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In a three-node network a half-duplex relay node enables bidirectional communication between two nodes with a spectral efficient two phase protocol. In the first phase, two nodes transmit their message to the relay node, which decodes the messages and broadcast a re-encoded composition in the second phase. In this work we determine the capacity region of the broadcast phase. In this scenario each receiving node has perfect information about the message that is intended for the other node. The resulting set of achievable rates of the two-phase bidirectional relaying includes the region which can be achieved by applying XOR on the decoded messages at the relay node. We also prove the strong converse for the maximum error probability and show that this implies that the $[\eps_1,\eps_2]$-capacity region defined with respect to the average error probability is constant for small values of error parameters $\eps_1$, $\eps_2$.Comment: 25 pages, 2 figures, submitted to IEEE Transactions on Information Theor

We derive a lower bound on the secrecy capacity of the compound wiretap channel with channel state information at the transmitter which matches the general upper bound on the secrecy capacity of general compound wiretap channels given by Liang et al. and thus establishing a full coding theorem in this case. We achieve this with a stronger secrecy criterion and the maximum error probability criterion, and with a decoder that is robust against the effect of randomisation in the encoding. This relieves us from the need of decoding the randomisation parameter which is in general not possible within this model. Moreover we prove a lower bound on the secrecy capacity of the compound wiretap channel without channel state information and derive a multi-letter expression for the capacity in this communication scenario.where in the first and the third line we have used the fact that the sets {j} × K c j,t , j ∈ J n , are mutually disjoint, the second line follows from (3), and in the fourth line we merely observed that for any non-negative numbers a 1 , . . . , a J with J j=1 a j = 1 we have J j=1 (1 − a j ) = J − 1. Consequently, the average (and hence maximum) error probability of every decoding strategy the eavesdropper might select tends to 1 as soon as J n → ∞. It should be remarked, however, that although for the vast majority of messages the eavesdropper will be in error there is still a possibility left that she/he can decode a small fraction of them correctly. As will follow from the proofs below we will have ε n = 2 −na , a > 0, and J n = 2 nR , R > 0, if the secrecy capacity is positive so that the speed of convergence in (4) will be exponential.Notice that (3) means that the random variables Z n t at the output of the channel to the eavesdropper are almost independent of the random variable J embodying the messages to be transmitted to the legitimate receiver. Therefore it is heuristically convincing that our criterion (2) offers secrecy to some extent for communication tasks going beyond the transmission of messages. To demonstrate this by an example we introduce, based on [10], the notion of identification attack as follows. Suppose that for each fixed t ∈ θ and

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We investigate entanglement transmission over an unknown channel in the presence of a third party (called the adversary), which is enabled to choose the channel from a given set of memoryless but non-stationary channels without informing the legitimate sender and receiver about the particular choice that he made. This channel model is called an arbitrarily varying quantum channel (AVQC). We derive a quantum version of Ahlswede's dichotomy for classical arbitrarily varying channels. This includes a regularized formula for the common randomness-assisted capacity for entanglement transmission of an AVQC. Quite surprisingly and in contrast to the classical analog of the problem involving the maximal and average error probability, we find that the capacity for entanglement transmission of an AVQC always equals its strong subspace transmission capacity. These results are accompanied by different notions of symmetrizability (zero-capacity conditions) as well as by conditions for an AVQC to have a capacity described by a single-letter formula. In the final part of the paper the capacity of the erasure-AVQC is computed and some light shed on the connection between AVQCs and zero-error capacities. Additionally, we show by entirely elementary and operational arguments motivated by the theory of AVQCs that the quantum, classical, and entanglementassisted zero-error capacities of quantum channels are generically zero and are discontinuous at every positivity point.

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We assume a multiuser downlink scenario, where the SINR at each mobile is controlled by adjusting spatial pre-filters and transmission powers at the base station, prior to transmission. In this context, an interesting duality between uplink and downlink beamforming was observed throughout the last decade. This duality allows the joint downlink optimization problem to be solved efficiently by considering the equivalent uplink problem instead, which is easier to handle. In this paper we characterize the interference scenarios and noise levels for which the SINR requirements can be supported for a given power constraint. Moreover, we provide necessary and sufficient conditions for duality. Finally, it is shown how duality can be applied in order to derive optimal transmission strategies for combined downlink beamforming and Costa pre-coding