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

An erasure channel with a fixed alphabet size q, where q 1, is studied . It is proved that over any erasure channel (with or without memory), Maximum Distance Separable (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.

Abstract-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 [1], [2]. 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.

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