A time-invariant (constant channel gains) K-user interference channel is considered, where all interference (cross) channel gains are integers. For such channels, previous results demonstrate that the number of degree...
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ISBN:
(纸本)9781457704376
A time-invariant (constant channel gains) K-user interference channel is considered, where all interference (cross) channel gains are integers. For such channels, previous results demonstrate that the number of degrees of freedom is very sensitive to slight variations in the direct channel gains. In this paper we derive an achievable rate region for such channels which is valid for finite SNR. At moderate values of SNR the derived rate region is robust to slight variations in the direct channel gains. At asymptotic high SNR conditions, the known results on the degrees of freedom are recovered. The new rate region is based on lattice interference alignment. The result is established via a new coding theorem for the two-user Gaussian multiple-access channel where both users use a single linear code.
The delta-mutual information between uncertain variables is introduced as a generalization of Nair's non-stochastic information functional. Several properties of this new quantity are illustrated, and used to prov...
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ISBN:
(纸本)9781538692912
The delta-mutual information between uncertain variables is introduced as a generalization of Nair's non-stochastic information functional. Several properties of this new quantity are illustrated, and used to prove a channel coding theorem in a non-stochastic setting. Namely, it is shown that the largest delta-mutual information between a metric space and its epsilon-packing equals the (epsilon, delta)-capacity of the space. This notion of capacity generalizes the Kolmogorov epsilon-capacity to packing sets of overlap at most delta, and is a variation of a previous definition proposed by one of the authors. These results provide a framework for developing a non-stochastic information theory motivated by potential applications in control and learning theories. Compared to previous non-stochastic approaches, the theory admits the possibility of decoding errors as in Shannon's probabilistic setting, while retaining its worst-case non-stochastic character.
We define the collection channel in a Wireless Sensor Network (WSN) and show how this collection channel can be used in the proofs of new types of coding theorems for WSNs. These coding theorems differ from traditiona...
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ISBN:
(纸本)9781424482641
We define the collection channel in a Wireless Sensor Network (WSN) and show how this collection channel can be used in the proofs of new types of coding theorems for WSNs. These coding theorems differ from traditional coding theorems in that they are used to describe aspects of the WSN other than source and channel codes. We also determine the capacity of the collection channel. This capacity is complementary to the transport capacity of a communication system and represents the WNS's ability to obtain information about a phenomenon that it is sensing.
We find that the asymptotic entanglement of assistance of a general bipartite mixed state is equal to the smaller of its two local entropies. Our protocol gives rise to the asymptotically optimal Einstein-Podolsky-Ros...
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We find that the asymptotic entanglement of assistance of a general bipartite mixed state is equal to the smaller of its two local entropies. Our protocol gives rise to the asymptotically optimal Einstein-Podolsky-Rosen (EPR) pair distillation procedure for a given tripartite pure state, and we show that it actually yields EPR and Greenberger-Horne-Zeilinger (GHZ) states; in fact, under a restricted class of protocols, which we call “one-way broadcasting,” the GHZ rate is shown to be optimal. This result implies a capacity theorem for quantum channels where the environment helps transmission by broadcasting the outcome of an optimally chosen measurement. We discuss generalizations to m parties and show (for m=4) that the maximal amount of entanglement that can be localized between two parties is given by the smallest entropy of a group of parties of which the one party is a member, but not the other. This gives an explicit expression for the asymptotic localizable entanglement and shows that any nontrivial ground state of a spin system can be used as a perfect quantum repeater if many copies are available in parallel. Finally, we provide evidence that any unital channel is asymptotically equivalent to a mixture of unitaries and any general channel to a mixture of partial isometries.
Quantum-state tomography—the practice of estimating a quantum state by performing measurements on it—is useful in a variety of contexts. We introduce “gentle tomography” as a version of tomography that preserves t...
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Quantum-state tomography—the practice of estimating a quantum state by performing measurements on it—is useful in a variety of contexts. We introduce “gentle tomography” as a version of tomography that preserves the measured quantum data. As an application of gentle tomography, we describe a polynomial-time method for universal source coding.
We give an operational definition of the quantum, classical, and total amounts of correlations in a bipartite quantum state. We argue that these quantities can be defined via the amount of work (noise) that is require...
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We give an operational definition of the quantum, classical, and total amounts of correlations in a bipartite quantum state. We argue that these quantities can be defined via the amount of work (noise) that is required to erase (destroy) the correlations: for the total correlation, we have to erase completely, for the quantum correlation we have to erase until a separable state is obtained, and the classical correlation is the maximal correlation left after erasing the quantum correlations. In particular, we show that the total amount of correlations is equal to the quantum mutual information, thus providing it with a direct operational interpretation. As a by-product, we obtain a direct, operational, and elementary proof of strong subadditivity of quantum entropy.
The authors of [1] were unaware of this one sentence in [2] (page 3237): 'Since the Renyi and Tsallis entropy are related by a simple monotone transformation, inequalities similar to (8) and (20) exist with Tsalli...
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The authors of [1] were unaware of this one sentence in [2] (page 3237): 'Since the Renyi and Tsallis entropy are related by a simple monotone transformation, inequalities similar to (8) and (20) exist with Tsallis entropy bounds.', and concerning the subject addressed in [1]. It is true that this sentence of [2] announces the possibility of the coding theorem which is explicitly worked out in [1]. In this respect, [2] should indeed be recognised for this contribution.
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