It is known that the achievable data rate per user can be increased when relays are deployed in wireless networks. However, the drawback of this solution is that some of the network's resources should be allocated to the relays. In this paper, we consider a two-tier network in which all users send or receive data in two hops. By applying vector quantization, we compute the relays' locations to improve network's average transmission rate. These locations are also computed analytically when the number of relays is less than six. Having determined the relays' locations, the network's average transmission rate is evaluated. Subsequently, we define the "neutrality-surface" such that the performance of any relay network operating below this surface is inferior to that of the same network without relays. Finally, we study the relative relaying gain for different network configurations.

This paper addresses a fundamental trade-off between rate and the diversity gain of an end-to-end connection in an erasure network. The erasure network is modeled by a directed graph whose links are orthogonal erasure channels. Furthermore, the erasure network is assumed to be non-ergodic, meaning that the erasure status of the links are assumed to be fixed during each block of transmission and change independently from block to block. The erasure status of the links is assumed to be known only by the destination node. First, we study the homogeneous erasure networks in which the links have the same erasure probability and capacity. We derive the optimum trade-off between diversity gain and the end-to-end rate and prove that a variant of the conventional routing strategy combined with an appropriate forward error correction at the end-nodes achieves the optimum diversity-rate trade-off. Next, we consider the general erasure networks in which different links may have different values of erasure probability and capacity. We prove that there exist general erasure networks for which any conventional routing strategy fails to achieve the optimum diversity-rate trade-off. However, for any general erasure graph, we show that there exists a linear network coding strategy which achieves the optimum diversity-rate trade-off. Unlike the previous works which suggest the potential benefit of linear network coding in the error-free multicast scenario (in terms of the achievable rate), our result introduces the benefit of linear network coding in the erasure single-source single-destination scenario (in terms of the diversity gain). Finally, we study the diversity-rate trade-off through simulations. The erasure graphs are constructed according to the Barabasi-Albert random model which is known to capture the scale-free property of the practical packet switched networks like the Internet. The error probability is depicted for different network strategies and different rate values. The depicted results confirm the trade-off between the rate and the diversity gain for each network strategy. Moreover, the diversity gain is plotted versus the rate for different conventional routing and the linear network coding strategies. It is observed that linear network coding outperforms all conventional routing strategies in terms of the diversity gain.

Path diversity works by setting up multiple parallel connections between the endpoints using the topological path redundancy of the network. In this paper, forward error correction (FEC) is applied across multiple independent paths to enhance the end-to-end reliability. We prove that the probability of irrecoverable loss (PE) decays exponentially with the number of paths. Furthermore, the rate allocation (RA) problem across independent paths is studied. Our objective is to find the optimal RA, i.e., the allocation that minimizesPE. The RA problem is solved for a large number of paths. Moreover, it is shown that in such asymptotically optimal RA, each path is assigned a positive rate iff its quality is above a certain threshold. Finally, using memoization technique, a heuristic suboptimal algorithm with polynomial runtime is proposed for RA over a finite number of paths. This algorithm converges to the asymptotically optimal RA when the number of paths is large. For a practical number of paths, the simulation results demonstrate the close-to-optimal performance of the proposed algorithm .

An erasure channel with a fixed alphabet size q, where q Gt 1, is studied. It is proved that over any erasure channel (with or without memory),maximumdistanceseparable(MDS) codes achieve the minimum probability of error (assuming maximum likelihood decoding). Assuming a memoryless erasure channel, the error exponent of MDS codes are compared with that of random codes. It is shown that the envelopes of these two exponents are identical for rates above the critical rate. Noting the optimality of MDS codes, it is concluded that random coding is exponentially optimal as long as the block size N satisfies N < q + 1.

It is known that the achievable data rate per user can be increased when relays are deployed in wireless networks. However, the drawback with this solution is that some of the network resources should be allocated to the relays. In this paper, we consider a two-tier network where all users should send/receive data in two hops (via a relay). Applying vector quantization, we approximately find the location of the relays. These approximate relays' locations are also computed analytically when the number of relays is less than six. Having the relays' locations, the network average transmission rate is evaluated in terms of a set of network parameters. Then, in the multi-dimensional space of these network parameters, we introduce the concept of neutrality-surface. The neutrality-surface is defined such that the performance of any relay network operating below this surface is inferior to that of a simple no-relay network with the same parameters. Finally, we study the relative and differential relaying gain for different network configurations.

Path diversity works by setting up multiple parallel connections between the end points using the topological path redundancy of the network. In this paper, forward error correction (FEC) is applied across multiple independent paths to enhance the end-to-end reliability. Internet paths are modeled as erasure Gilbert-Elliot channels. First, it is shown that over any erasure channel, maximum distance separable (MDS) codes achieve the minimum probability of irrecoverable loss among all block codes of the same size. Then, we prove the probability of irrecoverable loss decays exponentially for the asymptotically large number of paths. Moreover, it is shown that in the optimal rate allocation, each path is assigned a positive rate iff its quality is above a certain threshold. The quality of a path is defined as the percentage of the time it spends in the bad state. Finally, using dynamic programming, a heuristic suboptimal algorithm with polynomial runtime is proposed for rate allocation over the available paths. This algorithm converges to the asymptotically optimal rate allocation when the number of paths is large. The simulation results show that the proposed algorithm approximates the optimal rate allocation very closely, and provides significant performance improvement compared to the alternative schemes of rate allocation.

ESS mesh networks will soon provide extensive coverage deployment for outdoor WLAN hotzones. In these types of networks, solar powered mesh access points (MAPs) and mesh points (MPs) can be used to provide tether-less infrastructure extension in an inexpensive and flexible manner. Unlike conventional WLAN networks, power saving on the access points (APs) is an important feature which can result in significantly reduced solar-powered AP node costs. Unfortunately, when infrastructure nodes conserve power, they become less responsive and this can significantly lengthen the hand off process. In this paper we propose and analyze different algorithms for mitigating these effects, so that real-time handoff can occur as fast as possible. Three different algorithms are proposed for dynamically activating the power saving infrastructure. The proposed algorithms are tested and compared to conventional handoff algorithms via simulation and analysis