Comparison of Analog and Digital Relay Methods with Network Coding for Wireless Multicast

We study wireless multicasting from two sources to two destinations with the assistance of a single half-duplex relay. The objective is to evaluate the throughput and error performance of different analog and digital relay schemes with linear network coding at the relay. The analog relay node forwards either a scaled version of the received signal to the destinations, or alternatively, first filters the received signals to generate a linear Minimum Mean Squared Error (MMSE) estimate, which is subsequently forwarded. The digital relay scheme first detects the source transmissions, combines the packets with a network code, and forwards the resulting symbols to the destinations. For all schemes the destinations recover the source and relay signals by first applying linear MMSE filters, followed by decoding of the source bits. The performance of the schemes are compared in terms of normalized throughput (bits per channel use accounting for the delay due to the relay) and uncoded error probability, given a normalized power constraint. Both narrowband and wide-band transmission schemes are considered. Our results show that the analog relay schemes outperform the digital network coding scheme with respect to both throughput and error probability because of error propagation through the relay. Numerical results are presented, which illustrate throughput-reliability trade-offs for all schemes considered.