157,924 research outputs found

    Distributed Computing with Channel Noise

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    A group of nn users want to run a distributed protocol π\pi over a network where communication occurs via private point-to-point channels. Unfortunately, an adversary, who knows π\pi, is able to maliciously flip bits on the channels. Can we efficiently simulate π\pi in the presence of such an adversary? We show that this is possible, even when LL, the number of bits sent in π\pi, and TT, the number of bits flipped by the adversary are not known in advance. In particular, we show how to create a robust version of π\pi that 1) fails with probability at most δ\delta, for any δ>0\delta > 0; and 2) sends O~(L+T)\tilde{O}(L+T) bits, where the O~\tilde{O} notation hides a log(nL/δ)\log(nL/\delta) term multiplying LL. Additionally, we show how to improve this result when the average message size α\alpha is not constant. In particular, we give an algorithm that sends O(L(1+(1/α)log(nL/δ)+T)O(L(1 + (1/\alpha) \log(nL/\delta) + T ) bits. This algorithm is adaptive in that it does not require a priori knowledge of α\alpha. We note that if α\alpha is Ω(log(nL/δ))\Omega (log(nL/\delta)), then this improved algorithm sends only O(L+T)O(L + T) bits, and is therefore within a constant factor of optimal

    Bounds on the Capacity of Random Insertion and Deletion-Additive Noise Channels

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    We develop several analytical lower bounds on the capacity of binary insertion and deletion channels by considering independent uniformly distributed (i.u.d.) inputs and computing lower bounds on the mutual information between the input and output sequences. For the deletion channel, we consider two different models: independent and identically distributed (i.i.d.) deletion-substitution channel and i.i.d. deletion channel with additive white Gaussian noise (AWGN). These two models are considered to incorporate effects of the channel noise along with the synchronization errors. For the insertion channel case we consider the Gallager's model in which the transmitted bits are replaced with two random bits and uniform over the four possibilities independently of any other insertion events. The general approach taken is similar in all cases, however the specific computations differ. Furthermore, the approach yields a useful lower bound on the capacity for a wide range of deletion probabilities for the deletion channels, while it provides a beneficial bound only for small insertion probabilities (less than 0.25) for the insertion model adopted. We emphasize the importance of these results by noting that 1) our results are the first analytical bounds on the capacity of deletion-AWGN channels, 2) the results developed are the best available analytical lower bounds on the deletion-substitution case, 3) for the Gallager insertion channel model, the new lower bound improves the existing results for small insertion probabilities.Comment: Accepted for publication in IEEE Transactions on Information Theor

    High threshold distributed quantum computing with three-qubit nodes

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    In the distributed quantum computing paradigm, well-controlled few-qubit `nodes' are networked together by connections which are relatively noisy and failure prone. A practical scheme must offer high tolerance to errors while requiring only simple (i.e. few-qubit) nodes. Here we show that relatively modest, three-qubit nodes can support advanced purification techniques and so offer robust scalability: the infidelity in the entanglement channel may be permitted to approach 10% if the infidelity in local operations is of order 0.1%. Our tolerance of network noise is therefore a order of magnitude beyond prior schemes, and our architecture remains robust even in the presence of considerable decoherence rates (memory errors). We compare the performance with that of schemes involving nodes of lower and higher complexity. Ion traps, and NV- centres in diamond, are two highly relevant emerging technologies.Comment: 5 figures, 12 pages in single column format. Revision has more detailed comparison with prior scheme

    Pareto Boundary of the Rate Region for Single-Stream MIMO Interference Channels: Linear Transceiver Design

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    We consider a multiple-input multiple-output (MIMO) interference channel (IC), where a single data stream per user is transmitted and each receiver treats interference as noise. The paper focuses on the open problem of computing the outermost boundary (so-called Pareto boundary-PB) of the achievable rate region under linear transceiver design. The Pareto boundary consists of the strict PB and non-strict PB. For the two user case, we compute the non-strict PB and the two ending points of the strict PB exactly. For the strict PB, we formulate the problem to maximize one rate while the other rate is fixed such that a strict PB point is reached. To solve this non-convex optimization problem which results from the hard-coupled two transmit beamformers, we propose an alternating optimization algorithm. Furthermore, we extend the algorithm to the multi-user scenario and show convergence. Numerical simulations illustrate that the proposed algorithm computes a sequence of well-distributed operating points that serve as a reasonable and complete inner bound of the strict PB compared with existing methods.Comment: 16 pages, 9 figures. Accepted for publication in IEEE Tans. Signal Process. June. 201

    Communication on noisy channels: a coding theorem for computation

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    Communication is critical to distributed computing, parallel computing, or any situation in which automata interact-hence its significance as a resource in computation. In view of the likelihood of errors occurring in a lengthy interaction, it is desirable to incorporate this possibility in the model of communication. The author relates the noisy channel and the standard (noise less channel) complexities of a communication problem by establishing a `two-way' or interactive analogue of Shanon's coding theorem: every noiseless channel protocol can be simulated by a private-coin noisy channel protocol whose time bound is proportional to the original (noiseless) time bound and inversely proportional to the capacity of the channel, while the protocol errs with vanishing probability. The method involves simulating the original protocol while implementing a hierarchical system of progress checks which ensure that errors of any magnitude in the simulation are, with high probability, rapidly eliminated
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