TY - JOUR

T1 - Degraded broadcast channel with secrecy outside a bounded range

AU - Zou, Shaofeng

AU - Liang, Yingbin

AU - Lai, Lifeng

AU - Poor, H. Vincent

AU - Shitz, Shlomo Shamai

N1 - Funding Information:
Manuscript received September 20, 2016; revised August 23, 2017; accepted December 22, 2017. Date of publication January 11, 2018; date of current version February 15, 2018. S. Zou was supported in part by a National Science Foundation CAREER Award under Grant CCF-1026565 and in part by the National Science Foundation under Grant CNS-1116932. Y. Liang was supported in part by a National Science Foundation CAREER Award under Grant CCF-1026565, in part by the National Science Foundation under Grant CNS-1116932, and in part by the National Science Foundation under Grant CCF-1801846. L. Lai was supported by a National Science Foundation CAREER Award under Grant CCF-17-60889 and in part by the National Science Foundation under Grant CCF-16-65037 and Grant ECCS-16-60140. H. V. Poor was supported by the National Science Foundation under Grant CNS-1702808 and Grant ECCS-1647198. S. Shamai was supported in part by the European Commission in the Framework of the Network of Excellence in Wireless Communications NEWCOM and in part by the European Union’s Horizon 2020 Research and Innovation Programme under Grant 694630. This paper was presented in part at the 2015 IEEE Information Theory Workshop [1], the 2015 IEEE International Symposium on Information Theory [2], and the 2016 IEEE Information Theory Workshop [3].
Publisher Copyright:
© 1963-2012 IEEE.

PY - 2018/3

Y1 - 2018/3

N2 - The $K$-receiver degraded broadcast channel with secrecy outside a bounded range is studied, in which a transmitter sends $K$ messages to $K$ receivers, and the channel quality gradually degrades from receiver $K$ to receiver 1. Each receiver $k$ is required to decode message $W {1},\ldots,W {k}$ , for $1\leq k\leq K$ , and to be kept ignorant of $W {k+2},\ldots,W {K}$ , for $k=1,\ldots, K-2$. Thus, each message $W {k}$ is kept secure from receivers with at least two-level worse channel quality, i.e., receivers 1, $\ldots $ , $k-2$. The secrecy capacity region is fully characterized. The achievable scheme designates one superposition layer to each message with binning employed for each layer. Joint embedded coding and binning are employed to protect all upper-layer messages from lower-layer receivers. Furthermore, the scheme allows adjacent layers to share rates so that part of the rate of each message can be shared with its immediate upper-layer message to enlarge the rate region. More importantly, an induction approach is developed to perform Fourier-Motzkin elimination of $2K$ variables from the order of $K^{2}$ bounds to obtain a close-form achievable rate region. An outer bound is developed that matches the achievable rate region, whose proof involves recursive construction of the rate bounds and exploits the intuition gained from the achievable scheme.

AB - The $K$-receiver degraded broadcast channel with secrecy outside a bounded range is studied, in which a transmitter sends $K$ messages to $K$ receivers, and the channel quality gradually degrades from receiver $K$ to receiver 1. Each receiver $k$ is required to decode message $W {1},\ldots,W {k}$ , for $1\leq k\leq K$ , and to be kept ignorant of $W {k+2},\ldots,W {K}$ , for $k=1,\ldots, K-2$. Thus, each message $W {k}$ is kept secure from receivers with at least two-level worse channel quality, i.e., receivers 1, $\ldots $ , $k-2$. The secrecy capacity region is fully characterized. The achievable scheme designates one superposition layer to each message with binning employed for each layer. Joint embedded coding and binning are employed to protect all upper-layer messages from lower-layer receivers. Furthermore, the scheme allows adjacent layers to share rates so that part of the rate of each message can be shared with its immediate upper-layer message to enlarge the rate region. More importantly, an induction approach is developed to perform Fourier-Motzkin elimination of $2K$ variables from the order of $K^{2}$ bounds to obtain a close-form achievable rate region. An outer bound is developed that matches the achievable rate region, whose proof involves recursive construction of the rate bounds and exploits the intuition gained from the achievable scheme.

KW - Binning

KW - broadcast channel

KW - embedded coding

KW - multi-user

KW - secrecy capacity region

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U2 - 10.1109/TIT.2018.2791995

DO - 10.1109/TIT.2018.2791995

M3 - Article

AN - SCOPUS:85041230583

SN - 0018-9448

VL - 64

SP - 2104

EP - 2120

JO - IEEE Transactions on Information Theory

JF - IEEE Transactions on Information Theory

IS - 3

ER -