terms of between scrambled BCH and unscrambled BCH.

SYSTEM MODEL
In this research, the additive white gaussian noise (AWGN) wire-tap channel is utilized as the main transmission channel between the sender (Alice), the legitimate receiver (Bob) and eavesdropper node (Eve). This system model implemented firstly by [22]. Figure 1 illustrates the typical Wyner wiretap channel. The sender (Alice) uses any suitable transmission technique to send the data message to the legitimate receiver (Bob). The data is received by both Bob and Eve, where both are aware of the transmission technique used by the sender. As a result, the received data message at both Bob and Eve is recovered. However, the recovered messages differences in the channels between Eve and Alice, and Bob and Alice make the difference in the recovered message.

PERFORMANCE ANALYSIS FOR THE ERROR CORRECTION CODES
This section introduces each t-error correction codes techniques. The scrambled codes and the RS code are compared in terms of PLS.

Reed solomon (RS)
RS is a common error correcting code technique that is used with various bits. RS provides desirable results for correcting burst errors due to the correction of these errors done in the bits level. RS code is defined as ( ; ) code where denotes the message bits in the codeword and denotes the number of bits in the codeword. RS codes can correct ( − )/2 errors [11]. The advantages of RS are increasing the SNR and the transmission secrecy rate.

Galois field (GF)
Galois field (GF) is a special field that has a special property, the arithmetic operations addition, subtraction, multiplication, and division on field elements always have results.

Generator polynomial
In RS, the valid codeword can be divided by the generator polynomial. The general polynomial is defined as: the codeword is defined as where g(x), i(x) and c(x) are the generator polynomial, information block, and valid codeword, respectively.

Encoder
The 2t is calculated using: In RS encoder each register holds a symbol that consist of 8 bits.

Decoder
The received message consists of two parts, the transmitted codeword and the errors.
RS can find up to t error position and correct them. The probability of bit error of RS using hard decision decoding is calculated as, Where denotes the probability of the channel bit error, denotes the bits number in the codeword, and = ( − )/2 is the capability of the RS code to correct errors. RS codes have various decoding strategies. However, the strategy of hard decision-decoding is selected. Figure 2 illustrates the BER of the RS codes with several code-length. Based on Figure 2, the RS codes are observed to be highly imperfect due to the increament of the probability of error with the decrease of the SNR and the codeword. This imperfection is considered as an advantage for security.

Bose-chaudhuri-hocquenghem (BCH)
BCH is deemed as an error correction codes technique that is able for correcting and detecting several bits error [23][24][25]. BCH is an error correcting code technique that is suitable for WSNs due to its properties of enhancing the efficiency of the energy by 23% [20]. BCH was selected by [21] to be scrambled to reduce the between the eavesdropper and the legitimate receiver. In this section, BCH has been evaluated without using the scrambling techniques and compared against Reed Solomon without scrambling. Figure 3 indicates the impact of the scrambling on BCH code. The BER improves significantly with scrambling as the SNR increases and outperforms that without scrambling.

Scrambled t-error correction codes
The implementation of Non-systematic codes is firstly introduced in [22]. The authers of [20] utilize the scrambling techniques to reduce the . Thus, proving that scrambling has a significant impact on the . The scrambling technique assumed that the transmitter is going to encode the message as follow, where the is a generator matrix with dimension , and is scrambling matrix with dimension . The generator matrix can be written in different ways due to its systematic character. Now can be written as = [ | ], is identity matrix with dimension , and is ( − ) parity check matrix. Now with all mentioned above. The codeword can be written as, From the above equation, the is the first of the codeword while the is last rbits of the codeword. To ensure the PLS, the BER of the intended receiver should be low as well as the SNR should be high enough to ensure all the errors could be corrected and for that = = . 1 The bit error probability while theBER for the eavesdropper should be high, as well as the SNR, should be low so that the eavesdropper is not going to be able to decode the message and for that, the output of the descrambler for the eavesdropper can be written as, where is the left part of the error vector [ | ] for the perfect scrambling is calculated.
In (9) computes the probability of the bit error for perfect scrambling where denotes the total message bits in the codeword. The authors of [14] demonstrates the results of (9) using BCH codes. Figure 4 depicts the various level of scrambling as represents the column weight of the scrambling matrix. The lowest is retrieved with the perfect scrambling diagram. Figure 4. BER of different level of scrambling using BPSK over AWGN channel

Physical layer security for the error correction codes
The idea behind the coding techniques is to make the mutual information between the message and the encoded message is zero. The information leaked for the data may reach zero if the uncertainty of the randomization is small [15,17]. In this paper, the is performance metric used. The security for the transmitted data exists by maintaining the BER of the receiver close to aero and the eavesdropper to 0.5 and above. This condition ensures that the eavesdropper not able to decode the received message back. Let the BER average at the legitimate receiver and the eavesdropper be and respectively. Then, it is required that be high to ensure security and that be adequately low for ensuring the reliability. If the errors are identically independent distributed (IID) and is close to 0.5, then eavesdropper is incapable of extracting data from the received sequence . Let be the lowest for which a) holds and let be the highest for which b) holds. It is assumed that the receiver operates at and that eavesdropper is strictly lower than . The performance metric is defined as in dB. The authors of [22] introduced a scheme in terms of the which is the ratio between the SNR for the legitimate receiver and the SNR for the eavesdropper .

Energy efficiency analysis
Based on [4], the largest energy consumption in a communication system is the tasks of reception and transmission. In (10) calculates the consumption of energy for sending data bits throughout a wireless channel to the legitimate receiver at distance .
Where is the consumed energy in the transmitter and is the consumed energy at the receiver. At the transmitter the energy consumed is calculated as, where is the energy spent at the transmitter amplifier and is the spent energy by the transmitter circuit. The relationship between the energy spent per bit at the receiver and the energy spent per bit at the transmitter is assumed to be linear and can be found by the equation: where and are the components of the hardware. Finally, the relationship between energy consumption and the probability of bit error is illustrated as,

SIMULATION RESULTS AND DISCUSSION
This section presents and analyses the comparison between the RS and t-error correction codes in terms of metric. The codeword length for both techniques is considered as = 127. RS and scrambled t-error correction codes are applied on the AWGN channel. Moreover, the data bits length for RS and scrambled t-error correction codes are considered to be = 106. The error correcting ability for both RS and scrambled t-error correction codes are considered to be = 10. The channel bit error probability for AWGN channel for both error correction codes is calculated as, where is the code rate and is the . The is illustrates Table 1 for the error correction codes. Based on Table 1, RS correcting code technique is not added to another technique such as scrambling. Moreover, RS correcting code technique gives the smallist compared with the other t-error correcting code techniques. Based on the result, RS code is most secure error correcting without the addition of other techniques. Figure 5 shows the BER for the RS code and the scrambled t-error.  Table 2 compares the required time to simulate the error correction codes by using MATLAB version 7.14 (R2012a). Based on Table 2, we observe that the correcting code required less time (5.782384s) to execute the simulation of PLS. However, to execute the LDPC correcting code, more than 100 seconds are required. The computational complexity due to RS correcting code is seen to be less compared to scrambled error correcting, punctured LDPC, LDPC, and BCH codes.  Table 3 provides the required simulation parameters for compariong the efficiency of energy between RS and BCH. Based on Figure 6, the estimated consuming energy of the BCH code is less than the estimated consuming energy of the RS code. In the communication system the lower BER is estimated to consume low energy. In other word, the better quality of the channel is the lower energy consumption. At the probability for bit error of 0.04 the estimated consumption of energy is 0.05 for the BCH code. On the other hand, at the same probability of bit error for the RS code the consumption of energy is almost 0.16 joules/bit. It is clear that the BCH consume less energy than the RS within the conditions of wiretap channel.

CONCLUSION
We have presented the performance of RS and BCH codes in terms of energy consumption security aspects. We found that RS has almost the same as scrambled error correction codes which require more energy consumption than RS. On the other hand, BCH is poised to be a good candidate in WSNs for physical