arXiv subjects

Holger Boche

Publications and source records attributed to Holger Boche.

At least 181 records · Page 10Linked to original sources

arXiv2018

Secret Message Transmission over Quantum Channels under Adversarial Quantum Noise: Secrecy Capacity and Super-Activation

We determine the secrecy capacities of AVQCs (arbitrarily varying quantum channels). Both secrecy capacity with average error probability and with maximal error probability are derived. Both derivations are based on one common code construction. The code we construct fulfills a stringent secrecy requirement, which is called the strong code concept. We determine when the secrecy capacity is a continuous function of the system parameters and completely characterize its discontinuity points both for average error criterion and for maximal error criterion. Furthermore, we prove the phenomenon "super-activation" for secrecy capacities of AVQCs, i.e., two quantum channels both with zero secrecy capacity, which, if used together, allow secure transmission with positive capacity. We also discuss the relations between the entanglement distillation capacity, the entanglement generating capacity, and the strong subspace transmission capacity for AVQCs.

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arXiv2018

Message Transmission over Classical Quantum Channels with a Jammer with Side Information: Message Transmission Capacity and Resources

In this paper we propose a new model for arbitrarily varying classical-quantum channels. In this model a jammer has side information. We consider two scenarios. In the first scenario the jammer knows the channel input, while in the second scenario the jammer knows both the channel input and the message. The transmitter and receiver share a secret random key with a vanishing key rate. We determine the capacity for both average and maximum error criteria for both scenarios. We also establish the strong converse. We show that all these corresponding capacities are equal, which means that additionally revealing the message to the jammer does not change the capacity.

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arXiv2018

Fully Quantum Arbitrarily Varying Channels: Random Coding Capacity and Capacity Dichotomy

We consider a model of communication via a fully quantum jammer channel with quantum jammer, quantum sender and quantum receiver, which we dub quantum arbitrarily varying channel (QAVC). Restricting to finite dimensional user and jammer systems, we show, using permutation symmetry and a de Finetti reduction, how the random coding capacity (classical and quantum) of the QAVC is reduced to the capacity of a naturally associated compound channel, which is obtained by restricting the jammer to i.i.d. input states. Furthermore, we demonstrate that the shared randomness required is at most logarithmic in the block length, using a random matrix tail bound. This implies a dichotomy theorem: either the classical capacity of the QAVC is zero, and then also the quantum capacity is zero, or each capacity equals its random coding variant.

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arXiv2017

Reliable Communication under the Influence of a State-Constrained Jammer: A Novel Perspective on Receive Diversity

The question of robust direct communication in vehicular networks is discussed. In most state-of-the-art approaches, there is no central entity controlling channel access, so there may be arbitrary interference from other parties. Thus, a suitable channel model for Vehicle-to-X (V2X) communication is the Arbitrarily Varying Channel (AVC). Employing multiple antennas on a vehicle or sending over multiple frequencies to make use of diversity are promising approaches to combat interference. In this setup, an important question about diversity is how many antennas or orthogonal carrier frequencies are necessary in order to avoid system breakdown due to unknown interference in AVCs. For Binary Symmetric AVCs (AVBSC) and a physically meaningful identical state-constrained jammer, the deployment of a third, uncorrelated receiving antenna or the parallel transmission over three different orthogonal frequencies avoids symmetrizability and thus ensures positivity of the capacity of the overall communication channel. Furthermore, the capacity of the identical state-constrained composite AVBSC is continuous and shows super-activation, a phenomenon which was hitherto deemed impossible for classical communication without secrecy constraints. Subsuming, spatial and frequency diversity are enablers for reliable communication over communication channels with arbitrarily varying interference.

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arXiv2017

On the Continuity of the Secrecy Capacity of Compound and Arbitrarily Varying Wiretap Channels

The wiretap channel models secure communication between two users in the presence of an eavesdropper who must be kept ignorant of transmitted messages. The performance of such a system is usually characterized by its secrecy capacity which determines the maximum transmission rate of secure communication. In this paper, the issue of whether or not the secrecy capacity is a continuous function of the system parameters is examined. In particular, this is done for channel uncertainty modeled via compound channels and arbitrarily varying channels, in which the legitimate users know only that the true channel realization is from a pre-specified uncertainty set. In the former model, this realization remains constant for the entire duration of transmission, while in the latter the realization varies from channel use to channel use in an unknown and arbitrary manner. These models not only capture the case of channel uncertainty, but are also suitable for modeling scenarios in which a malicious adversary jams or otherwise influence the legitimate transmission. The secrecy capacity of the compound wiretap channel is shown to be robust in the sense that it is a continuous function of the uncertainty set. Thus, small variations in the uncertainty set lead to small variations in secrecy capacity. On the other hand, the deterministic secrecy capacity of the \emph{arbitrarily varying wiretap channel} is shown to be discontinuous in the uncertainty set meaning that small variations can lead to dramatic losses in capacity.

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arXiv2017

Randomness cost of symmetric twirling

We study random unitary channels which reproduce the action of the twirling channel corresponding to the representation of the symmetric groupon an n-fold tensor product. We derive upper andlower bounds on the randomness cost of implementing such a map which depend exponentially on the number of systems. Consequently, symmetrictwirling can be regarded as a reasonable Shannon theoretic protocol. On the other hand, such protocols are disqualified by their resource-inefficiency in situations where randomness is a costly resource.

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arXiv2017

Classical-Quantum Arbitrarily Varying Wiretap Channel: Secret Message Transmission under Jamming Attacks

We analyze arbitrarily varying classical-quantum wiretap channels.These channels are subject to two attacks at the same time: one passive (eavesdropping), and one active (jamming). We progress on previous works by introducing a reduced class of allowed codes that fulfills a more stringent secrecy requirement than earlier definitions. In addition, we prove that non-symmetrizability of the legal link is suficient for equality of the deterministic and the common randomness assisted secrecy capacities. At last, we focus on analytic properties of both secrecy capacities: We completely characterize their discontinuity points, and their super-activation properties.

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arXiv2017

Entanglement-assisted classical capacities of compound and arbitrarily varying quantum channels

We consider classical message transmission under entanglement assistance for compound memoryless and arbitrarily varying quantum channels. In both cases, we prove general coding theorems together with corresponding weak converse bounds. In this way, we obtain single-letter characterizations of the entanglement-assisted classical capacities for both channel models. Moreover, we show that the entanglement-assisted classical capacity does exhibit no strong converse property for some compound quantum channels for the average as well as the maximal error criterion. A strong converse to the entanglement-assisted classical capacities does hold for each arbitrarily varying quantum channel.

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arXiv2016

Classical - Quantum Arbitrarily Varying Wiretap Channel: Common Randomness Assisted Code and Continuity

We determine the secrecy capacities under common randomness assisted coding of arbitrarily varying classical-quantum wiretap channels.Furthermore, we determine the secrecy capacity of a mixed channel model which is compound from the sender to the legal receiver and varies arbitrarily from the sender to the eavesdropper. As an application we examine when the secrecy capacity is a continuous function of the system parameters and show that resources, i.e., having access to a perfect copy of the outcome of a random experiment. are helpful for channel stability.

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arXiv2016

Classical-Quantum Arbitrarily Varying Wiretap Channel: Ahlswede dichotomy, Positivity, Resources, Super Activation

We establish Ahlswede dichotomy for arbitrarily varying classical-quantum wiretap channels. This means that either the deterministic secrecy capacity of an arbitrarily varying classical-quantum wiretap channel is zero or it equals its randomness-assisted secrecy capacity. We analyze the secrecy capacity of arbitrarily varying classical-quantum wiretap channels when the sender and the receiver use various resources. It turns out that having randomness, common randomness, and correlation as resources are very helpful for achieving a positive deterministic secrecy capacity of arbitrarily varying classical-quantum wiretap channels. We prove the phenomenon super-activation for arbitrarily varying classical-quantum wiretap channels, i.e., if we use two arbitrarily varying classical-quantum wiretap channels, both with zero deterministic secrecy capacity together, they allow perfect secure transmission.

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arXiv2016

Distillation of secret key from a class of compound memoryless quantum sources

We consider secret-key distillation from tripartite compound classical-quantum-quantum (cqq) sources with free forward public communication under strong security criterion. We design protocols which are universally reliable and secure in this scenario. These are shown to achieve asymptotically optimal rates as long as a certain regularity condition is fulfilled by the the set of its generating density matrices. We derive a multi-letter formula which describes the optimal forward secret-key capacity for all compound cqq sources being regular in this sense. We also determine the forward secret-key distillation capacity for situations, where the legitimate sending party has perfect knowledge of his/her marginal state deriving from the source statistics. In this case regularity conditions can be dropped. Our results show that the capacities with and without the mentioned kind of state knowledge are equal as long as the source is generated by a regular set of density matrices. We demonstrate that regularity of cqq sources is not only a technical but also an operational issue. For this reason, we give an example of a source which has zero secret-key distillation capacity without sender knowledge, while achieving positive rates is possible if sender marginal knowledge is provided.

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arXiv2016

On Secure Computation Over the Binary Modulo-2 Adder Multiple-Access Wiretap Channel

In this paper, the problem of securely computing a function over the binary modulo-2 adder multiple-access wiretap channel is considered. The problem involves a legitimate receiver that wishes to reliably and efficiently compute a function of distributed binary sources while an eavesdropper has to be kept ignorant of them. In order to characterize the corresponding fundamental limit, the notion of secrecy computation-capacity is introduced. Although determining the secrecy computation-capacity is challenging for arbitrary functions, it surprisingly turns out that if the function perfectly matches the algebraic structure of the channel and the joint source distribution fulfills certain conditions, the secrecy computation-capacity equals the computation capacity, which is the supremum of all achievable computation rates without secrecy constraints. Unlike the case of securely transmitting messages, no additional randomness is needed at the encoders nor does the legitimate receiver need any advantage over the eavesdropper. The results therefore show that the problem of securely computing a function over a multiple-access wiretap channel may significantly differ from the one of securely communicating messages.

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arXiv2016

The Arbitrarily Varying Wiretap Channel - Secret Randomness, Stability and Super-Activation

We define the common randomness assisted capacity of an arbitrarily varying channel (AVWC) when the Eavesdropper is kept ignorant about the common randomness. We prove a multi-letter capacity formula for this model. We prove that, if enough common randomness is used, the capacity formula can be given a single-shot form again. We then consider the opposite extremal case, where no common randomness is available. It is known that the capacity of the system can be discontinuous under these circumstances. We prove here that it is still stable in the sense that it is continuous around its positivity points. We further prove that discontinuities can only arise if the legal link is symmetrizable and characterize the points where it is positive. These results shed new light on the design principles of communication systems with embedded security features. At last we investigate the effect of super-activation of the message transmission capacity of AVWCs under the average error criterion. We give a complete characterization of those AVWCs that may be super-activated. The effect is thereby also related to the (conjectured) super-activation of the common randomness assisted capacity of AVWCs with an eavesdropper that gets to know the common randomness. Super-activation is based on the idea of "wasting" a few bits of non-secret messages in order to enable provably secret transmission of a large bulk of data, a concept that may prove to be of further importance in the design of communication systems. In this work we provide further insight into this phenomenon by providing a class of codes that is capacity-achieving and does not convey any information to the Eavesdropper.

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arXiv2016

Secret-Key Generation Using Compound Sources and One-Way Public Communication

In the classical Secret-Key generation model, Common Randomness is generated by two terminals based on the observation of correlated components of a common source, while keeping it secret from a non-legitimate observer. It is assumed that the statistics of the source are known to all participants. In this work, the Secret-Key generation based on a compound source is studied where the realization of the source statistic is unknown. The protocol should guarantee the security and reliability of the generated Secret-Key, simultaneously for all possible realizations of the compound source. A single-letter lower-bound of the Secret-Key capacity for a finite compound source is derived as a function of the public communication rate constraint. A multi-letter capacity formula is further computed for a finite compound source for the case in which the public communication is unconstrained. Finally a single-letter capacity formula is derived for a degraded compound source with an arbitrary set of source states and a finite set of marginal states.

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arXiv2016

The Classical-Quantum Channel with Random State Parameters Known to the Sender

We study an analog of the well-known Gel'fand Pinsker Channel which uses quantum states for the transmission of the data. We consider the case where both the sender's inputs to the channel and the channel states are to be taken from a finite set (cq-channel with state information at the sender). We distinguish between causal and non-causal channel state information at the sender. The receiver remains ignorant, throughout. We give a single-letter description of the capacity in the first case. In the second case we present two different regularized expressions for the capacity. It is an astonishing and unexpected result of our work that a simple change from causal to non-causal channel state information at the encoder causes the complexity of a numerical computation of the capacity formula to change from trivial to seemingly difficult. Still, even the non-single letter formula allows one to draw nontrivial conclusions, for example regarding continuity of the capacity with respect to changes in the system parameters. The direct parts of both coding theorems are based on a special class of POVMs which are derived from orthogonal projections onto certain representations of the symmetric groups. This approach supports a reasoning that is inspired by the classical method of types. In combination with the non-commutative union bound these POVMs yield an elegant method of proof for the direct part of the coding theorem in the first case.

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arXiv2016

On The Capacity of Broadcast Channels With Degraded Message Sets and Message Cognition Under Different Secrecy Constraints

This paper considers a three-receiver broadcast channel with degraded message sets and message cognition. The model consists of a common message for all three receivers, a private common message for only two receivers and two additional private messages for these two receivers, such that each receiver is only interested in one message, while being fully cognizant of the other one. First, this model is investigated without any secrecy constraints, where the capacity region is established, showing that the straightforward extension of the Körner and Marton inner bound to the investigated scenario is optimal. In particular, this agrees with Nair and Wang's result, which states that the idea of indirect decoding - introduced to improve the Körner and Marton inner bound - does not provide a better region for this scenario. Further, some secrecy constraints are introduced by letting the private messages to be confidential ones. Two different secrecy criteria are considered: joint secrecy and individual secrecy. For both criteria, a general achievable rate region is provided. Moreover, the joint and individual secrecy capacity regions are established, if the two legitimate receivers are more capable than the eavesdropper. The established capacity regions indicate that the individual secrecy criterion can provide a larger capacity region as compared to the joint one, because each cognizant message can be used as a secret key for the other individual message. Further, the joint secrecy capacity is established for a more general class of more capable channels, where only one of the two legitimate receivers is more capable than the eavesdropper. This was done by showing that principle of indirect decoding introduced by Nair and El Gamal is optimal for this class of channels. This result is in contrast with the nonsecrecy case, where the indirect decoding does not provide any gain.

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arXiv2015

A channel under simultaneous jamming and eavesdropping attack---correlated random coding capacities under strong secrecy criteria

We give a complete characterization of the correlated random coding secrecy capacity of arbitrarily varying wiretap channels (AVWCs). We apply two alternative strong secrecy criteria, which both lead to the same multi-letter formula. The difference of these criteria lies in the treatment of correlated randomness, they coincide in the case of uncorrelated codes. On the basis of the derived formula, we show that the correlated random coding secrecy capacity is continuous as a function of the AVWC, in contrast to the discontinuous uncorrelated coding secrecy capacity. In the proof of the secrecy capacity formula for correlated random codes, we apply an auxiliary channel which is compound from the sender to the intended receiver and arbitrarily varying from the sender to the eavesdropper.

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arXiv2015

Broadcast Classical-Quantum Capacity Region of Two-Phase Bidirectional Relaying Channel

We study a three-node quantum network which enables bidirectional communication between two nodes with a half-duplex relay node. A decode-and-forward protocol is used to perform the communication in two phases. In the first phase, the messages of two nodes are transmitted to the relay node. In the second phase, the relay node broadcasts a re-encoded composition to the two nodes. We determine the capacity region of the broadcast phase.

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