Short-Block Length Polar-Coded Modulation for the Relay Channel

Short-block length communication is becoming increasingly important for applications such as machine-to-machine communication, among others. This paper studies polar-coded modulation in the short-block length regime for decode-forward, amplify-forward and compress-forward relays. Our work seamlessly combines multi-level signaling, polar coding/decoding, and the requirements of relaying, into encoders and decoders that exhibit excellent performance. Compared with the state of the art in decode-forward, our work demonstrates 2.5 dB improvement (at block length 512). For shorter block lengths 256 and 128, this work is the first reported implementation for any coded modulation and any relaying protocol. In the category of polar-coded full-duplex relaying, this work presents the first implementation at any block length and for any relaying protocol. For decode-forward, we propose and analyze joint iterative belief propagation decoding with polar codes, and successive list decoding with polarization-adjusted convolutional (PAC) codes. For amplify-forward, we utilize PAC codes and successive list decoding. For the three relaying protocols, the respective dispersion bounds are presented for comparison, and the error exponent of the multi-level relaying coded modulations are analyzed to shed light on the results. Extensive simulations verify the performance of the proposed coding schemes.