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.

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.

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.

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.

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.

Load balancing plays a key role in workload scheduling policies which count in the performance improvement of parallel applications. A critical problem of load balancing is to make a reasonable definition of load index. Unfortunately, few studies provided enough scientific justifications for the choice of load indices. In this paper, a reasonable approach for defining a load index based on factor analysis theory is introduced, which is helpful to reasonable designs of workload scheduling algorithms. An example testing on an accounting log of the CM-5 parallel machine is presented to show the usage of this method.