The capacity regions of vector, or multiple-input multiple-output, Gaussian interference channels are established for very strong interference and aligned strong interference. Furthermore, the sum-rate capacities are established for Z interference, noisy interference, and mixed (aligned weak/intermediate and aligned strong) interference. These results generalize known results for scalar Gaussian interference channels.
This paper studies the capacity of a class of discrete memoryless interference channels where interference is defined analogous to that of Gaussian interference channel with one-sided weak interference. The sum-rate capacity of this class of channels is determined. As with the Gaussian case, the sum-rate capacity is achieved by letting the transceiver pair subject to interference communicate at a rate such that its message can be decoded at the unintended receiver using single user detection. It is also established that this class of discrete memoryless interference channels is equivalent in c…
This paper studies the capacity of single-source single-sink noiseless networks under adversarial or arbitrary errors on no more than z edges. Unlike prior papers, which assume equal capacities on all links, arbitrary link capacities are considered. Results include new upper bounds, network error correction coding strategies, and examples of network families where our bounds are tight. An example is provided of a network where the capacity is 50% greater than the best rate that can be achieved with linear coding. While coding at the source and sink suffices in networks with equal link capaciti…
We determine the capacity of the classical compound quantum wiretapper channel with channel state information at the transmitter. Moreover we derive a lower bound on the capacity of this channel without channel state information and determine the capacity of the classical quantum compound wiretap channel with channel state information at the transmitter.
While capacities of discrete memoryless channels are well studied, it is still not possible to obtain a closed-form expression for the capacity of an arbitrary discrete memoryless channel. This paper describes an elementary technique based on Karush Kuhn Tucker (KKT) conditions to obtain (1) a good upper bound of a discrete memoryless channel having an invertible positive channel matrix and (2) a closed-form expression for the capacity if the channel matrix satisfies certain conditions related to its singular value and its Gershgorin disk.
The zero-error capacity of a channel is the rate at which it can send information perfectly, with zero probability of error, and has long been studied in classical information theory. We show that the zero-error capacity of quantum channels exhibits an extreme form of non-additivity, one which is not possible for classical channels, or even for the usual capacities of quantum channels. By combining probabilistic arguments with algebraic geometry, we prove that there exist channels E1 and E2 with no zero-error classical capacity whatsoever, C_0(E1) = C_0(E2) = 0, but whose joint zero-error quan…
Combining an information-theoretic approach to fingerprinting with a more constructive, statistical approach, we derive new results on the fingerprinting capacities for various informed settings, as well as new log-likelihood decoders with provable code lengths that asymptotically match these capacities. The simple decoder built against the interleaving attack is further shown to achieve the simple capacity for unknown attacks, and is argued to be an improved version of the recently proposed decoder of Oosterwijk et al. With this new universal decoder, cut-offs on the bias distribution functio…
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 …
In this work, we address the problem of optimal spectrum management in continuous frequency domain in multiuser interference channels. The objective is to maximize the weighted sum of user capacities. Our main results are as follows: (i) For frequency-selective channels, we prove that in an optimal solution, each user uses maximum power; this result also generalizes to the cases where the objective is to maximize the weighted product (i.e., proportional fairness) of user capacities. (ii) For the special case of two users in flat channels, we solve the problem optimally.
We focus on classical and quantum list decoding. The capacity of list decoding was obtained by Nishimura in the case when the number of list does not increase exponentially. However, the capacity of the exponential-list case is open even in the classical case while its converse part was obtained by Nishimura. We derive the channel capacities in the classical and quantum case with an exponentially increasing list. The converse part of the quantum case is obtained by modifying Nagaoka's simple proof for strong converse theorem for channel capacity. The direct part is derived by a quite simple ar…
Two new classes of quantum channels, which we call more capable and less noisy, are introduced. The more capable class consists of channels such that the quantum capacities of the complementary channels to the environments are zero. The less noisy class consists of channels such that the private capacities of the complementary channels to the environment are zero. For the more capable class, it is clarified that the private capacity and quantum capacity coincide. For the less noisy class, it is clarified that the private capacity and quantum capacity can be single letter characterized.
Uplink and downlink cloud radio access networks are modeled as two-hop K-user L-relay networks, whereby small base-stations act as relays for end-to-end communications and are connected to a central processor via orthogonal fronthaul links of finite capacities. Simplified versions of network compress-forward (or noisy network coding) and distributed decode-forward are presented to establish inner bounds on the capacity region for uplink and downlink communications, that match the respective cutset bounds to within a finite gap independent of the channel gains and signal to noise ratios. These …
Quantum capacities are fundamental quantities that are notoriously hard to compute and can exhibit surprising properties such as superadditivity. Thus, a vast amount of literature is devoted to finding tight and computable bounds on these capacities. We add a new viewpoint by giving operationally motivated bounds on several capacities, including the quantum capacity and private capacity of a quantum channel and the one-way distillable entanglement and private key of a quantum state. These bounds are generally phrased in terms of capacity quantities involving the complementary channel or state.…
The first result is on the separability of the unicast capacity of stationary multi-channel multi-radio wireless networks, i.e., whether the capacity of such a network is equal to the sum of the capacities of the corresponding single-channel single-radio wireless networks. For both the Arbitrary Network model and the Random Network model, given a channel assignment, the separability property does not always hold. However, if the number of radio interfaces at each node is equal to the number of channels, the separability property holds. The second result is on the impact of multi-channel routin…
Radio-frequency energy harvesting constitutes an effective way to prolong the lifetime of wireless networks, wean communication devices off the battery and power line, benefit the energy saving and lower the carbon footprint of wireless communications. In this paper, an interference aided energy harvesting scheme is proposed for cooperative relaying systems, where energy-constrained relays harvest energy from the received information signal and co-channel interference signals, and then use that harvested energy to forward the correctly decoded signal to the destination. The time-switching sche…
In communication networks, cooperative strategies are coding schemes where network nodes work together to improve network performance metrics such as sum-rate. This work studies encoder cooperation in the setting of a discrete multiple access channel with two encoders and a single decoder. A node in the network that is connected to both encoders via rate-limited links, referred to as the cooperation facilitator (CF), enables the cooperation strategy. Previously, the authors presented a class of multiple access channels where the average-error sum-capacity has an infinite derivative in the limi…
This work introduces the particle-intensity channel (PIC) as a model for molecular communication systems and characterizes the capacity limits as well as properties of the optimal (capacity-achieving) input distributions for such channels. In the PIC, the transmitter encodes information, in symbols of a given duration, based on the probability of particle release, and the receiver detects and decodes the message based on the number of particles detected during the symbol interval. In this channel, the transmitter may be unable to control precisely the probability of particle release, and the r…
The capacity of classical channels is convex. This is not the case for the quantum capacity of a channel: the capacity of a mixture of different quantum channels exceeds the mixture of the individual capacities and thus is non-convex. Here we show that this effect goes beyond the quantum capacity and holds for the private and classical environment-assisted capacities of quantum channels.
On the Capacity of DNA Labeling in the Single-Label Setting
Guangzhou Institute of Technology, Xidian University（西安电子科技大学广州研究院）；State Key Laboratory of Integrated Service Networks, Xidian University（西安电子科技大学综合业务网理论及关键技术国家重点实验室）
In this work we consider the large-coalition asymptotics of various fingerprinting and group testing games, and derive explicit expressions for the capacities for each of these models. We do this both for simple decoders (fast but suboptimal) and for joint decoders (slow but optimal). For fingerprinting, we show that if the pirate strategy is known, the capacity often decreases linearly with the number of colluders, instead of quadratically as in the uninformed fingerprinting game. For many attacks the joint capacity is further shown to be strictly higher than the simple capacity. For group te…
Due to structural and functional abnormalities or genetic variations and mutations, there may be dysfunctional molecules within an intracellular signaling network that do not allow the network to correctly regulate its output molecules, such as transcription factors. This disruption in signaling interrupts normal cellular functions and may eventually develop some pathological conditions. In this paper, computation capacity of signaling networks is introduced as a fundamental limit on signaling capability and performance of such networks. The computation capacity measures the maximum number of …
In this article, we investigate the additivity phenomenon in the dynamic capacity of a quantum channel for trading classical communication, quantum communication and entanglement. Understanding such additivity property is important if we want to optimally use a quantum channel for general communication purpose. However, in a lot of cases, the channel one will be using only has an additive single or double resource capacity, and it is largely unknown if this could lead to an superadditive double or triple resource capacity. For example, if a channel has an additive classical and quantum capacit…
We determine the secrecy capacity of the compound channel with quantum wiretapper and channel state information at the transmitter. Moreover, we derive a lower bound on the secrecy capacity of this channel without channel state information and determine the secrecy capacity of the compound classical-quantum wiretap channel with channel state information at the transmitter. We use this result to derive a new proof for a lower bound on the entanglement generating capacity of compound quantum channel. We also derive a new proof for the entanglement generating capacity of compound quantum channel …
A class of diamond networks is studied where the broadcast component is orthogonal and modeled by two independent bit-pipes. New upper and lower bounds on the capacity are derived. The proof technique for the upper bound generalizes bounding techniques of Ozarow for the Gaussian multiple description problem (1981) and Kang and Liu for the Gaussian diamond network (2011). The lower bound is based on Marton's coding technique and superposition coding. The bounds are evaluated for Gaussian and binary adder multiple access channels (MACs). For Gaussian MACs, both the lower and upper bounds strengt…
Although extensively investigated, the capacity of the two-hop half-duplex (HD) relay channel is not fully understood. In particular, a capacity expression which can be easily evaluated is not available and an explicit coding scheme which achieves the capacity is not known either. In this paper, we derive a new expression for the capacity of the two-hop HD relay channel by simplifying previously derived converse expressions. Compared to previous results, the new capacity expression can be easily evaluated. Moreover, we propose an explicit coding scheme which achieves the capacity. To achieve t…
Although extensively investigated, the capacity of the two-hop half-duplex (HD) relay channel is not fully understood. In particular, a capacity expression which can be evaluated straightforwardly is not available and an explicit coding scheme which achieves the capacity is not known either. In this paper, we derive a new expression for the capacity of the two-hop HD relay channel based on a simplified converse. Compared to previous results, this capacity expression can be easily evaluated. Moreover, we propose an explicit coding scheme which achieves the capacity. To achieve the capacity, the…
Establishing the capacity region of a Gaussian interference network is an open problem in information theory. Recent progress on this problem has led to the characterization of the capacity region of a general two user Gaussian interference channel within one bit. In this paper, we develop new, improved outer bounds on the capacity region. Using these bounds, we show that treating interference as noise achieves the sum capacity of the two user Gaussian interference channel in a low interference regime, where the interference parameters are below certain thresholds. We then generalize our techn…
The sum capacity of a class of discrete memoryless interference channels is determined. This class of channels is defined analogous to the Gaussian Z-interference channel with weak interference; as a result, the sum capacity is achieved by letting the transceiver pair subject to the interference communicates at a rate such that its message can be decoded at the unintended receiver using single user detection. Moreover, this class of discrete memoryless interference channels is equivalent in capacity region to certain discrete degraded interference channels. This allows the construction of a ca…
We propose an iterative method for approximately computing the capacity of discrete memoryless channels, possibly under additional constraints on the input distribution. Based on duality of convex programming, we derive explicit upper and lower bounds for the capacity. The presented method requires $O(M^2 N \sqrt{\log N}/\varepsilon)$ to provide an estimate of the capacity to within $\varepsilon$, where $N$ and $M$ denote the input and output alphabet size; a single iteration has a complexity $O(M N)$. We also show how to approximately compute the capacity of memoryless channels having a bound…
The capacity regions of multiple-input multiple-output Gaussian Z-interference channels are established for the very strong interference and aligned strong interference cases. The sum-rate capacity of such channels is established under noisy interference. These results generalize known results for scalar Gaussian Z-interference channels.
Communication over a noisy channel is often conducted in a setting in which different input symbols to the channel incur a certain cost. For example, for bosonic quantum channels, the cost associated with an input state is the number of photons, which is proportional to the energy consumed. In such a setting, it is often useful to know the maximum amount of information that can be reliably transmitted per cost incurred. This is known as the capacity per unit cost. In this paper, we generalize the capacity per unit cost to various communication tasks involving a quantum channel such as classica…
We propose an iterative method for approximating the capacity of classical-quantum channels with a discrete input alphabet and a finite dimensional output, possibly under additional constraints on the input distribution. Based on duality of convex programming, we derive explicit upper and lower bounds for the capacity. To provide an $\varepsilon$-close estimate to the capacity, the presented algorithm requires $O(\tfrac{(N \vee M) M^3 \log(N)^{1/2}}{\varepsilon})$, where $N$ denotes the input alphabet size and $M$ the output dimension. We then generalize the method for the task of approximatin…
Previous work on network coding capacity for random wired and wireless networks have focused on the case where the capacities of links in the network are independent. In this paper, we consider a more realistic model, where wireless networks are modelled by random geometric graphs with interference and noise. In this model, the capacities of links are not independent. By employing coupling and martingale methods, we show that, under mild conditions, the network coding capacity for random wireless networks still exhibits a concentration behavior around the mean value of the minimum cut.
Quantum information processing exploits the quantum nature of information. It offers fundamentally new solutions in the field of computer science and extends the possibilities to a level that cannot be imagined in classical communication systems. For quantum communication channels, many new capacity definitions were developed in comparison to classical counterparts. A quantum channel can be used to realize classical information transmission or to deliver quantum information, such as quantum entanglement. Here we review the properties of the quantum communication channel, the various capacity m…
Technion-Israel Institute of Technology（以色列理工学院）；Viterbi Faculty of Electrical and Computer Engineering, Technion-Israel Institute of Technology（以色列理工学院维特比电气与计算机工程学院）；Faculty of Mathematics, Technion-Israel Institute of Technology（以色列理工学院数学学院）
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 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 rel…
The generalized amplitude damping channel (GADC) is considered an important model for quantum communications, especially over optical networks. We make two salient contributions in this paper apropos of this channel. First, we consider a symmetric GAD channel characterized by the parameter $n=1/2,$ and derive its exact classical capacity, by constructing a specific induced classical channel. We show that the Holevo quantity for the GAD channel equals the Shannon capacity of the induced binary symmetric channel, establishing at once the capacity result and that the GAD channel capacity can be a…
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 "sup…
California Institute of Technology（加州理工学院）；Ben-Gurion University of the Negev（内盖夫本-古里安大学）
It is known that the majority of the human genome consists of repeated sequences. Furthermore, it is believed that a significant part of the rest of the genome also originated from repeated sequences and has mutated to its current form. In this paper, we investigate the possibility of constructing an exponentially large number of sequences from a short initial sequence and simple replication rules, including those resembling genomic replication processes. In other words, our goal is to find out the capacity, or the expressive power, of these string-replication systems. Our results include exac…
