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SCIENCE CHINA Information Sciences, Volume 63 , Issue 2 : 122303(2020) https://doi.org/10.1007/s11432-019-2660-3

Quasi-concave optimization of secrecy redundancy rate in HARQ-CC system

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  • ReceivedMay 2, 2019
  • AcceptedSep 3, 2019
  • PublishedJan 15, 2020

Abstract

In a hybrid automatic repeat request with chase combining (HARQ-CC) system,we analyze physical layer secure performance and determine the secrecy redundancy rateby proposed quasi-concave optimization methods with effective secrecy throughput (EST) criteria.First, key performance metrics, including connection outage probability (COP),secrecy outage probability (SOP), EST, and delay, are discussed.Then, under the constraint of COP, we optimize the secrecy redundancy rate to maximize the EST,which is a quasi-concave function, by both the bisection and fixed-point methods.Furthermore, under the simultaneous constraints of COP and SOP,the bisection and Lagrangian multiplier methods are applied to optimize the secrecy redundancy rate.From the comparison of the numerical and simulated results,it is concluded that EST demonstrates practical secure performance of HARQ-CC,and the proposed optimization methods adjust the secrecy redundancy rate for improved security.


Acknowledgment

This work was supported by National Natural Science Foundation of China (Grant No. 61673049) and Natural Science Foundation of the Higher Education Institutions of Anhui Province (Grant No. KJ2018A0441).


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  • Figure 1

    (Color online) Secure HARQ-CC system model.

  • Figure 4

    (Color online) EST versus $R_E$ for COP constraint $P_e^\star=10^{-4}$ and different average received SNR of wiretap channel $\bar~\lambda_E~\in~\left\{0,~5,~10~\right\}\textup{dB}$, $\bar~\lambda_B~=~10~\textup{dB}$, $K=10$.

  • Figure 5

    (Color online) EST versus $R_E$ for same COP constraint $P_e^\star~=~10^{-4}$ and different SOP constraints $P_s^\star~\in~\left\{0.6,~10^{-1},~10^{-3}\right\}$, $\bar~\lambda_B~=~20~\textup{dB}$, $\bar~\lambda_E=5~\textup{dB}$, $K=10$. (a) $P_s^\star~=~0.6$; (b) $P_s^\star~=~10^{-1}$; (c) $P_s^\star~=~10^{-3}$.

  • Figure 6

    (Color online) The relationship between delay and secrecy performances for different average received SNR of wiretap channel. $\bar~\lambda_B~=~20~\textup{dB}$, $\bar~\lambda_E~\in~\left\{0,~5,~10~\right\}\textup{dB}$, $R_B=5$, $R_E=3$. (a) SOP versus $K$; (b) EST versus $K$.

  •   

    Algorithm 1 Bisection method for solving quasi-concave problem (23)

    Require:$l=0$, $u=R_B^\star$, $\epsilon=10^{-3}$;

    while $u-l~\leq~\epsilon$ do

    $t~\Leftarrow~(u+l)/2$;

    Solve the concave feasible problem (33);

    if problem (33) is feasible then

    $l~\Leftarrow~t$;

    else

    $u~\Leftarrow~t$;

    end if

    end while

    Output:$R_E^{\rm~opt1}$;

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