An Energy Efficient Communication Scheme for Distributed Computing Applications in Wireless Sensor Networks Koushik Sinha1 and Bhabani P. Sinha2 1
Honeywell Technology Solutions, Bangalore, India, sinha
[email protected] 2 Indian Statistical Institute, Kolkata, India
[email protected]
Abstract. We propose a new energy efficient communication scheme for multihop wireless sensor networks (WSNs). Our run-zero encoding (RZE) communication scheme utilizes the concepts of the RBNSiZeComm protocol introduced in [1–3]. However, unlike RBNSiZeComm, RZE simultaneously saves energy at both the transmitter and receiver. Also, maintaining synchronization between transmitter and receiver is easier in RZE. Implementation of RZE is based on the transceiver design proposed in [1] that uses a hybrid modulation scheme involving FSK and ASK to keep the cost/complexity of the radio device low. With this non-coherent detection based receiver and assuming equal likelihood of all possible binary strings of a given length, we show that there is a 35.2% savings in energy on an average at the transmitter compared to binary FSK, for additive white gaussian noise (AWGN) channels. Simultaneously, the receiver experiences a savings of 12.5% on an average. These results establish the utility of RZE as a suitable candidate for communication in wireless sensor networks in order to enable distributed computing applications.
1 Introduction With advances in computing and communication technologies, networks such as wireless sensor networks (WSNs) are increasingly finding usage in carrying out various distributed computing applications in the areas of terrain monitoring, agriculture, surveillance, healthcare and military maneuvers, to name a few. Communication being a major source of power drain in the severely energy constrained sensor devices [6], the development of energy efficient communication schemes for WSNs in the context of distributed computing is of paramount importance. Such communication schemes can make possible execution of algorithms and applications that are currently not possible due to the prohibitive cost of message exchanges associated with them. [4] and [5] proposed CtS and VarBaTaC respectively, where communication involves the use of silent periods only. Both however, suffer from the disadvantage of having communication time significantly longer than n for an n-bit binary message. Extending the ideas of CtS and VarBaTaC, [2, 3] presented a new communication scheme, called RBNSiZeComm, that couples recoding of data to redundant binary number system (RBNS) and the use of silent periods to communicate the ’0’ bits. They showed that
by encoding a binary string of length n in RBNS and using their proposed transmission protocol, the theoretically obtainable fraction of energy savings at the transmitter is on n+2 an average, 1 − . [1] presents a non-coherent detection based transceiver design 4n for the RBNSiZeComm protocol and shows that the energy savings is about 41% on an average at the transmitter, for noisy channels. However, no energy savings are generated at the receiver by RBNSiZeComm. 1.1 Our Contribution In this paper, we propose a communication scheme that extends the concepts of RBNSiZeComm to simultaneously save energy at the transmitter and receiver. Our proposed run-zero encoding (RZE) communication scheme improves on RBNSiZeComm on two counts: i) it simultaneously generates savings at the transmitter and receiver and, ii) maintaining synchronization between transmitter and receiver is easier in RZE. Using a non-coherent detection based receiver as in [1] and assuming equal likelihood of all possible binary strings of a given length, we show in this work that there is a 35.2% savings in energy on an average at the transmitter compared to binary FSK, for additive white gaussian noise (AWGN) channels. Simultaneously, the receiver experiences a savings of 12.5% on an average. These results clearly outline the utility of RZE as a suitable candidate for communication in wireless sensor networks, especially for multihop communication.
2 Proposed RZE Scheme The RBNSiZeComm protocol couples encoding of messages in redundant binary number system (RBNS) along with silent zero communication. RBNS utilizes the digits from the set {-1, 0, 1} for representing numbers using radix 2. In the rest of the paper, for convenience, we denote the digit ’-1’ by ¯1. The fact that the number of 0’s in an RBNS encoded data is large [2, 3], provides the motivation for a proper recoding of this runs of 0’s to reduce the number of symbols to be transmitted. We show below that such a recoding will be associated with saving the energy of the transmitter as well as of the receiver (due to fewer number of transmitted symbols). It has been reported in [2, 3] that the percentage runs of ones (and also that of the runs of zeros, by symmetry) in all possible binary strings of length n drops down exponentially with their run length. Thus, for n = 8, the percentage runs of zeros of lengths 3, 4, 5 and 6 in a binary string are 11.11%, 4.86%, 2.08% and less than 0.86% respectively, while that of all runs of zeros of length greater than 6 is only 0.52%. Similarly, for n = 16, the percentage runs of zeros of lengths 3, 4, 5 and 6 are 11.76%, 5.51%, 2.57% and 1.19%, respectively, while that of all runs of zeros of length greater than 6 is only 1.01%. It has also been shown in [2,3] that in the RBN encoded data, two consecutive digits cannot assume any of the four values 11, 1¯1, ¯11 and ¯1¯1. Based on the above observations, we thus propose to recode the runs of zeros only of the lengths 3, 4, 5 and 6 by these four unused code values of two consecutive digits. Association of these four code values to the runs of zeros of lengths 3, 4, 5 and 6 can
be done in any order. Without any loss of generality, let us assume that the runs of zeros of lengths 3, 4, 5 and 6 are coded by two digits with the values 11, 1¯1, ¯11 and ¯1¯1 respectively. We call this recoding of the runs of zeros as run-zero encoding (RZE). Henceforth, a message obtained after applying RBN encoding followed by RZE will be termed as a RZE message. Note that the reductions in the number of symbols by recoding the runs of zeros of lengths 3, 4, 5 and 6 are 1, 2, 3 and 4, respectively.
3 Analysis of Energy Savings As explained above, the number of symbols in an RZE message may be less than those in the corresponding RBN encoded message. Considering all possible 2n binary messages each of length n, we now compute the total reduction in the number of transmitted symbols after applying RZE on the corresponding RBN encoded messages. Let Ni denote the number of runs of 1’s of length i in all possible 2n binary strings of length n. Due to symmetry, Ni will also be the number of runs of 0’s of length i in all possible 2n binary strings of length n, and is given by Nn = 1, Nn−1 = 2 and Nn−k = (k + 3)2k−2 , for k ≥ 2 [2, 3]. The total reduction, say R, in the number of transmitted symbols in the RZE message will then be contributed by four components - C1 , C2 , C3 and C4 as described below: – Component C1 : This component actually comes from the original runs of 1’s in the binary string. We note that the reduction in the number of transmitted symbols with the runs of 0’s of lengths equal to 3, 4, 5 and 6 will be 1, 2, 3 and 4, respectively. Hence, the total contribution to the reduction in number of symbols in the RZE messages due to these runs of 1’s in original binary message is C1 = N4 + 2N5 + 3N6 + 4N7 . – Component C2 : This component comes from the original runs of 0’s in the binary string which are always followed by at least two consecutive 1’s. Thus, C2 excludes the cases of i) a run of 0’s appearing on the rightmost bit positions, ii) a run of 0’s followed by a run of single 1. We note that the total number of runs of 0’s satisfying case 1 above is 2n−5 for runs of 0’s of length 4, 2n−6 for runs of 0’s of length 3, and so on. Let the total number of runs of 0’s satisfying case 2 be N41 , N51 , N61 and N71 for runs of 0’s of length 4, 5, 6 and 7, respectively. Hence we have, C2 = [N4 − (2n−5 + N41 )] + 2[N5 − (2n−6 + N51 )] + 3[N6 − (2n−7 + N61 )] + 4[N7 − (2n−8 + N71 )],
(1)
It can be easily shown that the terms N41 , N51 , N61 and N71 are given by: N41 = 2n−6 + (n − 6)2n−7 + 2n−6 = (n − 2)2n−7 , N51 = (n − 3)2n−8 , N61 = (n − 4)2n−9 , N71 = (n − 5)2n−10 ,
for n ≥ 7 for n ≥ 8 for n ≥ 9 for n ≥ 10
(2)
– Component C3 : This component comes from the runs of 0’s appearing in the rightmost bit positions of the original binary message. Hence, C3 = 2n−4 + 2.2n−5 + 3.2n−6 + 4.2n−7 . – Component C4 : This component comes from the runs of 0’s in the original binary message which are followed by a 10 . . . , or just a 1 in the least significant bit (lsb) position of the string. Thus, it can be shown that C4 = N31 + 2N41 + 3N51 + 4N61 , where, N31 = (n − 1) · 2n−6 ,
for n ≥ 6
(3)
Hence, the total reduction in the number of transmitted symbols using our proposed approach (for n ≥ 10) is then be given by, R = C1 + C2 + C3 + C4 = (65n − 80) · 2n−9
(4)
From [2, 3], the total number of symbols to be transmitted in the RBN encoded messages is (n + 1)2n . After applying RZE on the RBN encoded messages, the total number of symbols to be transmitted, considering all possible 2n binary messages for n ≥ 10, is thus reduced to: · ¸ 65n − 80 (n + 1)2n − (65n − 80)2n−9 = (n + 1)2n 1 − (5) 512(n + 1) Lemma 1. For n ≥ 10, if T is the time to transmit the (n + 1)2n symbols for the RBN encoded messages, then it follows from equation 5, that after the above encoding of 65n−80 runs of 0’s, the transmission time will be reduced to T (1 − 512(n+1) ) which for large 7T u t n, is approximately equal to 8 . However, the above process of encoding runs of 0’s has a negative effect of increasing the number of non-zero symbols of the original RBN encoded messages. This is because each such run of 0’s is encoded by two nonzero symbols - 11, 1¯1, ¯11, ¯1¯1. Following the above process of computing R, we can verify that the total number of such additional non-zero symbols for n ≥ 10 is given by (45n − 3)2n−9 . Hence, using the result from [3] that the total number of non-zero symbols in all possible RBN encoded messages is (n + 2)2n−2 , the fraction of non-zero symbols in the RZE messages is given by, F1¯1 =
45n−3 128(n+2) ] 65n−80 512(n+1) ]
(n + 2)2n−2 [1 + (n + 1)2n [1 −
(6)
For large n, F1¯1 is approximately equal to 38.5%. That is, in our proposed approach, the percentage energy savings at the transmitter for switching the transmitter off during zero symbols comes out to be 61.5%, for the noiseless channel condition, considering equal likelihood of occurrences of all possible binary messages. Note that our approach is further associated with a savings in the receiver energy by a factor of about 18 (i.e., 12.5%) due to the smaller amount of time needed for communicating the compressed message.
4 Analysis of Savings for Noisy Channels We now turn our attention to a realistic situation where the channel is a noisy one with an additive white gaussian noise (AWGN). We assume that the transmitter uses FSK modulation with two frequencies - fc and fc + ∆f corresponding to 1 and ¯1, respectively, and is switched off during 0’s. Effectively this will be a hybrid modulation scheme involving FSK and ASK. As a representative example for showing the energy savings, we use a non-coherent detection based receiver exactly as that in [1]. 4.1 Energy Savings Analysis Let P0 , P1 and P¯1 be the probabilities of occurrences of the symbols 0, 1 and ¯1, respectively in the transmitted message. Then, following a similar analysis as in [1], we get the bit error rate for different SNR values as shown in figure 1. This figure shows that for a given BER in the range 10−4 to 10−7 , the peak transmitter power in RZE scheme is about 2.84db higher than that in non-coherent binary FSK detection. However, in our proposed RZE scheme, the transmitter will be ON only during the non-zero symbols (1 or ¯1), and switched off during the zero symbols in the RZE message. Similar to the analysis in [1], this implies that the required average transmitter power for our proposed scheme will be reduced from the peak power by 10log10 (0.385) db = 4.15db. A plot of the scaled average transmitter power for our proposed RZE scheme as well as for binary FSK (with non-coherent detection) is depicted in figure 1. From figure 1, we see that for a given BER in the range 10−4 to 10−7 , RZE needs approximately 1.31 db less average power than binary FSK. Let Pb and Pr be the required average transmitter power for binary FSK and our proposed RZE scheme. Noting that 101.31/10 = 1.35, we have Pb /Pr = 1.35, i.e., Pr = 0.74Pb . Further, let Tb and Tr be the time required for transmission of symbols using binary FSK and our proposed RZE scheme. Noting that Tr = 7Tb /8, the energy Er required for the RZE scheme is related to the energy Eb for binary FSK as: Er = Pr · Tr = 0.648Pb Tb = 0.648Eb
(7)
From the above discussions and lemma 1, we get the following results : Theorem 1. For equal likelihood of all possible binary strings for a given message length, the amount of energy savings generated at the transmitter by the RZE protocol will on an average be 35.2% more than that by the binary FSK scheme. u t Theorem 2. For equal likelihood of all possible binary strings for a given message length, energy savings at the receiver will on an average be 12.5% as compared to binary FSK or the RBNSiZeComm protocol. u t Remark 1. In order to generate more savings in energy at the receiver than that stated in theorem 2, the transmitter can adopt the protocol of breaking down every long run of zeros into multiple runs of length ≤ 6. Such an implementation of RZE recoding will have an additional advantage of maintaining synchronization between transmitter and receiver simpler as there are no runs of zeros of length greater than 6 in the resultant RZE message.
Transmitter Power Comparison 7
6.5
−log10(BER)
6
5.5
5
4.5
4
3.5 10
Peak RZE Power Average RZE Power FSK Power 11
12
13
14
15
16
17
18
Transmitter Power (scaled) in dB
Fig. 1. Comparison of transmitter power (scaled) for given BER
5 Conclusion We have presented in this paper a low cost and low complexity implementation scheme based on a hybrid modulation utilizing FSK and ASK for the RZE scheme. For AWGN noisy channels, there is an average savings of 35.2% in battery energy at the transmitter for equal likelihood of all possible binary strings of a given length. Also, the receiver energy will be saved by 12.5% by our proposed scheme which make it useful in multihop routing of messages in ad hoc and sensor networks. Coupled with the low cost and low complexity of transceiver, these savings clearly demonstrate the usefulness of RZE for applications based on low power wireless networks, particularly for multi-hop communication.
References 1. K. Sinha, ”An energy efficient communication scheme for applications based on low power wireless networks,” to appear in Proc. 6th IEEE Consumer Communications and Networking Conference (CCNC), Las Vegas, USA, Jan. 10–13, 2009. 2. K. Sinha, ”A new energy efficient MAC protocol based on redundant radix for wireless networks,” Proc. Recent Trends in Inf. Sys. (RETIS), pp. 167–172, 2008. 3. K. Sinha and B. P. Sinha, ”A new energy-efficient wireless communication technique using redundant radix representation,” Tech. Rep., Indian Stat. Inst., ISI/ACMU-07/01, 2007. 4. Y. Zhu and R. Sivakumar, ”Challenges: communication through silence in wireless sensor networks,” Proc. 11th MobiCom, pp. 140–147, 2005. 5. Y. P. Chen, D. Wang and J. Zhang, ”Variable-base tacit communication: a new energy efficient communication scheme for sensor networks,” Proc. 1st Int. Conf. on Integrated Internet Ad hoc and Sensor Networks (InterSense), Nice, France, 2006. 6. J. Polastre, R. Szewczyk and D. Culler, ”Telos: enabling ultra-low power wireless research,” Proc. 4th Intl. Symp. on Information Processing in Sensor Networks, pp. 364–369, 2005.
