Section: New Results

Network coding in WSN

Participants : Jean-Marie Gorce, Cédric Lauradoux, Marco Fiore, Claire Goursaud, Marine Minier, Anya Apavatjrut, Yuanyuan Zhang, Wassim Znaidi.

Network coding associatedf with Fountain codes is a very efficient approach to increase the throughput of multi-hop networks. However severa outcomes are still expected, especially to develop robust and energy efficient approaches for transmitting data over a large sacle networks. Network coding is also very promising for security issues as presented below.

Diversity is a powerful means to increase the transmission performance of wireless communications. For the case of fountain codes relaying, it has been shown previously that introducing diversity is also beneficial since it counteracts transmission losses on the channel. Instead of simply hop-by-hop forwarding information, each sensor node diversifies the information flow using XOR combinations of stored packets. This approach has been shown to be efficient for random linear fountain codes. However, random linear codes exhibit high decoding complexity. In [19] , we propose diversity increased relaying strategies for the more realistic and lower complexity Luby Transform code in a linear network. Results are provided herein for a linear network assuming uniform imperfect channel states.

In [29] , the exact probability that a receiver obtains N linearly independent packets among K over N received packets is computed, when the sender/s use/s random linear network coding over a Galois Field of size q. Such condition maps to the receiver's capability to decode the original information, and its mathematical characterization helps to design the coding so to guarantee the correctness of the transmission. The proposed formulation represents an improvement over the current upper bound for the decoding probability, and provides theoretical grounding to simulative results in the literature.

In [35] , we focus on the proper use of fountain codes for the transmission of sporadic data in a wireless sensor network (WSN). Fountain codes offer great perspectives for the self-organization of WSNs: they self adapt to the channel error rate without any control data. When deploying fountain codes on a WSN, two problems arise. First, the size of the data transmitted by a sensor is small in comparison to the size considered traditionally with fountain codes. Second, the communications are done in an hop-by-hop fashion. It implies that the destination of the data can not acknowledge instantaneously its reception to the source. Therefore, the transmissions of useless packets for the destination can not be prevented. The flooding traffic has been evaluated as well through realistic simulations for three different relaying strategies where packets are lost due to both small scale fading and collisions for an unslotted IEEE 802.15.4 medium access layer.

Network coding has attracted the attention of many researchers in security and cryptography. We have investigated several aspects of network coding security. In [20] , we propose efficient solutions to thwart pollution attacks in which an adversary injects false information into data flow. This work was further expanded in [54] to find rational strategy to minimize the energy cost and the impact of the attack. We also came to the conclusion that dealing with pollution attacks was not enough as long as the acknowledgment messages are not also protected. The risk is to suffer from a flooding attack. This goes beyond the capabilities of cryptographic solutions and we investigate the security capabilities of multipath acknowledgment in [67] .