Abstract-Conventional hybrid RF and optical wireless communication systems make use of parallel Free Space Optical (FSO) and Radio Frequency (RF) channels to achieve higher reliability than individual channels. True hybridization can be accomplished when both channels collaboratively compensate the shortcomings of each other and thereby improve the performance of the system as a whole. In this paper, we propose a novel coding paradigm called "Hybrid Channel Coding" that not only optimally achieves the capacity of the combined FSO and RF channels but also can potentially provide carrier grade reliability (99.999%) for hybrid FSO/RF systems. The proposed mechanism uses non-uniform and rate-compatible LDPC codes to achieve the desired reliability and capacity limits. We propose a design methodology for constructing these Hybrid Channel Codes. Using analysis and simulation, we show that by using Hybrid Channel Codes, we can obtain significantly better availability results in terms of the required link margin while the average throughput obtained is more than 33% better than the currently existing systems. Also by avoiding data duplication, we preserve to a great extent the crucial security benefits of FSO communications. Simulations also show that Hybrid Channel Codes can achieve more than two orders of magnitude improvement in bit error rate compared to present systems.

In wireless sensor networks, both nodes and links are prone to failures. In this paper we study connectivity properties of large-scale wireless sensor networks and discuss their implicit effect on routing algorithms and network reliability. We assume a network model of n sensors which are distributed randomly over a field based on a given distribution function. The sensors may be unreliable with a probability distribution, which possibly depends on n and the location of sensors. Two active sensor nodes are connected with probability p e (n) if they are within communication range of each other. We prove a general result relating unreliable sensor networks to reliable networks. We investigate different graph theoretic properties of sensor networks such as k-connectivity and the existence of the giant component. While connectivity (i.e. k = 1) insures that all nodes can communicate with each other, k-connectivity for k [ 1 is required for multipath routing. We analyze the average shortest path of the k paths from a node in the sensing field back to a base station. It is found that the lengths of these multiple paths in a k-connected network are all close to the shortest path.These results are shown through graph theoretical derivations and are also verified through simulations.

Abstract-Today, due to the vast amount of literature on largescale wireless networks, we have a fair understanding of the asymptotic behavior of such networks. However, in real world we have to face finite networks for which the asymptotic results cease to be valid. We refer to networks as being finite when the number of nodes is less than a few hundred. Here we study a model of wireless networks, represented by random geometric graphs. In order to address a wide class of the network's properties, we study the threshold phenomena. Being extensively studied in the asymptotic case, the threshold phenomena occurs when a graph theoretic property (such as connectivity) of the network experiences rapid changes over a specific interval of the underlying parameter. Here, we find an upper bound for the threshold width of finite line networks represented by random geometric graphs. These bounds hold for all monotone properties of such networks. We then turn our attention to an important non-monotone characteristic of line networks which is the medium access (MAC) layer capacity, i.e. the maximum number of possible concurrent transmissions. Towards this goal, we provide an algorithm which finds a maximal set of concurrent non-interfering transmissions and further derive lower and upper bounds for the cardinality of the set. Using simulations, we show that these bounds serve as reasonable estimates for the actual value of the MAC-layer capacity.

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