Polar Codes with Differential Phase Shift Keying for Selective Detect-and-Forward Multi-Way Relaying Systems

Relaying with network coding forms a basis for a variety of collaborative communication systems. A linear block coding framework for multi-way relaying using network codes introduced in the literature shows great promise for understanding, analyzing, and designing such systems. So far, this technique has been used with low-density parity check (LDPC) codes and belief propagation (BP) decoding. Polar codes have drawn significant interest in recent years because of their low decoding complexity and good performance. Our paper considers the use of polar codes also as network codes with differential binary phase shift keying (DBPSK), bypassing the need for channel state estimation in multi-way selective detect-and-forward (DetF) cooperative relaying. We demonstrate that polar codes are suitable for such applications. The encoding and decoding complexity of such systems for linear block codes is analyzed using maximum likelihood (ML) decoding for LDPC codes with log-BP decoding and polar codes with successive cancellation (SC) as well as successive cancellation list (SCL) decoding. We present Monte-Carlo simulation results for the performance of such a multi-way relaying system, employing polar codes with different lengths and code rates. The results demonstrate a significant performance gain compared to an uncoded scheme. The simulation results show that the error performance of such a system employing polar codes is comparable to LDPC codes with log-BP decoding, while the decoding complexity is much lower. Furthermore, we consider a hard threshold technique at user terminals for determining whether a relay transmits or not. This technique makes the system practical without increasing the complexity and can significantly reduce the degradation from intermittent relay transmissions that is associated with such a multi-way relaying protocol.