We study communication over a Gaussian multiple-access channel (MAC) with two types of transmitters: Digital transmitters hold a message from a discrete set that needs to be communicated to the receiver with vanishing error probability. Analog transmitters hold sequences of analog values. Some functions of these distributed values (but not the values themselves) need to be conveyed to the receiver, subject to a fidelity criterion such as mean squared error (MSE) or a certain maximum error with given confidence. For the case in which the computed function for the analog transmitters is a sum of values in$[-1,1]$, we derive inner and outer bounds for the tradeoff of digital and analog rates of communication under peak and average power constraints for digital transmitters and a peak power constraint for analog transmitters. We then extend the achievability result to a class of functions that includes all linear and some non-linear functions. This extended scheme works over fading channels as long as full channel state information is available at the transmitter. The practicality of our proposed communication scheme is shown in channel simulations that use a version of the scheme based on low density parity check (LDPC) coding. We evaluate the system performance for different block lengths and Gaussian as well as non-Gaussian noise distributions.

We propose a new proof method for direct coding theorems for wiretap channels where the eavesdropper has access to a quantum version of the transmitted signal on an infinite-dimensional Hilbert space and the legitimate parties communicate through a classical channel or a classical input, quantum output (cq) channel. The transmitter input can be subject to an additive cost constraint, which specializes to the case of an average energy constraint. This method yields errors that decay exponentially with increasing block lengths. Moreover, it provides a guarantee of a quantum version of semantic security, which is an established concept in classical cryptography and physical layer security. Therefore, it complements existing works which either do not prove the exponential error decay or use weaker notions of security. The main part of this proof method is a direct coding result on channel resolvability which states that there is only a doubly exponentially small probability that a standard random codebook does not solve the channel resolvability problem for the cq channel. Semantic security has strong operational implications meaning essentially that the eavesdropper cannot use its quantum observation to gather any meaningful information about the transmitted signal. We also discuss the connections between semantic security and various other established notions of secrecy.

We study communication over a Gaussian multiple-access channel (MAC) with two types of transmitters: Digital transmitters hold a message from a discrete set that needs to be communicated to the receiver. Analog transmitters hold sequences of analog values, and some function of these distributed values (but not the values themselves) need to be conveyed to the receiver. For the digital messages, it is required that they can be decoded error free at the receiver with high probability while the recovered analog function values have to satisfy a fidelity criterion such as an upper bound on mean squared error (MSE) or a certain maximum error with a given confidence. For the case in which the computed function for the analog transmitters is a sum of values in [-1, 1], we derive inner and outer bounds for the tradeoff of digital and analog rates of communication under peak and average power constraints for digital transmitters and a peak power constraint for analog transmitters. We then extend the achievability part of our result to a larger class of functions that includes all linear, but also some non-linear functions.

Lagrange coded computation (LCC) is essential to solving problems about matrix polynomials in a coded distributed fashion; nevertheless, it can only solve the problems that are representable as matrix polynomials. In this paper, we propose AICC, an AI-aided learning approach that is inspired by LCC but also uses deep neural networks (DNNs). It is appropriate for coded computation of more general functions. Numerical simulations demonstrate the suitability of the proposed approach for the coded computation of different matrix functions that are often utilized in digital signal processing.

We propose a new proof method for direct coding theorems for wiretap channels where the eavesdropper has access to a quantum version of the transmitted signal on an infinite dimensional Hilbert space. This method yields errors that decay exponentially with increasing block lengths. Moreover, it provides a guarantee of a quantum version of semantic security, which is an established concept in classical cryptography and physical layer security. Semantic security has strong operational implications meaning essentially that the eavesdropper cannot use its quantum observation to gather any meaningful information about the transmitted signal. Therefore, it complements existing works which either do not prove the exponential error decay or use weaker notions of security. The main part of this proof method is a direct coding result on channel resolvability which states that there is only a doubly exponentially small probability that a standard random codebook does not solve the channel resolvability problem for the classical-quantum channel.

We propose a new method to protect Over-The-Air (OTA) computation schemes against passive eavesdropping. Our method uses a friendly jammer whose signal is – contrary to common intuition – stronger at the legitimate receiver than it is at the eavesdropper. It works for a large class of analog OTA computation schemes and we give two examples for such schemes that are contained in this class. The key ingredients in proving the security guarantees are a known result on channel resolvability and a generalization of existing results on coding for compound channels.

This paper addresses the problem of Over-The-Air (OTA) computation in wireless networks which has the potential to realize huge efficiency gains for instance in training of distributed ML models. We provide non-asymptotic, theoretical guarantees for OTA computation in fast-fading wireless channels where the fading and noise may be correlated. The distributions of fading and noise are not restricted to Gaussian distributions, but instead are assumed to follow a distribution in the more general sub-gaussian class. Furthermore, our result does not make any assumptions on the distribution of the sources and therefore, it can, e.g., be applied to arbitrarily correlated sources. We illustrate our analysis with numerical evaluations for OTA computation of two example functions in large wireless networks: the arithmetic mean and the Euclidean norm.

We characterize the resolvability region for a large class of point-to-point channels with continuous alphabets. In our direct result, we prove not only the existence of good resolvability codebooks, but adapt an approach based on the Chernoff-Hoeffding bound to the continuous case showing that the probability of drawing an unsuitable codebook is doubly exponentially small. For the converse part, we show that our previous elementary result carries over to the continuous case easily under some mild continuity assumption.

This paper extends the weak secrecy results of Liu et al. for broadcast channels with two confidential messages to strong secrecy. Our results are based on an extension of the techniques developed by Hou and Kramer on bounding Kullback-Leibler divergence in the context of resolvability and effective secrecy.

In this work the arbitrarily varying wiretap channel AVWC under the average error criterion and the strong secrecy criterion is studied. We show that in the case of a non-symmetrisable channel to the legitimate receiver the deterministic code secrecy capacity equals the random code secrecy capacity and thus we establish a result for the AVWC similar to that of Ahlswede's dichotomy for ordinary AVCs. We derive a lower bound on the random code secrecy capacity in the case of a best channel to the eavesdropper. We further prove upper bounds on the deterministic code secrecy capacity, which in special cases results in explicit expressions of the secrecy capacity.

We consider quantum state merging under uncertainty of the state held by the merging parties. More precisely we determine the optimal entanglement rate of a merging process when the state is unknown up to membership in a certain set of states. We find that merging is possible at the lowest rate allowed by the individual states.

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 quite strong secrecy 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 and a multi-letter converse to the secrecy capacity of the compound wiretap channel without channel state information.

The goal of this paper is to provide a rigorous information-theoretic analysis of subnetworks of interference networks. We prove two coding theorems for the compound multiple-access channel (MAC) with an arbitrary number of channel states. The channel state information at the transmitters is such that each transmitter has a finite partition of the set of states and knows which element of the partition the actual state belongs to. The receiver may have arbitrary channel state information. The first coding theorem is for the case that both transmitters have a common message and that each has an additional private message. The second coding theorem is for the case where rate-constrained, but noiseless transmitter cooperation is possible. This cooperation may be used to exchange information about channel state information as well as the messages to be transmitted. The cooperation protocol used here generalizes Willems' conferencing. We show how this models base station cooperation in modern wireless cellular networks used for interference coordination and capacity enhancement. In particular, the coding theorem for the cooperative case shows how much cooperation is necessary in order to achieve maximal capacity in the network considered.

The concept of bidirectional relaying is a key technique to improve the performance in wireless networks such as sensor, ad-hoc, and even cellular systems. It applies to three-node networks, where a relay node establishes a bidirectional communication between two other nodes using a decode-and-forward protocol. We assume that the communication is disturbed by unknown varying interference and analyze the impact of the degree of coordination. We show that the unknown variation of the interference has a dramatic impact on the communication. For traditional interference coordination it can lead to channels which completely prohibit any reliable communication. Anyhow, by allowing a relay-to-receivers coordination, communication can also be established in such situations where the traditional approach fails.

The concept of bidirectional relaying shows the potential to improve the performance in wireless networks such as sensor, ad-hoc, and even cellular systems. It applies to three-node networks, where a relay node establishes a bidirectional communication between two other nodes. In the first phase of a decode-and-forward protocol, the two nodes transmit their messages to a relay node, which decodes them. In the succeeding bidirectional broadcast phase, the relay broadcasts a re-encoded composition of them so that both nodes can decode the other's message using their own message as side information. We assume that the transmission is affected by unknown varying channels. Unfortunately, the unknown variation of the channel can lead to channels which completely prohibit any reliable communication. In this work, we analyze the bidirectional broadcast phase under list decoding and show that this decoding technique can improve the performance significantly in the sense that it allows to transmit reliably in scenarios where usual decoding schemes fail.

We derive a regularized formula for the common randomness assisted entanglement transmission capacity of finite arbitrarily varying quantum channels (AVQC's). For finite AVQC's with positive capacity for classical message transmission we show, by derandomization through classical forward communication, that the random capacity for entanglement transmission equals the deterministic capacity for entanglement transmission. This is a quantum version of the famous Ahlswede dichotomy. In the infinite case, we derive a similar result for certain classes of AVQC's. At last, we give two possible definitions of symmetrizability of an AVQC.

We characterize the capacity region of the compound Discrete Memoryless Multiple Access Channel, where both transmitters have an additional common message. The channel state information is as follows: for each transmitter, there is a finite partition of the set of channels. Each transmitter knows which element of his partition the channel actually used belongs to. The capacity region is not affected by the amount of channel state information at the receiver, which may be arbitrary.

The concept of bidirectional relaying is a key technique to improve the performance in future wireless networks. It applies to three-node networks, where a relay node establishes a bidirectional communication between two other nodes using a decode-and-forward protocol. It divides the whole communication into two phases, namely the multiple access and bidirectional broadcast phase. Here, we concentrate on the second phase, which is also known as the bidirectional broadcast channel, and assume that the transmission is affected by arbitrarily varying channels. We impose constraints on the permissible input and state sequences and derive the capacity regions for random and deterministic coding.

Bidirectional relaying is a promising approach to improve the performance in wireless networks such as sensor, ad-hoc, and even cellular systems. Bidirectional relaying applies to three-node networks, where a relay establishes a bidirectional communication between two other nodes using a decode-and-forward protocol. First, the two nodes transmit their messages to the relay which decodes them. Then, the relay broadcasts a reencoded message in such a way that both nodes can decode their intended message using their own message as side information. We consider uncertainty in the channel state information (CSI) and assume that all nodes only know that the channel over which the transmission takes place is from a pre-specified set of channels. In this work, we concentrate on the second phase, which is called the compound bidirectional broadcast channel. We present a robust coding strategy which enables reliable communication under channel uncertainty and show that this strategy actually achieves the compound capacity. Further, we analyze scenarios where either the receivers or the transmitter have perfect CSI. We show that CSI at the receivers does not affect the maximal achievable rates, while CSI at the transmitter improves the capacity region. A numerical example and a game-theoretic interpretation complete this work.

In this work we study optimal coding strategies for bidirectional relaying under the condition of arbitrarily varying channels. We consider a three-node network where a relay node establishes a bidirectional communication between two nodes using a spectrally efficient decode-and-forward protocol. In the first phase the two nodes transmit their messages to the relay node, which decodes them. In the succeeding bidirectional broadcast phase the relay node broadcasts an optimal re-encoded composition of them so that both nodes can decode the intended message using their own message as side information. We assume that the whole communication is affected by channels which vary in an unknown and arbitrary manner during the transmission so that all nodes have only imperfect channel state information. For both phases of the bidirectional relaying protocol we present robust coding strategies, which mitigate the uncertainty in channel state information so that reliable communication can be guaranteed. Further, we characterize the corresponding capacity regions for random and deterministic coding strategies.

We consider the broadcast phase of a spectrally efficient two-phase decode-and-forward protocol which is used by a relay node to establish a bidirectional communication between two nodes. In the first phase the two nodes transmit their message to the relay node which decodes the messages. In the succeeding phase the relay node broadcasts a re-encoded composition of them. We consider imperfect channel knowledge and assume that all nodes merely know that the channel used for the transmission belongs to a set of channels. This is called compound bidirectional broadcast channel. We derive a universal strategy which achieves capacity and show that perfect channel state information (CSI) at the receivers does not lead to an increased capacity region. Otherwise, perfect CSI at the transmitter can advantageously be used to enlarge the capacity region. Finally, we give a game-theoretic interpretation as a game against nature.

We determine the optimal achievable rate at which entanglement can be reliably transmitted when the memoryless channel used during transmission is unknown both to sender and receiver. To be more precise, we assume that both of them only know that the channel belongs to a given set of channels. Thus, they have to use encoding and decoding schemes that work well for the whole set.

We determine the capacity of compound classical-quantum channels. As a consequence, we obtain the capacity formula for the averaged classical-quantum channels. The capacity result for compound channels demonstrates, as in the classical setting, the existence of reliable universal classical-quantum codes in scenarios where the onlya prioriinformation about the channel used for the transmission of information is that it belongs to a given set of memoryless classical-quantum channels. Our approach is based on a universal classical approximation of the quantum relative entropy which in turn relies on a universal hypothesis testing result.

In this paper we extend recent coding results by Datta and Dorlas on classical capacity of averaged quantum channels with finitely many memoryless branches to arbitrary number of branches. Only assumption in our approach is that the channel satisfies some weak measurability properties. Our approach to the direct coding theorem is based on our previous work on compound classical-quantum channels. The weak converse requires an alternative characterization of the essential infimum and the remaining proof proceeds via application of Holevo’s bound and Fano’s inequality.

We consider transmission over a wireless multiple antenna communication system operating in a Rayleigh flat fading environment with no channel state information at the receiver and the transmitter. We show that, subject to the average power constraint, the support of the capacity achieving input distribution is bounded. Moreover, we show by a simple example concerning the identity theorem (or uniqueness theorem) from the complex analysis in several variables that some of the existing results in the field are not rigorous.

We consider the broadcast phase of a three-node network, where a relay node establishes a bidirectional communication between two nodes using a spectrally efficient two-phase decode-and-forward protocol. In the first phase the two nodes transmit their messages to the relay node. Then the relay node decodes the messages and broadcasts a re-encoded composition of them in the second phase. We consider Gaussian MIMO channels and determine the capacity region for the second phase which we call the Gaussian MIMO bidirectional broadcast channel.

We determine the capacity of compound classicalquantum channels. The capacity result for compound channels demonstrates, as in the classical setting, the existence of reliable universal classical-quantum codes in scenarios where the only a priori information about the channel used for the transmission of information is that it belongs to a given set of memoryless classical-quantum channels. Our approach is based on the universal classical approximation of the quantum relative entropy which in turn relies on the universal hypothesis testing results.

In this paper, we consider ergodic causal classical-quantum channels (cq-channels) which additionally have a decaying input memory. In the first part, we develop some structural properties of ergodic cq-channels and provide equivalent conditions for ergodicity. In the second part, we prove the coding theorem with weak converse for causal ergodic cq-channels with decaying input memory. Our proof is based on the possibility to introduce a joint input–output state for the cq-channels and an application of the Shannon–McMillan theorem for ergodic quantum states. In the last part of the paper, it is shown how this result implies a coding theorem for the classical capacity of a class of causal ergodic quantum channels.

In a three-node network bidirectional communication between two nodes can be enabled by a half-duplex relay node with a decode-and-forward protocol. In the first phase, the messages of two nodes are transmitted to the relay node. In the second phase a re-encoded composition is broadcasted by the relay node. In this work the capacity region of the broadcast phase in terms of the maximal probability of error is determined. It is characterized by the mutual informations of the separate channels coupled by the common input.

In this contribution we describe some structural properties of ergodic classical-quantum channels and provide several equivalent conditions of ergodicity of such channels. In the second part we sketch the coding theorem with the weak converse for ergodic input-memoryless causal classical-quantum channels. Full proofs and several extensions of the results described here are contained in a accompanying paper.

In our previous work we determined the weak capacity region for the broadcast phase of two-phase bidirectional relay channel. It turned out that the set of achievable rates obtained by optimizing over the two communication phases exceeds that obtained by using the network coding principle, i.e. by applying XOR to the decoded messages. In this paper we supplement our result by a proof of the strong converse with respect to the maximum error probability to the coding theorem for the broadcast phase. This result implies that the capacity region of that phase remains constant for a certain range of values of average error parameters [epsiv1,epsiv2].

We describe the structure of optimal Input covariance matrices for single user multiple-input/multiple-output (MIMO) communication system with covariance feedback and for general correlated fading. Our approach is based on the novel concept of right commutant and recovers previously derived results for the Kronecker product models. Conditions are derived which allow a significant simplification of the optimization problem.