In this paper, the available spatial Degrees-Of-Freedoms (DOF) in single antenna systems is exploited. A new coding scheme is proposed in which several data streams having fractional multiplexing gains are sent by transmitters and interfering streams are aligned at receivers. Viewed as a field over rational numbers, a received signal has infinite fractional DOFs, allowing simultaneous interference alignment of any finite number of signals at any finite number of receivers. The coding scheme is backed up by a recent result in the field of Diophantine approximation, which states that the convergence part of the Khintchine-Groshev theorem holds for points on nondegenerate manifolds. The proposed coding scheme is proved to be optimal for three communication channels, namely the Gaussian Interference Channel (GIC), the uplink channel in cellular systems, and the X channel. It is proved that the total DOF of the K-user GIC is K 2 almost surely, i.e. each user enjoys half of its maximum DOF. Having K cells and M users within each cell in a cellular system, the total DOF of the uplink channel is proved to be KM M +1 . Finally, the total DOF of the X channel with K transmitters and M receivers is shown to be KM K+M −1 .

Abstract:We demonstrate a polarization-managed 8-dimensional modulation format that is time domain coded to reduce inter-channel nonlinearity. Simulation results show a 2.33 dB improvement in maximum net system margin (NSM) relative to polarization multiplexed (PM)-BPSK, and a 1.0 dB improvement relative to time interleaved return to zero (RZ)-PM-BPSK, for a five channel fill propagating on 20x80 km spans of 90% compensated ELEAF. In contrast to the other modulations considered, the new 8-dimentional (8D) format has negligible sensitivity to the polarization states of the neighboring channels. Laboratory results from High-density WDM (HD-WDM) propagation experiments on a 5000 km dispersionmanaged link show a 1 dB improvement in net system margin relative to PM-BPSK.

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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. Network paths are modeled as erasure Gilbert-Elliot channels [1]- [5]. It is known 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 [6], [7]. Based on the adopted model for the error behavior, we prove that the probability of irrecoverable loss for MDS codes decays exponentially for an asymptotically large number of paths. Then, optimal rate allocation problem is solved for the asymptotic case where the number of paths is large. Moreover, it is shown that in such asymptotically 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 a finite number of 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 (found by exhaustive search) very closely for practical number of paths, and provides significant performance improvement compared to the alternative schemes of rate allocation.1

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