Secure HARQ With Multiple Encoding Over Block Fading Channels: Channel Set Characterization and Outage Analysis

We consider a scenario where agent Alice aims at transmitting a message to agent Bob, while keeping it secret from a third eavesdropper agent Eve. The transmissions occur on block-fading channels, and Alice only has a statistical channel state information (CSI) on both Bob and Eve channels. In this paper, we add secrecy features to hybrid automatic repeat request (HARQ) in what becomes a secure HARQ (S-HARQ) scheme. In particular, Alice encodes the secret message and splits the codeword into blocks. Then, she transmits one block at a time and after each transmission Bob feeds back an acknowledge (ACK) (not acknowledge (NACK)) packet, indicating he was (was not) able to decode the secret message. Upon an ACK Alice stops transmission, while upon a NACK Alice re-encodes the secret message into a new codeword and transmits it block by block, waiting for a new feedback. The process is iterated until either Bob decodes the message or a maximum number of codewords has been transmitted. We characterize the set of channels for which there exists a sequence of codes that ensure both vanishing error probability to Bob and vanishing rate of information leakage to Eve in the limit of infinitely long codewords. We also analyze the secrecy and decodability outage probabilities, providing closed form expressions for the case of additive white Gaussian noise channels with Rayleigh fading. The tradeoff between the number of blocks per codeword and the maximum number of codewords to be transmitted is also discussed.