On the Throughput of Secure Hybrid-ARQ Protocols for Gaussian Block-Fading Channels

<para xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> The focus of this paper is an information-theoretic study of retransmission protocols for reliable packet communication under a secrecy constraint. The <emphasis emphasistype="boldital">h</emphasis>ybrid <emphasis emphasistype="boldital">a</emphasis>utomatic <emphasis emphasistype="boldital">r</emphasis>etransmission re<emphasis emphasistype="boldital">q</emphasis>uest (HARQ) protocol is revisited for a block-fading wiretap channel. Here, two legitimate users communicate over a block-fading channel in the presence of a passive eavesdropper who intercepts the transmissions through an independent block-fading channel. In this model, the transmitter obtains a 1-bit ACK/NACK feedback from the legitimate receiver via an error-free <emphasis emphasistype="boldital">public</emphasis> channel. Both reliability and confidentiality of secure HARQ protocols are studied through the joint consideration of channel coding, secrecy coding, and retransmission protocols. In particular, the error and secrecy performance of <emphasis emphasistype="boldital">repetition time diversity</emphasis> (RTD) and <emphasis emphasistype="boldital">incremental redundancy</emphasis> (INR) protocols are investigated based on Wyner code sequences. These protocols ensure that the confidential message is decoded successfully by the legitimate receiver and is kept completely secret from the eavesdropper for a set of channel realizations. This paper illustrates that there exists a rate-compatible Wyner code family which ensures a secure INR protocol. Further, it defines the <emphasis emphasistype="boldital">connection outage</emphasis> and <emphasis emphasistype="boldital">secrecy outage</emphasis> probabilities to characterize the tradeoff between the reliability of the legitimate communication link and the confidentiality with respect to the eavesdropper's link. For a given connection/secrecy outage probability pair, an achievable throughput of secure HARQ protocols is derived for block-fading channels. Finally, both asymptotic analysis and numerical calculations demonstrate the benefits of HARQ protocols to throughput and secrecy. </para>