A Practical and Secure Lattice-based Scheme for Full-Duplex Gaussian One-Way Relay Channels

Unidirectional or one-way relaying, where two wireless nodes, each of which would like to create an in- formation flow from one node to the other one via a single decode-and-forward (DF) relay, has been an active area of recent research. We consider an additional secrecy constraint for protection against an honest but curious relay. Indeed, while the relay should decode the source message, it should be fully ignorant of the message content. We provide a secure lattice coding strategy based on quasi-cyclic low-density parity check (QC-LDPC) lattice codes for unidirectional Gaussian relay channels. QC-LDPC lattice codes are carved from infinite QC- LDPC lattices using a shaping algorithm. Due to the existence of low-overhead encoding and decoding algorithms, these lattice codes can be implemented practically in high dimensions. Our proposed scheme combines a Rao-Nam like encryption with a new DF relaying scheme for QC-LDPC lattice codes. Some chosen-plaintext attacks and recent attacks on the Rao- Nam like schemes are considered over the proposed scheme. Due to its low overhead encryption-decryption algorithms, the proposed scheme can be employed efficiently in high information rates. According to our simulation results, the proposed relaying scheme outperforms its counterparts in terms of error performance, efficiency and security.