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



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


    Solve the concave feasible problem (33);

    if problem (33) is feasible then




    end if

    end while