The problem of secret sharing over the Gaussian wiretap channel is considered. A source and a destination intend to share secret information over a Gaussian channel in the presence of a wiretapper who observes the transmission through another Gaussian channel. Two constraints are imposed on the source-to-destination channel; namely, the source can transmit only binary phase shift keyed (BPSK) symbols, and symbol-by-symbol hard-decision quantization is applied to the received symbols of the destination. An error-free public channel is also available for the source and destination to exchange messages in order to help the secret sharing process. The wiretapper can perfectly observe all messages in the public channel. It is shown that a secret sharing scheme that employs a random ensemble of regular low density parity check (LDPC) codes can achieve the key capacity of the BPSK-constrained Gaussian wiretap channel asymptotically with increasing block length. To accommodate practical constraints of finite block length and limited decoding complexity, fixed irregular LDPC codes are also designed to replace the regular LDPC code ensemble in the proposed secret sharing scheme.

Abstract-A coding scheme based on irregular low-density parity-check (LDPC) codes is proposed to send secret messages from a source over the Gaussian wiretap channel to a destination in the presence of a wiretapper, with the restriction that the source can send only binary phase-shift keyed (BPSK) symbols. The secrecy performance of the proposed coding scheme is measured by the secret message rate through the wiretap channel as well as the equivocation rate about the message at the wiretapper. A code search procedure is suggested to obtain irregular LDPC codes that achieve good secrecy performance in such context.

In our previous work, we have shown that hybrid ARQ (HARQ) can be used to achieve secret communication over a fast fading channel. This is a physical-layer technique that can be used in conjunction with conventional cryptography to provide further protection from an eavesdropper. The key to our previous work was to use reliability-based HARQ to improve the decoder performance at the desired user much faster than at an eavesdropper. In this paper, we propose a new HARQ approach that provides better secrecy performance by using the most-reliable received bits at the desired user to obfuscate information transmitted in the HARQ process. In addition, we present several other performance improvements, including transmitting incremental redundancy instead of repeating information and using bit-interleaved coded modulation with higher-order modulation. Performance measures such as information rate and fractional equivocation rate are provided to demonstrate that the obfuscated incremental-redundancy HARQ protocol is a promising candidate for secret sharing.

Consider a wireless transmission from Alice to Bob in the presence of an eavesdropper, Eve. We propose a technique to allow Alice to send a message such that Bob can decode it but Eve can get little information about the message. This scenario is a classic example of the wiretap channel, for which several researchers have begun to develop practical schemes. However, we consider a challenging version in which the channel from Alice to Eve may be as good or better than the channel from Alice to Bob. There have been no practical secrecy coding techniques that have been developed for this scenario. The key to allow secret communication in such a scenario is feedback from Bob to Alice (which Eve can also observe). The scheme we develop uses reliabilitybased hybrid automatic-repeat-request (RB-HARQ) over a fast fading channel to provide a decoding advantage at Bob. Bob requests information about received symbols that suffer from deep fades. The retransmitted symbols improve Bob's ability to decode the message faster than at Eve, who sees retransmission of bits with random reliabilities. We evaluate the proposed scheme by performance measures such as the probability of successful decoding and the equivocation rate at Eve.

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