On Hierarchical Network Coding Versus Opportunistic User Selection for Two-Way Relay Channels with Asymmetric Data Rates

We address in this paper the challenge of coping with asymmetric data rates in two-way relay channels. We consider a relay network comprising two sources and one relay. The sources communicate at different rates through the relay. That is, we assume that one source uses M
₁
-QAM (quadrature amplitude modulation) and the other uses M
₁
/M
₂
-QAM hierarchical modulation where M
₁
≠ M
₂
. For the underlying network, we consider two decode-and-forward (DF) relaying schemes. One scheme combines hierarchical zero padding and network coding (HZPNC) at the relay. The novelty of this scheme lies in the way the two signals (that have different lengths) are network-coded at the relay. The other scheme is referred to as opportunistic user selection (OUS) where the user with a better end-to-end channel quality is given priority for transmission. We analyze both schemes where we derive closedform expressions for the end-to-end (E2E) bit error rate (BER). Since the two schemes offer a trade-off between performance and throughput, we analyze and compare both schemes in terms of channel access probability and average throughput. We show that HZPNC offers better throughput and fairness for both users, whereas OUS offers better performance. We also compare the performance of HZPNC with existing schemes including the original zero padding, nesting constellation modulation and superposition modulation. We show through examples the superiority of the proposed HZPNC scheme in terms of performance and/or reduced complexity.