Joint network-channel code optimization for wireless sensor networks
© Alaoui et al.; licensee Springer. 2013
Received: 3 April 2013
Accepted: 16 October 2013
Published: 16 November 2013
Optimization of sensor network architecture in order to improve the overall system performance at the end processing station is an important challenge. A lot of architectures have been designed to optimize the bit error rate. Conventionally, this optimization is done by inserting relays between sensors and destination. These relays insert redundant information by mixing the incoming streams from sensor nodes, hence creating parity check information which is very useful to help decode the transmit information from sensors. The goal is to combine network and channel coding to match network on graph to code on graph, and this is called adaptive network coded cooperation (ANCC). Compared to the previous works in the field, we propose a new transmit protocol based on the use of beamforming technique which is very efficient in terms of throughput and is fully compatible with the physical network coding (PNC) principles. Furthermore, we propose a distributed coding scheme where the relay, the destination, and the sensors are all equipped with repeat accumulate (RA) channel code structures. The relay has a special RA structure to suit the need of the PNC multiple access channel.
Different protocols and architectures have been designed to improve the performance of sensor networks. The use of network coding has appeared recently as a promising way to help find an answer to this problem [1–5]. In network coding, some intermediate nodes mix the messages they received and forward this obtained mixture to several destinations simultaneously [6–8]. When compared to time sharing-based schemes where destinations are served sequentially, network coding improves considerably the throughput efficiency . Among the different network coding techniques for wireless sensor networks, one promising approach is the use of joint network-channel coding (JNCC). The basic principle consists in the use of relays which decode incoming streams and combine them to obtain additional redundant information. The redundant information from the relays is combined at the destination node with the original information from the sensors to obtain an equivalent powerful block code such as a LDPC one. Hence, the goal of this kind of architecture is to couple networks on graphs with codes on graph. This was first proposed in  and further developed in [11, 12] with some optimization of the coding scheme at the relay place. The transmission protocol can be summarized in the following way. In a first time slot, each source node broadcasts its information to both relays and destination. In a second time slot, the relays then decode the received packets and combine them by XOR operation to obtain parity check bits which are transmitted to the destination. The second task clearly corresponds to the network coding step and contains some challenging aspects. The main ones are of course the choice of the source incoming messages in the XOR operations and the degree of each XOR operation (the number of incoming streams which are combined). Finally, at the destination node, a graph code such as low-density parity check (LDPC) or low-density generator matrix (LDGM) codes is built and decoded using belief propagation (BP) algorithm.
Compared to the existing literature and particularly to , we propose, in this paper, new attractive features to further improve the performance of suck kind of systems. The first point concerns the improvement of the broadcast transmit phase. In , the authors propose to use orthogonal channels to make the transmissions from sources to relays error free. This is quite penalizing in terms of bandwidth or throughput efficiency depending on the used multiple access technique (FDMA or TDMA). In this paper, supposing that the relay and the destination are equipped with K antennas, we propose a new transmission protocol which enables 2.K uplink and downlink transmissions to be accomplished within (K + 2) time slots. This outstanding performance is obtained because we found a way to handle the co-channel interference at the relay place. The idea behind this comes from the concept of interference alignment  and consists in making the two messages delivered to and from the same sensor fall in the same direction at the relay. We propose precoding and beamforming techniques [14–18] to ensure that the signals delivered to and from the same sensor can be paired together. Another merit of our proposed system is that we consider two-way message exchanges between the destination and the sensors. We consider explicitly the case where the destination node sends back information controls toward the sensor nodes and this is not studied in .
Furthermore, since our proposed scheme is fully compatible with the physical network coding (PNC) principles, we propose a distributed coding scheme where channel coding is applied at the destination and at the sensors level and network coding is applied at the relay to encode the incoming mixed streams from the destination and the sensors. We show that our proposed system enables to transmit simultaneously the K encoded messages from the sensors and the control encoded messages from the destination. Thanks to the precoding matrices, these messages are combined at the relay in such a way that we have K streams to be network encoded at the relay place. We suppose that the end nodes (destination and sensors) are all equipped with repeat accumulate (RA) codes, and we show how to design the channel decoder at the relay which channel-decodes the superimposed channel-coded packets to obtain the soft version of the arithmetic summation of the source packets and transforms the superimposed source packets to the network coded packets. These processing tasks at the relay have been detailed in [19, 20] and the authors have named them: channel-decoding-network-coding process (CNC). Similar construction rules can be found in [21, 22]. The decoder at the relay uses a special repeat accumulate (RA) code structure to accommodate the obtained particular incoming streams with precoding.
The rest of the paper is organized as follows. In the second part (Section 2), the system model and the new proposed transmit protocol are described. In the third part (Section 3), the network coding scheme is detailed and we put the emphasis on the design of the decoder at the relay. In the fourth part (Section 4), we present the results of the simulation. Finally, concluding remarks are given in Section 5.
The following notations are used: (.) T , (.) H , and denote transpose, conjugate transpose, and expectation of (.), respectively.
2 System model
We consider a real wireless sensor network with K sensors, each sensor is equipped with one transmit/receive antenna and with a channel encoder/decoder. In this paper, we will use RA code structure for the coding of incoming streams from the sensors. No direct link between sensor and destination exists. The relay is equipped with Q multiple antennas and with K network-channel decoder/encoders. The destination node is equipped with N ≥ K multiple antennas too and contains K channel encoders/decoders. We will suppose classically that N ≥ Q ≥ K, i.e., the destination node has the best capability while some relays are more capable than the elementary sensors. The cooperation phases in such a system are decomposed into two main ones.
The first one is the broadcast phase where sensors and destination exchange their information with the help of the relay. We suppose that there is no direct available link between the sensors and the destination source.
The second one is the network coding phase at the relay. After decoding, the relay combines the incoming streams and retransmits them to the destination and sensor nodes. The way the relay operates the network coding tasks is described in the next section.
2.1 Transmit protocols
where H DR is the Q × N channel matrix between the destination node and the relay, H jR is the Q × 1 channel vector between the relay and the j th sensor and n R denotes the Q × 1 additive white Gaussian noise vector.
where H Rj is the 1 × Q channel vector between the j th sensor and the relay. Supposing that the uplink and downlink channels are reciprocal, we have . Of course, during this phase, the destination does not take into account the received data.
One possible choice for G and F consists in: and . Once again, we suppose that: .
2.2 Precoding matrix design at the destination source for the first time slot
3 Network coding at the relay
As mentioned in [19, 20], there are two classical solutions to address the problem of cooperative network coding at the relay (CNC). The first one consists in decoding m i and s i from y R separately. The relay can first decode m i while regarding the other message s i as interference, and can then decode s i after removing the decoded information m i from the decoded signal. Combining the soft outputs of the decoder Pmi,si(a, b) = Pr(m i = a, s i = b/y R )Pmi,si(a, b) = Pr(m i = a, s i = b/y R ), we can generate: m i ⊕ s i . The second solution consists in estimating from the received vector y R with for example the method in . By decoding the estimate of Xs,j ⊕ XD,j i.e.: with a soft input decoder, the relay can obtain: m i ⊕ s i .
3.1 The proposed decoding scheme
when: sR,j[l] = m j [l] + s j [l]
For encoding, the Tanner graph is read from left to right. For decoding, the Tanner graph is read backward from right to left. The well-known principle is to exchange a posteriori probabilities between information and check nodes until the probabilities converge after several iterations and we could decode: m j [l] + s j [l].
3.2 Tanner graph and decoding algorithm
Another solution may consist in employing a list sphere decoder  to weight the coded symbol before entering the belief propagation decoding module. This affords to obtain better performances than using ZF equalization since it is well known that LSD, which approximates the ML solution, exhibits better performances compared to ZF equalization.
Concerning the decoding algorithm using BP, it proceeds as follows. Let P[h,t] denote the message passed between a check node and a variable node (information node or code node), the message is associated with the edge from node h to node t; one of h or t is a variable node and the other is a check node. As in [19, 20], we denote P k as the message from the k th evidence node to the k th code node. Hence, we have the following notations:
The messages for the variable nodes are initialized to (1/4, 1/2, 1/4).
3.3 Message update rules
(a) The first update rule concerns the update equations for Output Messages going out of a Variable Node. This corresponds to the cases of Figure 5 a,c.
where ; we assumed in Equation (17) that the two input messages are independent, given the value of the variable node, i.e., Pr(P, Q|x) = Pr(P|x), and we suppose that Pr(x = 0) = 1/4. In a similar way, we would obtain , and .
(1) The update equations for the scenario of Figure 5 c are similar except that the variable node is an information node rather than a code node, and the associated probabilities are related to the source symbol rather than the code symbol.
(2) If we consider the messages in log-likelihood (LLR) form, i.e., , we find that Equation (17) is equivalent to the summation of all the incoming LLRs.
(3) For the lowest code node in Figure 4, the output message is always the same at the input message from the last evidence node, which remains constant throughout the iterations.
The second update rule concerns the update equations for Output Messages going out of a Check Node. This corresponds to the cases of Figure 5 b,d.
4 Simulation results
Where the factor 0.5 denotes the half multiplexing loss due to relaying compared with a relay-free scenario. ρ SR denotes the signal-to-noise power ratio for the link between sensors and relay and ρ RD denotes the signal to noise power ratio for the link between relay and destination. In the following, supposing that the relay is located at the same distances from the sensor network and the destination, we will assume that: ρ SR = ρ RD = ρ
All of these results constitute an outstanding performance since we are able, in all the cases, to work close to the theoretical ergodic capacity of the system.
In this paper, we have proposed a physical network coding-based system to improve the throughput efficiency of a wireless sensor network. Thanks to powerful beamforming techniques, supposing that the relay and the destination are equipped with K antennas, we built a new transmission protocol which enables 2.K uplink and downlink transmissions to be accomplished within (K + 2) time slots. This outstanding performance is obtained because we found a way to handle the co-channel interference despite the poor capacities of elementary wireless sensors which have only one antenna.
Furthermore, since our proposed scheme is fully compatible with the physical network coding (PNC) principles, we propose a distributed coding scheme where channel coding is applied at the destination and at the sensors level and network coding is applied at the relay to encode the incoming mixed streams from the destination and the sensors. We show that our proposed system enables to transmit simultaneously the K encoded messages from the sensors and the control encoded messages from the destination. Simulation results demonstrate that our proposed distributed coding scheme enables to work close to the theoretical ergodic capacity of the system. Typically, considering different kinds of receiver architectures, we are always within less than 2 dB from the ergodic capacity of the equivalent system.
NA received the engineering degree from the Ecole Nationale Supérieure d'Ingénieurs de Limoges in September 2010. He is now a PhD student at the University of Limoges since October 2010. His research activities concern the cooperative communication in mobile ad hoc networks, especially for physical and MAC layer. He is also a temporary teacher at the University of Limoges; he participated in many international conferences.
VM received the BSc and MSc degrees from Sharif University of Technology, Tehran, Iran, respectively, in 1988 and 1991 and PhD degree from the University of Limoges, France in 1998. He has been working at the department of electronic and telecommunication of ENSIL/University of Limoges as an assistant professor since 2000 and as an associate professor since 2007. He received in 2008 and 2012 from the French ministry of research and higher education the award of scientific excellence. His main interest in research is the telecommunication systems including MIMO systems, coding, network coding, cooperative communications, sensor network, and smart grid. Since 1998, he has been scientific manager for more than ten research projects in the field of ICT (information and Communications Technology). He is the (co-)author of more than 100 publications in scientific journals and conferences and served as TPC members in several international conferences.
JPC received the engineering degree from the Ecole Nationale Supérieure des Télécommunications de Bretagne in 1990. He also received the Aggregation degree in Physics in 1993 and the HDR degree in 2002 from the University of Limoges. He became a IEEE senior member in 2007. He is now a full professor in signal processing at the Ecole Nationale d'Ingénieurs de Limoges (ENSIL) since 2006. His research activities concern signal processing algorithms for digital communications including cooperative networks, network coding, space-time coding, and joint optimization of physical and MAC layers of future communication systems. He is getting involved in several French and European research programs.
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