arXiv subjects

Christian Deppe

Publications and source records attributed to Christian Deppe.

At least 127 records · Page 7Linked to original sources

arXiv2021

Common Randomness Generation over Slow Fading Channels

This paper analyzes the problem of common randomness (CR) generation from correlated discrete sources aided by unidirectional communication over Single-Input Single-Output (SISO) slow fading channels with additive white Gaussian noise (AWGN) and arbitrary state distribution. Slow fading channels are practically relevant for wireless communications. We completely solve the SISO slow fading case by establishing its corresponding outage CR capacity using our characterization of its channel outage capacity. The generated CR could be exploited to improve the performance gain in the identification scheme. The latter is known to be more efficient than the classical transmission scheme in many new applications, which demand ultra-reliable low latency communication.

cs.IT↗

arXiv2021

The Computational and Latency Advantage of Quantum Communication Networks

This article summarises the current status of classical communication networks and identifies some critical open research challenges that can only be solved by leveraging quantum technologies. By now, the main goal of quantum communication networks has been security. However, quantum networks can do more than just exchange secure keys or serve the needs of quantum computers. In fact, the scientific community is still investigating on the possible use cases/benefits that quantum communication networks can bring. Thus, this article aims at pointing out and clearly describing how quantum communication networks can enhance in-network distributed computing and reduce the overall end-to-end latency, beyond the intrinsic limits of classical technologies. Furthermore, we also explain how entanglement can reduce the communication complexity (overhead) that future classical virtualised networks will experience.

cs.IT↗

arXiv2021

On the Semi-Decidability of Remote State Estimation and Stabilization via Noisy Communication Channels

We consider the task of remote state estimation and stabilization of disturbed linear plants via noisy communication channels. In 2007 Matveev and Savkin established a surprising link between this problem and Shannon's theory of zero-error communication. By applying very recent results of computability of the channel reliability function and computability of the zero-error capacity of noisy channels by Boche and Deppe, we analyze if, on the set of linear time-invariant systems paired with a noisy communication channel, it is uniformly decidable by means of a Turing machine whether remote state estimation and stabilization is possible. The answer to this question largely depends on whether the plant is disturbed by random noise or not. Our analysis incorporates scenarios both with and without channel feedback, as well as a weakened form of state estimation and stabilization. In the broadest sense, our results yield a fundamental limit to the capabilities of computer-aided design and autonomous systems, assuming they are based on real-world digital computers.

math.OC↗

arXiv2021

Coding with Noiseless Feedback over the Z-channel

In this paper, we consider encoding strategies for the Z-channel with noiseless feedback. We analyze the combinatorial setting where the maximum number of errors inflicted by an adversary is proportional to the number of transmissions, which goes to infinity. Without feedback, it is known that the rate of optimal asymmetric-error-correcting codes for the error fraction $τ\ge 1/4$ vanishes as the blocklength grows. In this paper, we give an efficient feedback encoding scheme with $n$ transmissions that achieves a positive rate for any fraction of errors $τ<1$ and $n\to\infty$. Additionally, we state an upper bound on the rate of asymptotically long feedback asymmetric error-correcting codes.

cs.IT↗

arXiv2021

Quantum Channel State Masking

Communication over a quantum channel that depends on a quantum state is considered when the encoder has channel side information (CSI) and is required to mask information on the quantum channel state from the decoder. A full characterization is established for the entanglement-assisted masking equivocation region, and a regularized formula is given for the quantum capacity-leakage function without assistance. For Hadamard channels without assistance, we derive single-letter inner and outer bounds, which coincide in the standard case of a channel that does not depend on a state.

cs.IT↗

arXiv2020

Algorithms for $q$-ary Error-Correcting Codes with Limited Magnitude and Feedback

Berlekamp and Zigangirov completely determined the capacity error function for binary error correcting codes with noiseless feedback. It is still an unsolved problem if the upper bound for the capacity error function in the non-binary case of Ahlswede, Lebedev, and Deppe is sharp. We consider wraparound channels with limited magnitude and noiseless feedback. We completely determine the capacity error function for all $q$-ary wraparound channels with a magnitude of level $r$. All of our algorithms use partial noiseless feedback. Furthermore, a special case of the problem is equivalent to Shannon's zero-error problem.

cs.IT↗

arXiv2020

Computability of the Zero-Error capacity with Kolmogorov Oracle

The zero-error capacity of a discrete classical channel was first defined by Shannon as the least upper bound of rates for which one transmits information with zero probability of error. The problem of finding the zero-error capacity $C_0$, which assigns a capacity to each channel as a function, was reformulated in terms of graph theory as a function $Θ$, which assigns a value to each simple graph. This paper studies the computability of the zero-error capacity. For the computability, the concept of a Turing machine and a Kolmogorov oracle is used. It is unknown if the zero-error capacity is computable in general. We show that in general the zero-error capacity is semi computable with the help of a Kolmogorov Oracle. Furthermore, we show that $C_0$ and $Θ$ are computable functions if and only if there is a computable sequence of computable functions of upper bounds, i.e. the converse exist in the sense of information theory, which pointwise converge to $C_0$ or $Θ$. Finally, we examine Zuiddam's characterization of $C_0$ and $Θ$ in terms of algorithmic computability.

cs.IT↗

arXiv2020

Performance Analysis of Identification Codes

In this paper we analyse the construction of identification codes. Identification codes are based on the question "Is the message I have just received the one I am interested in?", as opposed to Shannon's transmission, where the receiver is interested in not only one, but any message. The advantage of identification is that it allows rates growing double exponentially in the blocklength at the cost of not being able to decode every message, which might be beneficial in certain applications. We focus on a special identification code construction based on two concatenated Reed-Solomon codes and have a closer look at its implementation, analyzing the trade-offs of identification with respect to transmission and the trade-offs introduced by the computational cost of identification codes.

cs.IT↗

arXiv2020

How to apply the rubber method for channels with feedback

We give an overview of applications of the rubber method. The rubber method is a coding algorithm that was developed in 2005 by Ahlswede, Deppe and Lebedev for channels with feedback. It was a big surprise that an encoding strategy that reserves one symbol exclusively as a rubber can sometimes reach the capacity of a channel. Since then, generalizations of the algorithm have been developed. These generalizations can be used for special channels. There are also other ideas for modifying the rubber method.

cs.IT↗

arXiv2020

Bounds for the capacity error function for unidirectional channels with noiseless feedback

In digital systems such as fiber optical communications, the ratio between probability of errors of type $1\to 0$ and $0 \to 1$ can be large. Practically, one can assume that only one type of error can occur. These errors arecalled asymmetric. Unidirectional errors differ from asymmetric type of errors; here both $1 \to 0$ and $0 \to 1$ type of errors are possible, but in any submittedcodeword all the errors are of the same type. This can be generalized for the $q$-ary case. We consider $q$-ary unidirectional channels with feedback and give bounds for the capacity error function. It turns out that the bounds depend on the parity of the alphabet $q$. Furthermore, we show that for feedback, the capacity error function for the binary asymmetric channel is different from the symmetric channel. This is in contrast to the behavior of the function without feedback.

cs.IT↗

arXiv2019

Extending Quantum Links: Modules for Fiber- and Memory-Based Quantum Repeaters

We analyze elementary building blocks for quantum repeaters based on fiber channels and memory stations. Implementations are considered for three different physical platforms, for which suitable components are available: quantum dots, trapped atoms and ions, and color centers in diamond. We evaluate and compare the performances of basic quantum repeater links for these platforms both for present-day, state-of-the-art experimental parameters as well as for parameters that could in principle be reached in the future. The ultimate goal is to experimentally explore regimes at intermediate distances, up to a few 100 km, in which the repeater-assisted secret key transmission rates exceed the maximal rate achievable via direct transmission. We consider two different protocols, one of which is better adapted to the higher source clock rate and lower memory coherence time of the quantum dot platform, while the other circumvents the need of writing photonic quantum states into the memories in a heralded, non-destructive fashion. The elementary building blocks and protocols can be connected in a modular form to construct a quantum repeater system that is potentially scalable to large distances.

quant-ph↗

arXiv2019

Secure and Robust Identification via Classical-Quantum Channels

We study the identification capacity of classical-quantum channels ("cq-channels"), under channel uncertainty and privacy constraints. To be precise, we consider first compound memoryless cq-channels and determine their identification capacity; then we add an eavesdropper, considering compound memoryless wiretap cqq-channels, and determine their secret identification capacity. In the first case (without privacy), we find the identification capacity always equal to the transmission capacity. In the second case, we find a dichotomy: either the secrecy capacity (also known as private capacity) of the channel is zero, and then also the secrecy identification capacity is zero, or the secrecy capacity is positive and then the secrecy identification capacity equals the transmission capacity of the main channel without the wiretapper. We perform the same analysis for the case of arbitrarily varying wiretap cqq-channels (cqq-AVWC), with analogous findings, and make several observations regarding the continuity and super-additivity of the identification capacity in the latter case.

quant-ph↗

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.

cs.IT↗

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.

quant-ph↗

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.

cs.IT↗

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.

cs.IT↗

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.

cs.IT↗

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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