Compress-forward coding with BPSK modulation for the half-duplex Gaussian relay channel

Cover and El Gamal derived the tightest bounds on the capacity of the relay channel using random coding and suggested two coding strategies, namely, decode-forward (DF) and compress-forward (CF), to provide the best known lower bound of the achievable rate. Practical code designs proposed recently mainly exploit DF to approach the lower bound. Following the latest development in practical distributed source-channel coding, this paper studies CF coding with BPSK modulation for the relay channel. In CF scheme, Wyner-Ziv coding is applied at the relay to exploit the joint statistics between signals at the relay and the destination. We employ Slepian-Wolf coded nested scalar quantization (SWCNSQ) in practical Wyner-Ziv coding at the relay and compute the achievable rates of this scheme with BPSK modulation for the half-duplex Gaussian relay channel. We present a code design based on LDPC codes for error protection at the source and NSQ and IRA codes for CF at the relay. Simulation results show that our design comes within 1.48-1.92 dB of the SWCNSQ limit.