In this paper, we use a linear programming (LP) optimization approach to evaluate the equivocation when coding over a wiretap channel model where the main channel is noiseless and the eavesdropper’s channel is a binary symmetric channel (BSC). Using this technique, we present a numerically-derived upper bound for the achievable secrecy rate in the finite blocklength regime that is tighter than traditional infinite blocklength bounds. We also propose a secrecy coding technique that outperforms random binning codes. When there is one overhead bit, this coding technique is optimum and achieves the newly derived bound. For cases with additional bits of overhead, our coding scheme can achieve equivocation rates close to the new bound. Furthermore, we explore the patterns of the generator matrix and the parity-check matrix for linear codes and we present binning techniques for both linear and nonlinear codes using two different approaches: recursive and non-recursive. To our knowledge, this is the first optimization solution for secrecy coding obtained through linear programming. Our new bounds and codes mark a significant breakthrough towards understanding fundamental limits of performance (and how to achieve them in some instances) for the binary symmetric wiretap channel with real finite blocklength coding constructions. Our techniques are especially useful for codes of small to medium blocklength, such as those that may be required by applications with small payloads, such as the Internet of Things.

Abstract In this work, multiple energy‐limited Internet of Things (IoT) users are intended to communicate with their destination (). The scheduled IoT user harvests the energy from a source signal and uses this energy to forward a mixture of its message and the source message to the and the source destination based on non‐orthogonal multiple access (NOMA). Since the messages are transmitted at the same resource block, the far untrusted user (source destination) has the opportunity to access the message destined for the near user () by successive interference cancellation. Therefore, an IoT user scheduling strategy is proposed to achieve the reliability and security of transmission in the network. To indicate the superiority of the proposed scheduling scheme and the impact of different parameters on the network performance under untrusted users, the secrecy outage probability of the system is derived by tracking exact and asymptotic analyses and then it is compared with that of benchmarks through simulations. The results reveal the crucial role of the near user threshold secrecy rate as the system's bottleneck and the negligible impact of the power allocation coefficients and the untrusted far user threshold rate on the secrecy performance with increasing the signal‐to‐noise‐ratio.

Abstract To enhance the performance and the coverage area of the next‐generation heterogeneous wireless networks (HetNets), smaller cells such as femtocells are deployed. A reasonable resource allocation strategy is crucial for the operation of such systems. In this work, the Nash bargaining solution (NBS), Kalai–Smorodinsky bargaining solution (KSBS), and a proposed bargaining solution, which is the combination of NBS and KSBS, are studied to ensure the efficiency and fairness in the transmission rate allocation among femtocells. The mentioned bargaining solutions are optimised subject to the rate constraints due to the Han–Kobayashi (HK) rate splitting scheme, and a maximum tolerable interference caused by femtocell base stations (FBSs) at the macrocell user equipment. Two methods are used to address the bargaining solutions' optimisations. First, the conventional optimisation‐based method is used for the situations where the channel gains are known, then a reinforcement learning‐based algorithm for a real environment is proposed without being aware of the channel gains. To accelerate the speed of the learning process and to initialise the values of quality functions, the hotbooting technique is used. The bargaining solutions are compared by fairness and efficiency criteria in both methods. Numerical simulations show that the proposed reinforcement learning‐based algorithm achieves the same performance derived from the conventional optimisation method. First, this paper studies the two well‐known Nash and Kalai–Smorodinsky bargaining solutions as the good tools to establish fairness in rate allocation problem among femtocells in a HetNet. Then a new bargaining solution is proposed as the combination of the two bargaining solutions. The fairness and the efficiency of the allocated rates to femtocells as the output of optimisation problems of bargaining solutions are compared via Jain index criterion (as the fairness metric) and inverse price of anarchy criterion (as the efficiency metric). Moreover, the femtocell base stations are allowed to use Han–Kobayashi signalling scheme to send their signals in private and common messages which results in the best‐known achievable rate region. Two methods are used to solve the optimisation problems: the conventional optimisation method and the reinforcement learning‐based method (to formulate a real‐world model with the unknown channel gains). It is shown that the proposed bargaining solution (in both methods) results in fairer rates than Nash and Kalai–Smorodinsky bargaining solutions while all of them are efficient.

In this study, a two‐user single‐input single‐output X‐channel with confidential messages is addressed. In this model, the authors assume that the transmitters have access to synergistic alternating channel state information. During different time slots, the channel state information at transmitters (CSIT) alternate between three states including perfect CSIT, delayed CSIT, and no CSIT. By using the eminent synergistic benefits of the CSIT pattern, some schemes capable of attaining the maximum achievable secure degrees of freedom (SDoF) are presented. Additionally, in devising the schemes, the minimal CSIT patterns required to achieve optimal SDoF are introduced. It is shown that for CSIT patterns which are weaker than minimal ones, using a half‐duplex relay can assist the network in obtaining the optimal SDoF. Indeed, the relay alleviates the effects of the lack of knowledge at transmitters on achievable SDoF.

The authors study the problem of two‐user Gaussian multiple access channel (GMAC) in the presence of an external eavesdropper, where all transmitted messages should be kept confidential against the eavesdropper. For this purpose, they propose a secure coding scheme on this channel which utilises low‐density parity‐check (LDPC) codes by employing random bit insertion and puncturing techniques. At each encoder, the confidential message with some random bits as a random message are systematically encoded, and then the associated bits to the confidential message are punctured. Next, the encoders send their unpunctured bits over a Gaussian multiple access wiretap channel (GMAC‐WT). The puncturing distribution applied to the LDPC code is considered in random and optimised cases. They utilise a modified extrinsic information transfer chart analysis to optimise the puncturing distributions. The security gap is used as a measure of secrecy. They compared the achieved secure rate pair with an achievable secrecy rate region of GMAC‐WT to show the effective performance of the proposed scheme. In this study, equal and unequal power conditions at the transmitters are investigated. For both cases, they attain a fairly small security gap which is equivalent to achieve the points near the secrecy rate region of GMAC‐WT.

The authors study the problem of secret communication over a multiple‐access channel with a common message. Here, the authors assume that two transmitters have confidential messages, which must be kept secret from the wiretapper (the second receiver), and both of them have access to a common message which can be decoded by the two receivers. The authors call this setting as multiple‐access wiretap channel with common message (MAWC‐CM). For this setting, the authors derive general inner and outer bounds on the secrecy capacity region for the discrete memoryless case and show that these bounds meet each other for a special case called the switch channel. As well, for a Gaussian version of MAWC‐CM, the authors derive inner and outer bounds on the secrecy capacity region. Providing numerical results for the Gaussian case, the authors illustrate the comparison between the derived achievable rate region and the outer bound for the considered model and the capacity region of compound multiple access channel.

In this paper, we study the problem of secret communication over a compound Multiple Access Channel (MAC). In this channel, we assume that one of the transmitted messages is confidential, which is only decoded by its corresponding receiver and kept secret from the other receiver. We call this proposed setting the compound MAC with a confidential message. For this model, we derive general inner and outer bounds for both imperfect and perfect secrecy conditions for the second receiver. Also, as examples, we investigate less noisy and Gaussian versions of this channel, and extend the results of the discrete memoryless version to these cases. Moreover, providing numerical examples for the Gaussian case, we illustrate the comparison between achievable rate regions of compound MAC and compound MAC with a confidential message. In addition, for the Gaussian case, we show that using cooperative jamming strategy can increase the achievable secrecy rate between the legitimate transmitter and the receiver.

In this paper, we study the problem of secret communication over a Compound Multiple Access Channel (MAC). In this channel, we assume that one of the transmitted messages is confidential that is only decoded by its corresponding receiver and kept secret from the other receiver. For this proposed setting (compound MAC with confidential messages), we derive general inner and outer bounds on the secrecy capacity region. Also, as examples, we investigate `Less noisy' and `Gaussian' versions of this channel, and extend the results of the discrete memoryless version to these cases. Moreover, providing numerical examples for the Gaussian case, we illustrate the comparison between achievable rate regions of compound MAC and compound MAC with confidential messages.

In this paper, we investigate reliable transmission of three correlated discrete memoryless sources over a two-relay network. In our considered model, one of the sources is available at the sender whereas, the other two sources are known to the first and the second relay. We present both joint and separate source-channel coding schemes, and derive the corresponding sets of sufficient conditions for reliable sources transmission. The manner of cooperation in both schemes is Decode-and-Forward strategy. In the joint approach, we generalize the correlation preserving mapping technique to our model using nested backward decoding. Our proposed separate approach is based on Slepian-Wolf source coding and irregular encoding/successive decoding strategy. Furthermore, we obtain necessary conditions for reliable sources transmission over the network. Our results can be reduced to the several known results in the literature.

This study investigates the capacity region of a three-user cognitive radio network with two primary users and one cognitive user. A three-user cognitive interference channel (C-IFC) is proposed by considering a three-user interference channel (IFC) where one of the transmitters has cognitive capabilities and knows the messages of the other two transmitters in a non-causal manner. First, two inner bounds on the capacity region of the three-user C-IFC are obtained based on using the schemes which allow all receivers to decode all messages with two different orders. Next, two sets of conditions are derived, under which the capacity region of the proposed model coincides with the capacity region of a three-user C-IFC in which all three messages are required at all receivers. Under these conditions, referred to as strong interference conditions, the capacity regions for the proposed three-user C-IFC are characterised. Moreover, the Gaussian three-user C-IFC is considered and the capacity results are derived for the Gaussian case. Some numerical examples are also provided.

In this paper, taking into account the effect of link delays, we investigate the capacity region of the cognitive interference channel (C-IFC), where cognition can be obtained from either causal or noncausal generalized feedback. For this purpose, we introduce the causal C-IFC with delay (CC-IFC-WD) in which the cognitive user's transmission can depend onLfuture received symbols as well as the past ones. We show that the CC-IFC-WD model is equivalent to a classical causal C-IFC (CC-IFC) with link delays. Moreover, CC-IFC-WD extends both genie-aided and causal cognitive radio channels and bridges the gap between them. First, we derive an outer bound on the capacity region for the arbitrary value ofLand specialize this general outer bound to the strong interference case. Then, under strong interference conditions, we tighten the outer bound. To derive the achievable rate regions, we concentrate on three special cases: 1) classical CC-IFC (L=0); 2) CC-IFC without delay (L=1) ; and 3) CC-IFC with unlimited look ahead in which the cognitive user noncausally knows its entire received sequence. In each case, we obtain a new inner bound on the capacity region. The derived achievable rate regions under special conditions reduce to several previously known results. Moreover, we show that the coding strategy which we use to derive an achievable rate region for the classical CC-IFC achieves the capacity for the classes of degraded and semideterministic classical CC-IFC under strong interference conditions. Furthermore, we extend our achievable rate regions to the Gaussian case. Providing some numerical examples for Gaussian CC-IFC-WD, we compare the performances of the different strategies and investigate the rate gain of the cognitive link for different delay values. We show that one can achieve larger rate regions in the “without delay” and “unlimited look-ahead” cases than in the classical CC-IFC; this improvement is likely due to the fact that, in the former two cases, the cognitive user can cooperate more effectively with the primary user by knowing the current and future received symbols.

The authors consider ‘partially’ and ‘fully cooperative’ state-dependent relay broadcast channels (RBCs), where partial channel state information (CSI) is available at the nodes causally. First, the authors derive an achievable rate region for general discrete memoryless partially cooperative RBC (PC-RBC) with partial causal CSI, by exploiting superposition coding at the source, decode-and-forward scheme at the relay and Shannon's strategy at the source and the relay. Then, they establish the capacity region of the discrete memoryless physically degraded PC-RBC with partial causal CSI. They also characterise the capacity region of discrete memoryless PC-RBC with feedback and partial causal CSI, and show that feedback does not affect the capacity region of the physically degraded channel. Moreover, for the fully cooperative RBC (FC-RBC) with partial causal CSI the authors obtain the same results as for the state-dependent PC-RBC. The authors' results subsume the previously known results for the degraded broadcast and relay channels with causal CSI. Finally, they extend their achievable rate regions to the Gaussian cases. Providing some numerical examples for the Gaussian cases, they compare the achievable rate regions derived for different situations.

In this paper, we introduce a discrete memoryless State-Dependent Relay Channel with Private Messages (SD-RCPM) as a generalization of the state-dependent relay channel. We investigate two main cases: SD-RCPM with non-causal Channel State Information (CSI), and SD-RCPM with causal CSI. In each case, it is assumed that partial CSI is available at the source and relay. For non-causal case, we establish an achievable rate region using Gel'fand-Pinsker type coding scheme at the nodes informed of CSI, and Compress-and-Forward (CF) scheme at the relay. Using Shannon's strategy and CF scheme, an achievable rate region for causal case is obtained. As an example, the Gaussian version of SD-RCPM is considered, and an achievable rate region for Gaussian SD-RCPM with non-causal perfect CSI only at the source, is derived. Providing numerical examples, we illustrate the comparison between achievable rate regions derived using CF and Decode-and-Forward (DF) schemes.

In this paper, we introduce discrete memoryless Interference Channel (IFC) with two relays as two interfering transmitter-receiver pairs that are aided by two relays. We propose two different coding strategies for this channel. In the first strategy, we assume that each relay tries to mainly help one of the transmitter-receiver pairs through signal relaying and interference cancellation, while in the second strategy we assume that each relay tries to help both transmitter-receiver pairs. In our coding schemes, we employ rate-splitting, generalized block Markov coding, superposition coding and Gel'fand-Pinsker binning to cancel parts of the interference known to be experienced at the receivers. The derived achievable rate regions can be specialized to new achievable rate regions for discrete memoryless IFC with a relay. Under special conditions, the derived achievable rate regions also reduce to some previously known ones.transmitter-receiver pairs.

The Partially Cooperative Relay-Broadcast Channel (PC-RBC) is a generalization of Relay Channel in which the relay node decodes its own private message. In this paper, we introduce a class of parallel PC-RBCs with three unmatched subchannels, in which the first component of the channel is assumed to be degraded, the second to be orthogonal and the third to be deterministic. We characterize the capacity region of this channel for the case where the source sends a private message for each of the users. We also investigate a class of parallel relay channels with three unmatched subchannels, in which the first component of the channel is degraded, the second is orthogonal and the third is semi-deterministic, and characterize the capacity of it. Our capacity results enlarge the family of PC-RBCs and relay channels for which the capacity region is known.

We consider the Gaussian Dirty Tape Channel (DTC) Y = X + S + Z, where S is an additive Gaussian interference known causally to the transmitter. The general expression maxPU,f(·),X = f(U, S)I(U; Y) is proposed for the capacity of this channel. For linear assignment to f(-), i.e., X = U - βS, this expression leads to the compensation strategy proposed previously by Willems to obtain an achievable rate for the DTC. We show that linear assignment to f(·) is optimal under the condition that there exists a real number β* such that the pair (X + β S, U) is independent of the interference S. Furthermore, by applying a time-sharing technique to the achievable rate derived by linear assignment to f (·), an improved lower bound on the capacity of DTC is obtained. We also consider the Gaussian multiple access channel with additive interference, and study two different scenarios for this system. In the first case, both transmitters know interference causally while in the second, one transmitter has access to the interference noncausally and the other causally. Achievable rate regions for these two scenarios are then established.

In this paper, we investigate Causal Cognitive Interference Channel (CC-IFC) with delay in which the cognitive user transmission can depend on L future received symbols as well as the past ones. We study two special cases: CC-IFC without delay (L = 1), where the cognitive user can use only current and past received symbols, and CC-IFC with a block length delay (L = n), wherein the entire received sequence can be used. In each case, we obtain an inner bound on the capacity region. Our coding schemes are based on the generalized block Markov superposition coding and instantaneous relaying for CC-IFC without delay, and non-causal partial Decode-and-Forward (DF) for CC-IFC with a block length delay. Further, providing converse proofs, we show that the derived inner bounds are tight in some cases. Hence, we characterize the capacity regions for the classes of degraded and semi-deterministic CC-IFC without delay and CC-IFC with a block length delay, under strong interference conditions.

The discrete memoryless state-dependent relay channel (SD-RC) is considered in this study. Two main cases are investigated: SD-RC with non-causal channel state information (CSI) and SD-RC with causal CSI. In each case, the SD-RC with partial CSI at the source and the relay is considered. As special cases it includes three different situations in which perfect CSI is available: (i) only at the source, (ii) only at the relay and (iii) both at the source and the relay. For the non-causal situation, the authors establish lower bound on capacity (achievable rate) of the SD-RC, using Gel'fand-Pinsker coding at the nodes informed of CSI and compress-and-forward (CF) strategy at the relay. Using the Shannon's strategy and CF relaying, the authors derive lower bound on capacity of SD-RC in the causal case. Furthermore, in order to compare their derived bounds with the previously obtained results, which are based on the decode-and-forward (DF) strategy, the authors consider general Gaussian relay channel (RC) with additive independent and identically distributed Gaussian state and noise, and obtain lower bounds on capacity for the cases in which perfect CSI is available non-causally at the source or at the relay. They also present cases in which their lower bounds outperform DF-based bounds, and can achieve rates close to the upper bound. For causal case, a numerical example of the binary fading Gaussian RC with additive noise is provided.

In this paper, we consider a discrete memoryless state-dependent relay channel with non-causal channel state information (CSI). We investigate three different cases in which perfect channel states can be known non-causally: (i) only to the source, (ii) only to the relay or (iii) both to the source and to the relay node. For these three cases we establish lower bounds on the channel capacity (achievable rates) based on using Gel'fand-Pinsker coding at the nodes where the CSI is available and using compress-and-forward (CF) strategy at the relay. Furthermore, for the general Gaussian relay channel with additive independent and identically distributed (i.i.d) states and noise, we obtain lower bounds on the capacity for the cases in which CSI is available at the source or at the relay. We also compare our derived bounds with the previously obtained results which were based on decode-and-forward (DF) strategy, and we show the cases in which our derived lower bounds outperform DF based bounds, and can achieve the rates close to the upper bound.

In this paper, we consider partially and fully cooperative state-dependent relay broadcast channels with perfect causal channel state information (CSI). For these two channels, we study three different situations: 1) both the source and the relay nodes have access to perfect CSI, 2) perfect CSI is only known to the relay nodes, 3) perfect CSI is only available at the source node. In each situation we obtain the capacity region for a degraded version of the channel. Our work subsumes previously obtained results for the degraded broadcast and relay channels with perfect causal CSI.

We investigate the parallel partially cooperative relay broadcast channel with unmatched degraded subchannels. We characterize the capacity region of this channel in the general setting that, transmitter sends a common message for both users and a private message for each of them. Our achievability result is based on the choosing appropriate parameters for the general achievable rate region of partially cooperative relay broadcast channel. We provide a converse proof for this achievable region as well, which establishes the capacity region.

In this paper, we consider reliable transmission of a discrete memoryless source over multi-relay networks with correlated Side Information (SI) available at the relay nodes and the final receiver. We obtain a necessary condition for reliable source transmission over a multi-terminal network with SI, which results in a necessary condition for a multi-relay network with SI, as a special case. We also propose a separate source-channel coding scheme, and based on it, a sufficient condition for a multi-relay network with SI is derived. Based on a partitioning method and the nature of a degraded relay network, we propose another coding scheme which results in a sufficient condition for a degraded relay network with SI. We show that these proposed schemes which are based on operational separation, achieve the same rates as the joint source-channel codes and these sufficient conditions are indeed necessary conditions for the degraded relay networks with degraded SI.