This paper studies the capacity limits for quantum secret sharing (QSS). The goal of a QSS scheme is to distribute a quantum secret among multiple participants, such that only authorized parties can recover it through collaboration, while no information can be obtained without such collaboration. We introduce an information-theoretic model for the rate analysis of QSS and its relation to compound quantum channels, following a similar approach as of Zou et al. (2015) on classical secret sharing. We establish a regularized characterization for the QSS capacity, and determine the capacity for QSS with dephasing noise.

We determine the covert capacity for entanglement generation over a noisy quantum channel. While secrecy guarantees that the transmitted information remains inaccessible to an adversary, covert communication ensures that the transmission itself remains undetectable. The entanglement dimension follows a square root law (SRL) in the covert setting, i.e., $O(\sqrt{n})$ Einstein-Podolsky-Rosen (EPR) pairs can be distributed covertly and reliably over $n$ channel uses. We begin with covert communication of classical information under a secrecy constraint. We then leverage this result to construct a coding scheme for covert entanglement generation. Single-letter expressions are derived for the covert key-assisted and unassisted secrecy capacities, as well as for the covert entanglement-generation capacity.

Communication over a fully quantum relay channel is considered. We establish three bounds based on different coding strategies, i.e., partial decode-forward, measure-forward, and assist-forward. Using the partial decode-forward strategy, the relay decodes part of the information, while the other part is decoded without the relay's help. Based on our partial decode-forward bound, the capacity is determined for Hadamard relay channels. In the measure-forward coding scheme, the relay performs a sequence of measurements and then transmits a compressed representation. At last, the assist-forward bound is based on a new approach, whereby the transmitter sends the message to the relay and simultaneously generates entanglement assistance between the relay and the destination receiver. Subsequently, the relay can transmit with rate-limited entanglement assistance.

The understanding of achievable rates for quantum identification is far behind that of quantum transmission, as well as classical identification and transmission. Notably, in the classical case, common randomness shared between Alice and Bob before communication begins can greatly enhance the identification capacity. In the quantum regime, pre-shared entanglement may have an even more profound impact on the quantum identification (ID) capacity. This paper presents a regularized expression for the quantum ID capacity with entanglement assistance and demonstrates how it grows with the entanglement rate. Additionally, we provide deeper insights into the nature of quantum ID capacity. Interestingly, while the classical ID capacity becomes unbounded with unlimited common randomness, we find that the quantum ID capacity remains bounded even with unlimited entanglement assistance. Additionally, we find that entanglement plays the same role as an additional noiseless channel that is amortized, i.e., only used to make the rate positive.

We determine the covert capacity for entanglement generation over a noisy quantum channel. While secrecy guarantees that the transmitted information remains inaccessible to an adversary, covert communication ensures that the transmission itself remains undetectable. The entanglement dimension follows a square root law (SRL) in the covert setting, i.e., $O\left( {\sqrt n } \right)$ EPR pairs can be distributed covertly and reliably over n channel uses. We begin with covert communication of classical information under a secrecy constraint. We then leverage this result to construct a coding scheme for covert entanglement generation. Consequently, the covert entanglement-generation capacity is the same as for classical information without secrecy, albeit our scheme employs a larger key.

We introduce the notion of empirical coordination for quantum correlations. Quantum mechanics enables the calculation of probabilities for experimental outcomes, emphasizing statistical averages rather than detailed descriptions of individual events. This makes empirical coordination a natural and operationally meaningful framework for quantum systems, particularly in the context of nonlocal games, which rely on repeated measurements to assess performance. We discuss how coordination performance provides new insights into the implementation and simulation of quantum nonlocal games in the empirical regime.We begin by analyzing networks with classical links, focusing on the cascade network. We establish the optimal coordination rates, which indicate the minimal resources required to simulate a quantum state on average. We then consider networks with quantum links, focusing on a broadcast setting where a single transmitter distributes entanglement between multiple receivers. Our capacity result determines the necessary and sufficient resources required for preparing correlations that can subsequently be used in quantum nonlocal games.

Quantum coordination is considered in networks with classical and quantum links. We begin with networks withclassical links, and characterize the generation of separable and classical-quantum correlations in three primary models: 1) a two-node network with limited common randomness (CR), 2) a no-communication network, and 3) a broadcast network, which consists of a single sender and two receivers. We establish the optimal tradeoff between the classical communication and CR rates in each setting, thus characterizing the minimal resources for simulating classical-quantum correlations. Next, we consider coordination in networks withquantum links. We study the following models: 1) a cascade network with limited entanglement, 2) a broadcast network, and 3) a multiple-access network with two senders and a single receiver. We establish the optimal tradeoff between quantum communication and entanglement rates in each setting, characterizing the minimal resources for entanglement coordination. The examples demonstrate that coordination of entanglement and coordination of separable correlations behave differently. At last, we show the implications of our results on nonlocal games with quantum strategies.

Communication over a fully quantum relay channel is considered. We establish three bounds based on different coding strategies, i.e., partial decode-forward, measure-forward, and assist-forward. Using the partial decode-forward strategy, the relay decodes part of the information, while the other part is decoded without the relay’s help. The result by Savov et al. (2012) for a classical-quantum relay channel is obtained as a special case. Based on our partial decode-forward bound, the capacity is determined for Hadamard relay channels. In the measure-forward coding scheme, the relay performs a sequence of measurements and then sends a compressed representation of the measurement outcome to the destination receiver. The measure-forward strategy can be viewed as a generalization of the classical compress-forward bound. At last, we consider quantum relay channels with orthogonal receiver components. The assist-forward bound is based on a new approach, whereby the transmitter sends the message to the relay and simultaneously generates entanglement assistance between the relay and the destination receiver. Subsequently, the relay can transmit the message to the destination receiver with rate-limited entanglement assistance.

Communication over a classical multiple-access channel (MAC) with entanglement resources is considered, whereby two transmitters share entanglement resources a priori before communication begins. Leditzky et al. (2020) presented an example of a classical MAC, defined in terms of a pseudo telepathy game, such that the sum rate with entangled transmitters is strictly higher than the best achievable sum rate without such resources. Here, we establish inner and outer bounds on the capacity region for the general MAC with entangled transmitters, and show that the previous result can be obtained as a special case. It has long been known that the capacity region of the classical MAC under a message-average error criterion can be strictly larger than with a maximal error criterion (Dueck, 1978). We observe that given entanglement resources, the regions coincide. Furthermore, we address the combined setting of entanglement resources and conferencing, where the transmitters can also communicate with each other over rate-limited links. Using superdense coding, entanglement can double the conferencing rate.

We consider entanglement-assisted communication over the qubit depolarizing channel under the security requirement of covert communication, where the transmission itself must be concealed from detection by an adversary. Previous work showed that$O(\sqrt {n})$information bits can be reliably and covertly transmitted innchannel uses without entanglement assistance. However, Gagatsos et al. (2020) showed that entanglement assistance can increase this scaling to$O(\sqrt {n}\log {n})$for continuous-variable bosonic channels. Here, we present a finite-dimensional parallel, and show that$O(\sqrt {n}\log {n})$covert bits can be transmitted reliably overnuses of a qubit depolarizing channel. The coding scheme employs “weakly” entangled states such that their squared amplitude scales as$O\left ({{{\scriptstyle \text {}^{\scriptstyle 1}}\hspace {-0.224em}/\hspace {-0.112em}{\scriptstyle \sqrt {n}}}}\right)$.

Secure communication is considered with unreliable entanglement assistance, where the adversary may intercept the legitimate receiver's entanglement resource before communication takes place. The communication setting of unreliable assistance, without security aspects, was originally motivated by the extreme photon loss in practical communication systems. The operational principle is to adapt the transmission rate to the availability of entanglement assistance, without resorting to feedback and repetition. Here, we require secrecy as well. An achievable secrecy rate region is derived for general quantum wiretap channels, and a multi-letter secrecy capacity formula for the special class of degraded channels.

Semantic security is considered with unreliable entanglement assistance, due to one of two reasons: Interception or loss. We consider two corresponding models. In the first model, Eve may intercept the entanglement resource. In the second model, Eve is passive, and the resource may dissipate to the environment beyond her reach. We derive achievable rates for both models, subject to a maximal error criterion and semantic security. As an example, we consider the amplitude damping channel. Under interception, time division is not necessarily possible, and the boundary of our achievable region is disconnected. In the passive model, our rate region outperforms time division.

Network coordination is considered in three basic settings, characterizing the generation of separable and classicalquantum correlations among multiple parties. First, we consider the simulation of a classical-quantum state between two nodes with rate-limited common randomness (CR) and communication. Furthermore, we study the preparation of a separable state between multiple nodes with rate-limited CR and no communication. At last, we consider a broadcast setting, where a sender and two receivers simulate a classical-quantum-quantum state using rate-limited CR and communication. We establish the optimal tradeoff between communication and CR rates in each setting.

The optimal coordination rates are determined in three primary settings of multi-user quantum networks, thus char-acterizing the minimal resources for simulating a joint quantum state among multiple parties. We study the following models: (1) a cascade network with limited entanglement, (2) a broadcast network, which consists of a single sender and two receivers, (3) a multiple-access network with two senders and a single receiver. We establish the necessary and sufficient conditions on the asymptotically-achievable communication and entanglement rates in each setting. At last, we show the implications of our results on nonlocal games with quantum strategies.

Communication over a classical multiple-access channel (MAC) with quantum entanglement resources is considered, whereby two transmitters share entanglement resources a priori. Leditzky et al. (2020) presented an example, defined in terms of a pseudo telepathy game, such that the sum rate with entangled transmitters is strictly higher than the best achievable sum rate without such resources. Here, we establish inner and outer bounds on the capacity region for the general MAC with entangled transmitters, and show that the previous result can be obtained as a special case. It has long been known that the capacity region of the classical MAC under a message-average error criterion can be strictly larger than with a maximal error criterion (Dueck, 1978). We observe that given entanglement resources, the regions coincide.

Several applications of molecular communications (MC) feature an alarm-prompt behavior for which the prevalent Shannon capacity may not be the appropriate performance metric. The identification capacity as an alternative measure for such systems has been motivated and established in the literature. In this paper, we study deterministic identification (DI) for the discrete-time Poisson channel (DTPC) with intersymbol interference (ISI) where the transmitter is restricted to an average and a peak molecule release rate constraint. Such a channel serves as a model for diffusive MC systems featuring long channel impulse responses and employing molecule counting receivers. We derive lower and upper bounds on the DI capacity of the DTPC with ISI when the number of ISI channel taps$K$may grow with the codeword length$n$(e.g., due to increasing symbol rate). As a key finding, we establish that for deterministic encoding, the codebook size scales as$2^{(n\log n)R}$assuming that the number of ISI channel taps scales as$K=2^{\kappa\log n}$, where$R$is the coding rate and$\kappa$is the ISI rate. Moreover, we show that optimizing$\kappa$leads to an effective identification rate [bits/s] that scales linearly with$n$, which is in contrast to the typical transmission rate [bits/s] that is independent of$n$.

An upper bound to the identification capacity of discrete memoryless wiretap channels is derived under the requirement of semantic effective secrecy, combining semantic secrecy and stealth constraints. A previously established lower bound is improved by applying it to a prefix channel, formed by concatenating an auxiliary channel and the actual channel. The bounds are tight if the legitimate channel is more capable than the eavesdropper’s channel. An illustrative example is provided for a wiretap channel that is composed of a point-to-point channel, and a parallel, reversely degraded wiretap channel. A comparison with results for message transmission and for identification with only secrecy constraint is provided.

We consider entanglement-assisted communication over the qubit depolarizing channel under the security requirement of covert communication, where not only the information is kept secret, but the transmission itself must be concealed from detection by an adversary. Previous work showed that $O(\sqrt n )$ information bits can be reliably and covertly transmitted in n channel uses without entanglement assistance. However, Gagatsos et al. (2020) showed that entanglement assistance can increase this scaling to $O(\sqrt n \log n)$ for continuous-variable bosonic channels. Here, we present a finite-dimensional parallel, and show that $O(\sqrt n \log n)$ covert bits can be transmitted reliably over n uses of a qubit depolarizing channel.

Entanglement resources can increase transmission rates substantially. Unfortunately, entanglement is a fragile resource that is quickly degraded by decoherence effects. In order to generate entanglement for optical communication, the transmitter and the receiver first prepare entangled spin-photon pairs locally, and then the photon at the transmitter is sent to the receiver through an optical fiber or free space. Without feedback, the transmitter does not know whether the entangled photon has reached the receiver. The present work introduces a new model of unreliable entanglement assistance, whereby the communication system operates whether entanglement assistance is present or not. While the sender is ignorant, the receiver knows whether the entanglement generation was successful. In the case of a failure, the receiver decodes less information. In this manner, the effective transmission rate is adapted according to the assistance status. Regularized formulas are derived for the classical and quantum capacity regions with unreliable entanglement assistance, characterizing the tradeoff between the unassisted rate and the excess rate that can be obtained from entanglement assistance. It is further established that time division between entanglement-assisted and unassisted coding strategies is optimal for the noiseless qubit channel, but can be strictly suboptimal for a noisy channel.

The identification capacity region of the compound broadcast channel is determined under an average error criterion, where the sender has no channel state information. We give single-letter identification capacity formulas for discrete channels and multiple-input multiple-output Gaussian channels under an average input constraint. The capacity theorems apply to general discrete memoryless broadcast channels. This is in contrast to the transmission setting, where the capacity is only known for special cases, notably the degraded broadcast channel and the multipleinput multiple-output broadcast channel with private messages. Furthermore, the identification capacity region of the compound multiple-input multiple-output broadcast channel can be larger than the transmission capacity region. This is a departure from the single-user behavior of identification, since the identification capacity of a single-user channel equals the transmission capacity.

The identification (ID) capacity region of the compound broadcast channel is determined under an average error criterion, where the sender has no channel state information. We give single-letter ID capacity formulas for discrete channels and MIMO Gaussian channels, under an average input constraint. The capacity theorems apply to general broadcast channels. This is in contrast to the transmission setting, where the capacity is only known for special cases, notably the degraded broadcast channel and the MIMO broadcast channel with private messages. Furthermore, the ID capacity region of the compound MIMO broadcast channel is in general larger than the transmission capacity region. This is a departure from the single-user behavior of ID, since the ID capacity of a single-user channel equals the transmission capacity.

Communication over a quantum multiple-access channel (MAC) with cribbing encoders is considered, whereby Transmitter 2 performs a measurement on a system that is entangled with Transmitter 1. Based on the no-cloning theorem, perfect cribbing is impossible. This leads to the introduction of a MAC model with noisy cribbing. In the causal and non-causal cribbing scenarios, Transmitter 2 performs the measurement before the input of Transmitter 1 is sent through the channel. Hence, Transmitter 2’s cribbing may inflict a "state collapse" for Transmitter 1. Achievable regions are derived for each setting. Furthermore, a regularized capacity characterization is established for robust cribbing, i.e. when the cribbing system contains all the information of the channel input, and a partial decode-forward region for non-robust cribbing. For the classical-quantum (c-q) MAC with cribbing encoders, the capacity region is determined with perfect cribbing of the classical input, and a cutset region is derived for noisy cribbing.

Entanglement resources can increase transmission rates substantially. Unfortunately, entanglement is a fragile resource that is quickly degraded by decoherence effects. The present work introduces a new model of unreliable entanglement assistance, whereby the communication system operates whether entanglement assistance is present or not. While the sender is ignorant, the receiver knows whether the entanglement generation was successful. In the case of a failure, the receiver decodes less information. In this manner, the effective transmission rate is adapted according to the assistance status. Regularized formulas are derived for the classical and quantum capacity regions with unreliable entanglement assistance, characterizing the tradeoff between the unassisted rate and the excess rate that can be obtained from entanglement assistance.

In the identification problem, as opposed to the information transmission task, the decoder only identifies whether a message of his choosing was sent or not. This relaxation allows for a double-exponential code size. An achievable identification region is derived for a quantum broadcast channel, and a full characterization for the class of classical-quantum broadcast channels. The results are demonstrated for a depolarizing broadcast channel. Furthermore, the identification capacity region of the single-mode pure-loss bosonic broadcast channel is obtained as a consequence. In contrast to the single-user case, the capacity region for identification can be significantly larger than for transmission.

To capture the problem of joint communication and sensing in the quantum regime, we consider the problem of reliably communicating over a Classical-Quantum (c-q) channel that depends on a random parameter while simultaneously estimating the random parameter at the transmitter through a noisy feedback channel. Specifically, for non-adaptive estimation strategies, we obtain an exact characterization of the optimal tradeoffs between the rate of communication and the error exponent of parameter estimation. As in the classical setting, the tradeoff is governed by the empirical distribution of the codewords, which simultaneously controls the rate of reliable communication and the error exponent.

Communication over a quantum multiple-access channel (MAC) with cribbing encoders is considered, whereby Transmitter 2 performs a measurement on a system that is entangled with Transmitter 1. Based on the no-cloning theorem, perfect cribbing is impossible. This leads to the introduction of a MAC model with noisy cribbing. In the causal and non-causal cribbing scenarios, Transmitter 2 performs the measurement before the input of Transmitter 1 is sent through the channel. Hence, Transmitter 2's cribbing may inflict a "state collapse" for Transmitter 1. Achievable regions are derived for each setting. Furthermore, a regularized capacity characterization is established for robust cribbing, i.e. when the cribbing system contains all the information of the channel input. Building on the analogy between the noisy cribbing model and the relay channel, a partial decode-forward region is derived for a quantum MAC with non-robust cribbing. For the classical-quantum MAC with cribbing encoders, the capacity region is determined with perfect cribbing of the classical input, and a cutset region is derived for noisy cribbing. In the special case of a classical-quantum MAC with a deterministic cribbing channel, the inner and outer bounds coincide.

The deterministic identification (DI) capacity is developed in multiple settings of channels with power constraints. A full characterization is established for the DI capacity of the discrete memoryless channel (DMC) with and without input constraints. Originally, Ahlswede and Dueck established the identification capacity with local randomness at the encoder, resulting in a double exponential number of messages in the block length $n$ . In the deterministic setup, the number of messages scales exponentially, as in Shannon's transmission paradigm, but the achievable identification rates are higher. An explicit proof was not provided for the deterministic setting. In this paper, a detailed proof is presented for the DMC. Furthermore, Gaussian channels with fast and slow fading are considered, when channel side information is available at the decoder. A new phenomenon is observed as we establish that the number of messages scales as $2^{n\log (n)R}$ by deriving lower and upper bounds on the DI capacity on this scale. Consequently, the DI capacity of the Gaussian channel is infinite in the exponential scale and zero in the double exponential scale, regardless of the channel noise.

Identification capacity is developed without randomization at neither the encoder nor the decoder. In particular, full characterization is established for the deterministic identification (DI) capacity for the Gaussian channel and for the general discrete memoryless channel (DMC) with and without constraints. Originally, Ahlswede and Dueck established the identification capacity with local randomness given at the encoder, resulting in a double exponential number of messages. In the deterministic setup, the number of messages scales exponentially, as in Shannon’s transmission paradigm, but the achievable identification rates can be significantly higher than those of transmission. Ahlswede and Dueck further stated a capacity result for the deterministic setting of a DMC, but did not provide an explicit proof. In this paper, a detailed proof is given for both the Gaussian channel and the general DMC. The DI capacity of a Gaussian channel is infinite regardless of the noise.

The bosonic channel is addressed with modulation interference and side information at the transmitter. The model can be viewed as the quantum counterpart of the classical random-parameter Gaussian channel. Based on Costa's writing-on-dirty-paper result, the effect of the interference can be canceled. For both homodyne and heterodyne detection, we observe the same phenomenon, as the model reduces to a classical Gaussian channel. Then, we consider the bosonic channel with joint detection, for which the classical results do not apply, and derive a dirty-paper coding lower bound. We demonstrate that the optimal coefficient for dirty paper coding is not necessarily the MMSE estimator coefficient as in the classical setting.

Communication over a quantum broadcast channel with cooperation between the receivers is considered. The first form of cooperation addressed is classical conferencing. Another cooperation setting involves quantum conferencing, where Receiver 1 can teleport a quantum state to Receiver 2. The conferencing setting is intimately related to quantum repeaters, as the sender, Receiver 1, and Receiver 2 can be viewed as the transmitter, the repeater, and the destination receiver, respectively. We develop lower and upper bounds on the capacity region in each setting. At last, we show that as opposed to the MAC with entangled encoders, entanglement between decoders does not increase the classical communication rates for the broadcast dual.

Secret-sharing building blocks based on quantum broadcast communication are studied. The confidential capacity region of the pure-loss bosonic broadcast channel is determined with key assistance, under the assumption of the long-standing minimum output-entropy conjecture. If the main receiver has a transmissivity of $\eta\lt\frac{1}{2}$, then confidentiality solely relies on the key-assisted encryption of the one-time pad. We also address conference key agreement for the distillation of two keys, a public key and a secret key. A regularized formula is derived for the key-agreement capacity region. In the pure-loss bosonic case, the key-agreement region is included within the capacity region of the corresponding broadcast channel with confidential messages. We then consider a network with layered secrecy, where three users with different security ranks communicate over the same broadcast network. We derive an achievable layered-secrecy region for a pure-loss bosonic channel that is formed by the concatenation of two beam splitters.

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 with a maximally correlated channel state, 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.

Communication over a random-parameter quantum channel when the decoder is required to reconstruct the parameter sequence is considered. We study scenarios that include either strictly-causal, causal, or non-causal channel side information (CSI) available at the encoder, and also when CSI is not available. This model can be viewed as a form of quantum metrology, and as the quantum counterpart of the classical rate-and-state channel with state estimation at the decoder. Regularized formulas for the capacity-distortion regions are derived. In the special case of measurement channels, single-letter characterizations are derived for the strictly-causal and causal settings. Furthermore, in the more general case of entanglement-breaking channels, a single-letter characterization is derived when CSI is not available. As a consequence, we obtain regularized formulas for the capacity of random-parameter quantum channels with CSI, generalizing previous results by Bocheet al., 2016, on classical-quantum channels. Bosonic dirty paper coding is introduced as a consequence, where we demonstrate that the optimal coefficient is not necessarily that of minimum mean-square error estimation as in the classical setting.

We address the AVC with colored Gaussian noise. The paper consists of three parts. First, we study the AVC with fixed parameters, a model that combines the AVC and the time-varying channel. We determine both the deterministic and random code capacities and demonstrate super-additivity. In the second part, we consider the arbitrarily varying Gaussian product channel. The random code capacity was previously characterized by "double" water filling. We establish the deterministic code capacity and show that using independent scalar codes is suboptimal. Finally, we establish the capacity of the AVC with colored Gaussian noise, where double water filling is performed in the frequency domain. The analysis relies on our preceding results.

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.

Deterministic identification (DI) is addressed for Gaussian channels with fast and slow fading, where channel side information is available at the decoder. In particular, it is established that the number of messages scales as 2nlog(n)R, where n is the block length and R is the coding rate. Lower and upper bounds on the DI capacity are developed in this scale for fast and slow fading. Consequently, the DI capacity is infinite in the exponential scale and zero in the double-exponential scale, regardless of the channel noise.

In this paper, we study the arbitrarily varying broadcast channel (AVBC) when the state information is available at the transmitter in a causal manner. We establish the inner and outer bounds on both the random code capacity region and the deterministic code capacity region with degraded message sets. The capacity region is then determined for a class of channels satisfying a condition on the mutual information between the strategy variables and the channel outputs. As an example, we consider the arbitrarily varying binary symmetric broadcast channel. We show the cases where the condition holds and, hence, the capacity region is determined and other cases where there is a gap between the bounds. This gap shows that the minimax theorem does not hold for rate regions.

We determine both the random code capacity region and the deterministic code capacity region of the arbitrarily varying multiple access channel (AVMAC) under input and state constraints. For the AVMAC without constraints, the characterization due to Ahlswede and Cai is complete except for two cases, pointed out in the literature as an open problem. The missing piece is obtained as a special case of our results.

We study the arbitrarily varying channel (AVC) with input and state constraints, when the encoder has state information in a causal or noncausal manner. For the causal state information setting, we develop lower and upper bounds on the random code capacity. A lower bound on the deterministic code capacity is established in the case of a message-averaged input constraint. In the setting where a state constraint is imposed on the jammer, while the user is under no constraints, the random code bounds coincide, and the random code capacity is determined. Furthermore, for this scenario, a generalized non-symmetrizability condition is stated, under which the deterministic code capacity coincides with the random code capacity. For the noncausal state information setting, we determine the random code capacity of the AVC under input and state constraints. In addition, a condition on the channel is stated, under which the deterministic code capacity coincides with the random code capacity.

We study the arbitrarily varying relay channel, and establish the cutset bound, decode-forward bound and partial decode-forward bound on the random code capacity. We further determine the random code capacity for special cases. Then, we consider deterministic coding schemes, and derive the deterministic code capacity, under certain conditions.

In this work, we study the arbitrarily varying degraded broadcast channel (AVDBC), when state information is available at the transmitter in a causal manner. We establish inner and outer bounds on both the random code capacity region and the deterministic code capacity region. The capacity region is then determined for a class of channels satisfying a condition on the mutual informations between the strategy variables and the channel outputs. As an example, we show that the condition holds for the arbitrarily varying binary symmetric broadcast channel, and we find the corresponding capacity region.

We study the arbitrarily varying channel (AVC) with input and state constraints, when the encoder has state information in a causal manner. Lower and upper bounds on the random code capacity are developed. A lower bound on the deterministic code capacity is established in the case of a message-averaged input constraint. In the setting where a state constraint is imposed on the jammer, while the user is under no constraints, the random code bounds coincide, and the random code capacity is determined. Furthermore, for this scenario, a generalized non-symmetrizability condition is stated, under which the deterministic code capacity coincides with the random code capacity.

Consider a single-user or multiple-access channel with a large output alphabet. A method to approximate the channel by an upgraded version having a smaller output alphabet is presented and analyzed. The original channel is not necessarily symmetric and does not necessarily have a binary input alphabet. Also, the input distribution is not necessarily uniform. The approximation method is instrumental when constructing capacity achieving polar codes for an asymmetric channel with a non-binary input alphabet. Other settings in which the method is instrumental are the wiretap setting as well as the lossy source coding setting.

Consider a single-user or multiple-access channel with a large output alphabet. A method to approximate the channel by an upgraded version having a smaller output alphabet is presented and analyzed. The gain in symmetric channel capacity is controlled through a fidelity parameter. The larger the fidelity parameter, the better the approximation on the one hand, but the larger the new output alphabet on the other. The approximation method is instrumental when constructing polar codes. No assumption is made on the symmetry of the original channel, and the input alphabet need not be binary.