In the literature, it has been shown that the secrecy capacity of the additive white Gaussian noise (AWGN) wiretap channel with noise-free feedback equals the capacity of the same model without secrecy constraint, and the classical Schalkwijk-Kailath (SK) scheme achieves the secrecy capacity. In this paper, we show that in finite blocklength regime, the SK scheme is not optimal, and propose a modified SK scheme which may perform better than the classical one. Besides this, this paper establishes a finite blocklength converse for the AWGN wiretap channel with feedback, which can also be viewed as a converse for the same model without secrecy constraint. To the best of the authors' knowledge, this is the first paper to address such a problem, and the results of this paper are further explained via numerical examples.

In wireless communication systems, the intended receiver is able to obtain the perfect channel state information (CSI) as long as the training sequence is sufficiently long, and then through a quantized feedback channel (QFC), the transmitter gets imperfect CSI caused by the quantized noise. In general, the design of efficient coding schemes for wireless channels with imperfect CSI at the transmitter (I-CSIT) is difficult and challenging, and one possible method is to construct such a scheme by using channel feedback. In the literature, it has already been shown that the classical Schalkwijk-Kailath (SK) scheme for the additive white Gaussian noise (AWGN) channel with noiseless feedback is a highly efficient coding scheme since its coding complexity is extremely low and the decoding error doubly exponentially decays as the coding blocklength tends to infinity. Existing SK-type schemes mainly focus on the case that perfect CSI is known at the transceiver, and adopt modulo lattice function to eliminate the impact of feedback channel noise (often considered as AWGN) on the performance of SK-type schemes. However, for channels with I-CSIT and QFC, this does not work since the distribution of quantized noise is unknown and I-CSIT brings additional non-convergence estimation error to the transceiver, leading to the application of SK-type schemes to practical wireless scenarios becomes challenging. In this paper, first, for the quasi-static fading channel with I-CSIT and QFC, we design a modulo lattice based SK-type scheme where the receiver adopts an auxiliary signal to decode the message, and numerical results show that the rate of our scheme almost approaches that of the same model with perfect CSI at the transceiver and noise-free feedback for some cases. Next, we further extend the above scheme to the two-path fading scenario, which is modeled as the two-ray channel with I-CSIT and QFC. Treating the signal of the second path as a relay, our extended scheme combines the amplify-and-forward relay strategy and the previously proposed scheme for the same model without ISI. However, this extended scheme cannot be applied to multi-path fading scenario, to this end, we propose a new SK-type scheme for the multi-path fading case. The intuition behind this scheme is to transform the multi-path fading channel into a fading MIMO channel by discrete fourier transform (DFT), and then apply the SK-type scheme to the MIMO channel in frequency domain and use inverse DFT to obtain the codeword in time domain. The study of this paper may provide a way to design efficient coding scheme for fading channels in the presence of imperfect CSI and quantized feedback.

In this paper, coding for the covert computation over Gaussian multiple-access channel (GMAC) with feedback is investigated, where a receiver wishes to decode a function of the sources transmitted over the GMAC while ensuring a low probability of detection by a warden. Traditionally, in covert communication, the feedback from the receiver to the transmitters helps to share a secret key which is used to confuse the warden. This paper shows that a slight modification of the existing Schalkwijk-Kailath (SK) type feedback scheme for computation over GMAC satisfies covert constraint by itself, which indicates that the SK-type feedback coding schemes in the literature can also be viewed as covert computation/communication schemes for channels with feedback.

In the literature, it has been shown that feedback does not increase the optimal rate-distortion region of the dirty paper channel with state estimation at the receiver (SE-R). On the other hand, it is well-known that feedback helps to construct low-complexity coding schemes in Gaussian channels, such as the elegant Schalkwijk-Kailath (SK) feedback scheme. This motivates us to explore capacity-achieving SK-type schemes in dirty paper channels with SE-R and feedback. In this paper, we first propose a capacity-achieving feedback scheme for the dirty paper channel with SE-R (DPC-SE-R), which combines the superposition coding and the classical SK-type scheme. Then, we extend this scheme to the dirty paper multiple-access channel with SE-R and feedback, and also show the extended scheme is capacity-achieving. Finally, we discuss how to extend our scheme to a noisy state observation case of the DPC-SE-R. However, the capacity-achieving SK-type scheme for such a case remains unknown.

The classical Schalkwijk-Kailath (SK) scheme for the additive Gaussian noise channel with noiseless feedback is highly efficient since its coding complexity is extremely low and the decoding error doubly exponentially decays as the coding blocklength tends to infinity. However, its application to the fading channel with imperfect CSI at the transmitter (I-CSIT) is challenging since the SK scheme is sensitive to the CSI. In this paper, we investigate how to design SK-type scheme for the quasi-static fading channel with I-CSIT and quantized feedback. By introducing modulo lattice function and an auxiliary signal into the SK-type encoder-decoder of the transceiver, we show that the decoding error caused by the I-CSIT can be perfectly eliminated, resulting in the success of designing SK-type scheme for such a case. The study of this paper provides a way to design efficient coding scheme for fading channels in the presence of imperfect CSI and quantized feedback.

Finite blocklength (FBL) coding is an important way to realize ultra-reliable and low latency communication (URLLC), which is one of the key requirements in future wireless communication systems. In this paper, a FBL approach is proposed for the two-user multi-input single-output (MISO) multiple-access channel (MAC) with noisy feedback channel for the first time, which generalizes the classical Schalkwijk–Kailath (SK) schemes for additive white Gaussian noise (AWGN) channels. In the proposed scheme, by using minimum mean square error estimate and modulo lattice function, the variance of the receiver’s estimation error converges after several iterations, and for a desired demodulation error probability, the required codeword length is significantly short. We further explore security and robustness performances of the proposed scheme, and the numerical examples show that the proposed scheme almost meets the physical layer security requirement in some cases, and when the receiver’s power is sufficiently large, the sum-rate almost approaches the sum-rate capacity.

Linear feedback coding scheme, such as the elegant Schalkwijk-Kailath (SK) scheme, receives much attention in the literature since its decoding error probability decreases as a second-order exponential in the coding blocklength. In recent years, a linear feedback scheme has been proposed for the Gaussian relay channel (GRC) with destination-source feedback, which combines the SK scheme and the amplify-and-forward (AF) relay strategy. Since there exists three possible feedback links in the GRC, then one question beckons: is there any rate gain if there exist multiple feedback links in the GRC, and can any other relay strategy outperform the AF strategy? In this paper, we answer this question by investigating four feedback models of the GRC, namely, the GRC with destination-source and destination-relay feedback, the GRC with destination-relay and relay-source feedback, the GRC with destination-source and relay-source feedback, and the GRC with all feedback links, respectively. We propose SK-type schemes for these feedback models, and numerical examples show that when the coding blocklength is not long, the rates of our proposed schemes almost approach their asymptotic values, and these rates may be larger than those of existing schemes in the literature. The study of this paper shows that different number/location of feedback links may bring additional rate gain in finite blocklength regime.

The problem of reliably reconstructing a function of sources over a multiple-access channel (MAC) is revisited by considering channel feedback. First, a linear feedback scheme is proposed to compute the average of the Gaussian sources transmitted over the Gaussian MAC. Next, numerical results show that in some cases, our proposed scheme performs better than the existing ones without using channel feedback. Finally, we show that with a slight modification, our scheme can be directly extended to compute any linear function of the Gaussian sources transmitted over the Gaussian MAC.

This paper investigates the file and demand private coded caching system, which ensures that each user learns no information about other users' demands and non-demanded files. By proposing the innovative multi-layered coded caching schemes, this study significantly improves the achievable memory-load tradeoff compared to baseline caching schemes designed by the optimal file private scheme and demand private scheme. In particular, the proposed schemes increase the quantity of achievable memory-load points, markedly reduce the delivery load at low memory regime, and attain a tighter minimal-rate point$(M=N(K-1),\ R=1)$than the baseline schemes.

Linear feedback coding scheme, such as the elegant Schalkwijk-Kailath (SK) scheme, receives much attention in the literature since its decoding error probability decreases as a second-order exponential in the coding blocklength. In recent years, a linear feedback scheme has been proposed for the Gaussian relay channel (GRC) with destination-source feedback, which combines the SK scheme and the amplify-and-forward (AF) relay strategy. Since there exists three possible feedback links in the GRC, then one question beckons: is there any rate gain if there exist two feedback links in the GRC, and can any other relay strategy outperform the AF strategy? In this paper, we answer this question by investigating two feedback models of the GRC, namely, the GRC with destination-source and destination-relay feedback, and the GRC with destination-relay and relay-source feedback. We propose two SK-type schemes which are respectively based on the decode-and-forward (DF) relay strategy and the compress-and-forward (CF) relay strategy. Numerical examples show that the achievable rates of our proposed schemes may be larger than that of the AF relay strategy based SK-type scheme in the literature.

In this paper, the sum-capacity of the symmetric finite-state Gaussian multiple access channel (FS-GMAC) with delayed feedback is determined, where the channel state is perfectly obtained by the receiver, and the receiver sends the state and channel output back to the two transmitters through two noiseless feedback channel after same time delay. We first propose a linear-feedback coding scheme for this model, which is based on multiplexing coding and a variant of Schalkwijk- Kailath scheme, and derive the corresponding achievable sum-rate. Then, by establishing an upper bound on the sum-capacity of the same model, we further show that the proposed scheme is capacity-achieving.

Reliably reconstructing a function of independent Gaussian sources over a white Gaussian multiple-access channel (GMAC) is reconsidered by exploring channel feedback. First, an efficient linear feedback scheme is proposed to compute arbitrary linear functions of sources over GMAC in the presence of noiseless feedback, which is based on a variation of the well-known Schalkwijk-Kailath type scheme. Next, we extend our proposed scheme to the noisy feedback case (the feedback channel is a white Gaussian channel) by introducing modulo lattice function and dither signal into the original scheme. Finally, the results of this paper are further explained by numerical examples, and it is shown that our proposed schemes outperform the existing ones in some cases.

In the literature, channel feedback has already been shown to be an effective way to realize ultra-reliable and low-latency communication (URLLC). In this paper, we aim to extend the point-to-point Schalkwijk-Kailath (SK)-type noisy feedback scheme to Vehicle-to-Everything (V2X) communication scenario. Although enhanced mobile broadband (eMBB) and URLLC services are considered as key enablers for V2X communication, here we mainly focus on URLLC service due to the urgency nature of the practical transportation systems. To be specific, based on the SK-type noisy feedback scheme, we propose a finite blocklength feedback coding scheme for URLLC message by mitigating the interference of eMBB message through dirty paper coding. Then, we explore security performance of the proposed scheme by calculating the information leakage to the eavesdropper. Numerical results show that the blocklength of the proposed scheme is significantly short for the desired decoding error probability, and the proposed scheme almost meets the physical layer security requirement for some cases. The study in this paper provides a new method for the secure URLLC in V2X communication.

The classical Schalkwijk-Kailath (SK) scheme, which achieves the capacity of the additive white Gaussian noise (AWGN) channel with noiseless feedback, is also shown to be an excellent secure finite blocklength (FBL) coding scheme for the AWGN wiretap channel with noiseless feedback. In this paper, the dirty tape channel (AWGN channel with Gaussian state interference causally known by the transmitter) with noiseless/noisy feedback is investigated. First, SK-type feedback schemes are proposed for this model by introducing a lattice-based strategy into the classical SK scheme, and it is shown that this strategy helps to eliminate the impact of the state interference and the feedback channel noise on the performance of the SK scheme. Then, we analyze the security performance of the proposed schemes, in particular, for the dirty tape channel with noisy feedback and eavesdropper, we give a lower bound on the normalized eavesdropper’s equivocation by establishing a novel inequality about the differential entropy of the Gaussian modulo-lattice function. Finally, performances of our proposed schemes are further explained by numerical examples.

The two-user Gaussian broadcast wiretap channel with common message and feedback (GBC-WTC-CM-F) is revisited. Traditionally, achievable secrecy rate of this model is achieved by combining Marton’s coding scheme for the two-user broadcast channel (BC) and the secret-key based feedback scheme, where both of the two feedback links are used to transmit secret keys shared between the transceivers. Recently, it has been shown that for the Gaussian wiretap channel with feedback, the Schalkwijk-Kailath (SK) feedback scheme achieves its secrecy capacity. Then it is natural to ask: can we do better when applying the SK-type scheme to the GBC-WTC-CM-F? In this paper, we answer this question by proposing two kinds of SK-type schemes. Specifically, first, we propose a hybrid scheme where one feedback link is used to transmit a secret key, and the other one is used for SK-type coding. We show that this hybrid scheme may perform better than the existing one in some cases. Next, we show that Ozarow’s extended SK scheme for the two-user Gaussian BC with feedback, where both feedback links are used for SK-type coding, is self-secure (satisfying perfect weak secrecy constraint by itself) and may perform the best. We further show that Ozarow’s scheme is in fact a secure finite blocklength coding scheme, and extend it to the static fading SISO and SIMO cases. Finally, the results of this paper are further explained by numerical examples.

For the point-to-point additive white Gaussian noise (AWGN) channel with eavesdropper and feedback, it has already been shown that the secrecy capacity can be achieved by a secret key based feedback scheme, where the channel feedback is used for secret sharing, and then encrypting the transmitted message by the shared key, any capacity-achieving coding scheme for the AWGN channel without feedback is secure by itself, which indicates that the capacity of the same model without secrecy constraint is also an achievable secrecy rate of the AWGN channel with eavesdropper and feedback. Then it is natural to ask: is the secret key based feedback scheme still an optimal scheme for the AWGN multiple-access channel (MAC) with external eavesdropper and channel feedback (AWGN-MAC-E-CF), namely, achieving the secrecy capacity region of the AWGN-MAC-E-CF? In this paper, we show that the answer to the aforementioned question is no, and propose an optimal feedback coding scheme for the AWGN-MAC-E-CF, which combines an existing linear feedback scheme for the AWGN MAC with feedback and the secret key scheme in the literature. The study of this paper provides a way to find optimal coding schemes for AWGN multi-user channels in the presence of external eavesdronner and channel feedback.

Ultra-reliable low-latency communication (URLLC) and reconfigurable intelligent surface (RIS) aided communication are two key technologies in future wireless communications. However, secure URLLC over RIS-adied communication channels receives little attention in the literature. In this paper, we propose finite blocklength (FBL) coding schemes for RIS aided SISO/SIMO/MIMO systems in the presence of an eavesdropper (no direct link between the transceiver), which are based on an existing coding scheme for the point-to-point white Gaussian channel with noiseless feedback. Then, we show that the proposed schemes are self-secure when the blocklengths are larger than certain thresholds. Finally, numerical results show that for given decoding error probability and secrecy level, the required coding blocklengths of our proposed schemes are extremely short, and the secrecy capacities of the RIS-aided systems without channel feedback are significantly enhanced by our feedback schemes.

In this paper, the dirty-tape channel (the white Gaussian channel with causal state interference at the trans-mitter) is revisited by considering a noisy feedback link between the transmitter and receiver. A finite blocklength (FBL) coding scheme is proposed for this model, which is based on the classical Schalkwijk-Kailath (SK) scheme and an existing lattice-based interference canceling scheme. Based on the proposed scheme, an achievable rate for given blocklength and decoding error probability is obtained, and the results of this paper are further illustrated via numerical examples.

In this paper, the two-way full-duplex Gaussian channel (TW-FD-GC) is revisited by considering Gaussian state interference non-causally known by the corresponding transmitter, which is also called the two-way full-duplex dirty paper channel (TW-FD-DPC). We propose a novel coding scheme for the TW-FD-DPC, which perfectly eliminates the effect of the state interference. Numerical result shows that for a fixed decoding error probability, the encoding-decoding complexity of this scheme is extremely low.

In this paper, the role of feedback in two-way full-duplex Gaussian channel (TW-FD-GC) is revisited. First, we propose a practical coding scheme for the TW-FD-GC, which is based on the noisy type of the well-known Schalkwijk-Kailath (SK) feedback scheme. We show that though this scheme cannot achieve the capacity of the TW-FD-GC, the codeword length that achieves desired decoding error probability is extremely short. Then, we further prove that the proposed scheme is secure by itself, i.e., the achievable rate region of the proposed scheme is also an achievablesecrecyrate region of the two-way full-duplex Gaussian wiretap channel (TW-FD-GWTC). In addition, for the TW-FD-GWTC, numerical result shows that thesecrecysum rate of our proposed scheme can be as large as those achieved by existing schemes in the literature for some cases. Next, we extend the proposed scheme to the TW-FD-GC with Gaussian state interference non-causally known by the corresponding transmitter. We show that the interference can be perfectly canceled by this extended scheme. Finally, we prove that this extended scheme is also secure by itself, and numerical result shows that this extended scheme may perform better than the existing ones in the literature.

It has been shown that the SK scheme, which was proposed by Schalkwijk and Kailath, is a self-secure capacity-achieving (SSCA) feedback scheme for the Gaussian wiretap channel, i.e., the SK scheme not only achieves the feedback capacity of the Gaussian channel, but also is secure by itself and achieves the feedback secrecy capacity of the Gaussian wiretap channel. For the multi-user wiretap channels, very recently, it has been shown that Ozarow’s capacity-achieving feedback scheme for the two-user Gaussian multiple-access channel (GMAC) is the SSCA feedback scheme for the two-user Gaussian multiple-access wiretap channel (GMAC-WT). In this paper, first, we propose a SSCA feedback scheme for the two-user GMAC-WT with degraded message sets (GMAC-WT-DMS). Next, we extend the above scheme to the two-user GMAC-WT-DMS with noncausal channel state information at the transmitters (NCSIT), and show that the extended scheme is also a SSCA feedback scheme. Finally, we derive outer bounds on the secrecy capacity regions of the two-user GMAC-WT-DMS with or without NCSIT, and numerical results show the rate gains by the feedback.

The Schalkwijk-Kailath (SK) feedback scheme is a capacity-achieving coding scheme for the point-to-point white Gaussian channel with feedback. Recently, it has been shown that the SK scheme, which is not designed with consideration of secrecy, already achieves perfect weak secrecy by itself, i.e., the secrecy capacity of the Gaussian wiretap channel with feedback equals the capacity of the same model without secrecy constraint. In this paper, we propose a capacity-achieving SK type feedback scheme for the two-user Gaussian multiple-access channel with degraded message sets (GMAC-DMS). Similarly to the inherent secrecy nature of the classical SK scheme, we show that the proposed scheme is also secure by itself, which indicates that the feedback secrecy capacity of the two-user Gaussian multiple-access wiretap channel with degraded message sets (GMAC-WT-DMS) equals the capacity of the same model without secrecy constraint.

The r th relative generalised Hamming weight (RGHW) of an linear code C and an subcode , a generalisation of generalised Hamming weight (GHW), characterises code performances of wiretap channel of type II, secure network coding, linear ramp secret sharing scheme, trellis complexity etc. In this study, the authors investigate non‐asymptotic and asymptotic bounds on RGHW. In the non‐asymptotic setting, they present a new proof of the Griesmer bound on RGHW by residue code and introduce the new concept of relative chain condition. They show that code pairs meeting the Griesmer, Singleton, and weak Plotkin bounds satisfy this condition. The notion of relative chain condition and these results provide a new perspective on researches including evaluating trellis complexity and determining the weight hierarchy of code pairs etc. In the asymptotic setting, they improve previous work by introducing two new metrics, respectively, for the cases r is fixed and r is proportionally increasing with n . They show the asymptotic Singleton, Plotkin, and Gilbert–Varshamov bounds on the first metric and determine the value of the second metric, which is helpful for characterising the optimal asymptotic performances of applications and constructing the optimal coding schemes.

Mobile-edge nodes, as an efficient approach to the performance improvement of wireless sensor networks (WSNs), play an important role in edge computing. However, existing works only focus on connected networks and suffer from high calculational costs. In this article, we propose a rendezvous selection strategy for data collection of disjoint WSNs with mobile-edge nodes. The goal is to achieve full network connectivity and minimize path length. From the perspective of the application scenario, this article is distinctive in two aspects. On the one hand, it is specially designed for partitioned networks which are much more complex than conventional connected scenarios. On the other hand, this article is specially designed for delay-harsh applications rather than usual energy-oriented scenarios. From the viewpoint of the implementation method, a simplified ant colony optimization (ACO) algorithm is performed and displays two characteristics. The first one is the path segmenting mechanism, simplifying the path construction of each part and consequently reducing the computational cost. The second one is the candidate grouping mechanism, reducing the search space and accordingly speeding up the convergence speed. Simulation results demonstrate the feasibility and advantages of this approach.

In this article, a general framework for enhancing the physical layer security (PLS) in the Internet of Things (IoT) systems via channel feedback is established. To be specific, first, we study the compound wiretap channel (WTC) with feedback, which can be viewed as an ideal model for enhancing the PLS in the downlink transmission of IoT systems via feedback. A novel feedback strategy is proposed and a corresponding lower bound on the secrecy capacity is constructed for this ideal model. Next, we generalize the ideal model (i.e., the compound WTC with feedback) by considering channel states and feedback delay, and this generalized model is called the finite state compound WTC with delayed feedback. The lower bounds on the secrecy capacities of this generalized model with or without delayed channel output feedback are provided, and they are constructed according to variations of the previously proposed feedback scheme for the ideal model. Finally, from a Gaussian fading example, we show that the delayed channel output feedback enhances the achievable secrecy rate of the finite state compound WTC with only delayed state feedback, which implies that feedback helps to enhance the PLS in the downlink transmission of the IoT systems.

Connectivity restoration plays an important role in maintaining the long-term operation in wireless sensor networks (WSNs), especially, in environment-harsh cases. However, current solutions lack the ability to handle the second damages and the capacity of designing requirement-different connectivity approaches according to different needs. In this article, we propose a durability-based connectivity establishment (DBCE) scheme for disjoint segments of WSNs. This scheme includes three approaches regarding segment evaluation or segment selection: 1) a segment shape evaluation approach; 2) a region different connectivity approach; and 3) a data traffic transfer approach, for their respective objectives. The unique characteristics of this article are twofold. On the one hand, this is the first attempt to investigate segment shapes, which we demonstrate have great impact on the robustness of the network. On the other hand, distinguished from the existing networks with uniform connectivity rule, the network is divided into two parts and different connectivity sequences and connectivity approaches are designed according to disparate features and requirements of the network. The performance of DBCE is validated through extensive simulation experiments.

We investigate the state-dependent Gaussian wiretap channel with noncausal channel state information at the transmitter (GWTC-N-CSIT), and explore whether three strategies (i.e., taking action on the state, legitimate receiver's channel output feedback, and combining the former two strategies together) help to enhance the secrecy capacity of the GWTC-N-CSIT. To be specific, we first determine the secrecy capacity of the GWTC-N-CSIT with noiseless feedback. Next, we derive lower and upper bounds on the secrecy capacity of the GWTC-N-CSIT with action-dependent state. Finally, we derive lower and upper bounds on the secrecy capacity of the GWTC-N-CSIT with both action-dependent state and noiseless feedback, and show that these bounds meet for a special case. Numerical results of this paper indicate that all three strategies enhance the secrecy capacity of the GWTC-N-CSIT. The study of this paper offers new options for enhancing the secrecy rates of the state-dependent wiretap channel models.

The dirty paper wiretap channel, also referred to as the Gaussian wiretap channel with noncausal state at the transmitter, is revisited. First, we determine the secrecy capacity of the dirty paper wiretap channel with noiseless feedback, where the feedback channel is from the legitimate receiver to the transmitter. Next, we obtain lower and upper bounds on the secrecy capacity of the action-dependent dirty paper wiretap channel with noiseless feedback, and show that these bounds meet for a special case. Unlike the fact that action on the state helps to enhance the capacity of the dirty paper channel with feedback, numerical results of this paper indicate that it may not help to enhance the secrecy capacity of the dirty paper wiretap channel with feedback.

The broadcast channel with mutual secrecy requirement at the receivers (BC-MSR-R) is a basic model characterizing the physical layer security (PLS) in the down-link of the wireless communication systems, where one transmitter sends two independent messages to two receivers via a broadcast channel, and each receiver can successfully decode his/her intended message and wishes to overhear the other one's message. This paper studies how to enhance the already existing secrecy rate region of the BC-MSR-R via receivers' feedback. Specifically, we propose two feedback strategies for the BC-MSR-R, where one uses the feedback to generate pure secret keys protecting the transmitted messages, and the other uses the feedback to generate not only keys but also cooperative messages helping the receivers to improve their decoding performance. Different inner bounds on the secrecy capacity region of the BC-MSR-R with noiseless feedback are constructed according to different feedback strategies, and these bounds are further illustrated by a Dueck-type example.

The model of wiretap channel (WTC) is important as it constitutes the essence of physical layer security. Recently, it has been shown that a noiseless feedback channel from the legitimate receiver to the transmitter helps to increase the secrecy capacity of the WTC. However, the present feedback strategy focuses only on generating the key from the feedback signal and using this key to protect part of the transmitted message. This secret key-based feedback strategy has been proved to be optimal only for some degraded cases. In this paper, we propose a new feedback strategy for the WTC, where the feedback signal is not only used to generate the key but also used to generate cooperative information helping the legitimate parties to improve their encoding and decoding performance. We show that the proposed new strategy performs better than the already existing one, and the results are further explained via a binary example.

The model of wiretap channel (WTC) is important as it constitutes the essence of physical layer security (PLS). Wiretap channel with noiseless feedback (WTC-NF) is especially interesting as it shows what can be done when a private feedback is available. The already existing secret key based feedback coding scheme focuses on generating key from the feedback and using this key to protect part of the transmitted message. It has been shown that this secret key based feedback coding scheme is only optimal for the degraded WTC-NF, and finding an optimal feedback scheme for the general WTC-NF motivates us to exploit other uses of the feedback. In this paper, a new feedback coding scheme for the general WTC-NF is proposed, where the feedback is not only used to generate key, but also used to generate help information which helps the legitimate parties to improve the communication between them. We show that the proposed new feedback scheme performs better than the already existing one, and a binary example is given to further explain the results of this paper.

Recently, it has been shown that the time-varying multiple-access channel (MAC) with perfect channel state information (CSI) at the receiver and delayed feedback CSI at the transmitters can be modeled as the finite state MAC (FS-MAC) with delayed state feedback, where the time variation of the channel is characterized by the statistics of the underlying state process. To study the fundamental limit of the secure transmission over multi-user wireless communication systems, we re-visit the FS-MAC with delayed state feedback by considering an external eavesdropper, which we call the finite state multiple-access wiretap channel (FS-MAC-WT) with delayed feedback. The main contribution of this paper is to show that taking full advantage of the delayed channel output feedback helps to increase the secrecy rate region of the FS-MAC-WT with delayed state feedback. Moreover, by a degraded Gaussian fading example, we show the effects of feedback delay and channel memory on the secrecy sum rate of the FS-MAC-WT with delayed feedback.

The finite state Markov channel (FSMC) has been shown to be a useful model for the time-varying fading channels. In this paper, we study the security issue in the wireless communication systems by considering the FSMC with an eavesdropper, which we call the finite state Markov wiretap channel (FSM-WC). More specifically, the FSM-WC is a channel with one input (the transmitter) and two outputs (the legitimate receiver and the eavesdropper). The transition probability of the FSM-WC is controlled by a channel state which takes values in a finite set, and it undergoes a Markov process. We assume that the state is perfectly known by the legitimate receiver and the eavesdropper, and through a noiseless feedback channel, the legitimate receiver sends the state back to the transmitter after some time delay. Measuring the eavesdropper's uncertainty about the transmitted message by equivocation, we provide inner and outer bounds on the capacity-equivocation region of this novel model, and show that these bounds meet (the capacity-equivocation region is determined) if the channel output for the eavesdropper is a degraded version of that for the legitimate receiver. The capacity results of this paper are further explained via degraded Gaussian and Gaussian fading examples.

The physical layer security in the up‐link of the wireless communication systems is often modelled as the multiple access wiretap channel (MAC‐WT), and recently it has received a lot attention. In this paper, the MAC‐WT has been re‐visited by considering the situation that the legitimate receiver feeds his received channel output back to the transmitters via two noiseless channels, respectively. This model is called the MAC‐WT with noiseless feedback. Inner and outer bounds on the secrecy capacity region of this feedback model are provided. To be specific, we first present a decode‐and‐forward (DF) inner bound on the secrecy capacity region of this feedback model, and this bound is constructed by allowing each transmitter to decode the other one's transmitted message from the feedback, and then each transmitter uses the decoded message to re‐encode his own messages, i.e. this DF inner bound allows the independent transmitters to co‐operate with each other. Then, we provide a hybrid inner bound which is strictly larger than the DF inner bound, and it is constructed by using the feedback as a tool not only to allow the independent transmitters to co‐operate with each other but also to generate two secret keys, respectively, shared between the legitimate receiver and the two transmitters. Finally, we give a sato‐type outer bound on the secrecy capacity region of this feedback model. The results of this paper are further explained via a Gaussian example, and from this example, we see that the noiseless feedback helps to enhance the achievable secrecy rate region of the Gaussian MAC‐WT without feedback.

The finite-state Markov channel (FSMC), where the channel transition probability is controlled by a state undergoing a Markov process, is a useful model for the mobile wireless communication channel. In this paper, we investigate the security issue in the mobile wireless communication systems by considering the FSMC with an eavesdropper, which we call the finite-state Markov wiretap channel (FSM-WC). We assume that the state is perfectly known by the legitimate receiver and the eavesdropper, and through a noiseless feedback channel, the legitimate receiver sends his received channel output and the state back to the transmitter after some time delay. Inner and outer bounds on the capacity-equivocation regions of the FSM-WC with delayed state feedback and with or without delayed channel output feedback are provided in this paper, and we show that these bounds meet if the eavesdropper's received symbol is a degraded version of the legitimate receiver's. The above-mentioned results are further explained via a degraded Gaussian fading example.

In this paper, we investigate the effects of a trusted relay node on the secrecy of the broadcast channel by considering the model of relay broadcast channel with confidential messages (RBC-CM). Inner and outer bounds on the capacity-equivocation region of the RBC-CM are provided, and the capacity results are further explained via a degraded Gaussian example, which we call the degraded Gaussian relay broadcast channel with one common and one confidential messages. Numerical results show that this trusted relay node helps to enhance the security of the Gaussian broadcast channel with one common and one confidential messages.

Incorporating information security and error correction in network coding, which has various applications in communication theory, for example, secret key sharing through a network, is of special interest and has been widely studied. To make a more intensive analysis of secure error‐correcting network codes, we investigate how to secure k source symbols transmission in a multicast network against an adversary that can obtain k 1 source symbols as side information, eavesdrop μ channels and contaminate d channels. We introduce relative network generalised Hamming weight (RNGHW) with network error correction (NEC), or briefly NEC‐RNGHW, to measure the equivocation to the adversary. Network generalised singleton bound on NEC‐RNGHW is obtained and code constructions achieving the bound are provided. By these constructions, the maximum rate of a secure linear multicast is n − 2 d − μ − k 1 , where n is the minimum value of the maxflows from a source node to sink nodes. We also characterise the equivocation by the relative profiles of a linear code and a subcode, and tighten the singleton bound on equivocation by the generalised Griesmer bound on relative profiles.

In this paper, we investigate the effects of an additional trusted relay node on the secrecy of multiple-access wiretap channel (MAC-WT) by considering the model of multiple-access relay wiretap channel (MARC-WT). More specifically, first, we investigate the discrete memoryless MARC-WT. Three inner bounds [with respect to decode-and-forward (DF), noise-and-forward (NF), and compress-and-forward (CF) strategies] on the secrecy capacity region are provided. Second, we investigate the degraded discrete memoryless MARC-WT, and present an outer bound on the secrecy capacity region of this degraded model. Finally, we investigate the Gaussian MARC-WT, and find that the proposed relay strategies (DF, NF, CF strategies) help to enhance Tekin-Yener's achievable secrecy rate region of the Gaussian MAC-WT.

The multiple‐access wiretap channel (MAC‐WTC) with common channel state information (CSI) at the encoders is studied, where two transmitters wish to send their confidential messages (no common message) to a legitimate receiver, while keeping a wiretapper as ignorant of the confidential messages as possible. Meanwhile, the channel is controlled by CSI, and it is available at the transmitters in a non‐causal manner or causal manner. This model can be viewed as a MAC extension of the WTC with CSI. Both the situation that the encoders can cooperate with each other and the situation that cooperation is not allowed between the encoders are investigated. More specifically, first, the cooperative MAC‐WTC with common CSI at the encoders is investigated, inner bounds on the secrecy capacity regions are provided for both non‐causal and causal manners. Secondly, the non‐cooperative MAC‐WTC with common CSI at the encoders is investigated, and also provide inner bounds on the secrecy capacity regions for both non‐causal and causal manners. Finally, by calculating the binary examples, the authors find that the cooperation between the encoders helps to obtain a larger secrecy rate region, that is, cooperation enhances the security of the MAC‐WTC with common CSI at the encoders.

In this paper, we investigate the model of degraded broadcast channel with noncausal side information, confidential messages and noiseless feedback. This work is from Steinberg's work on the degraded broadcast channel with noncausal side information, and Csiszár and Körner's work on broadcast channel with confidential messages. In this new model, the transmitter sends a confidential message to the non-degraded receiver, and meanwhile sends a common message to both the degraded and non-degraded receivers. Moreover, the channel for the non-degraded receiver is controlled by channel state information (side information), and it is available to the transmitter in a noncausal manner (termed here noncausal side information). In addition, we assume that there is a noiseless feedback from the output of the channel for the non-degraded receiver to the transmitter, and it helps them share a secret key, which enlarges the degraded receiver's uncertainty about the confidential message. Measuring the uncertainty by equivocation (conditional entropy), the capacity-equivocation region composed of all achievable rates-equivocation triples is determined for this new model. Furthermore, the secrecy capacity is formulated, which provides the best transmission rate with perfect secrecy.

The non-degraded wiretap channel with noiseless feedback is first investigated by R. Ahlswede and N. Cai, where lower and upper bounds on the secrecy capacity are provided in their work. However, the capacity-equivocation region has not been determined yet. In this paper, the capacity-equivocation region is determined for the non-degraded wiretap channel with noiseless feedback. Furthermore, the secrecy capacity of this model is formulated, which provides the best transmission rate with perfect secrecy.