In this paper, we assess the random coding error
exponents (EEs) corresponding to decode-and-forward (DF),
compress-and-forward (CF) and quantize-and-forward (QF) relaying
strategies for a parallel relay network (PRN), consisting
of a single source and two relays. Moreover, through numerical
analysis we show that the EEs achieved by using QF relaying
along with non-Gaussian signaling (coded modulation, M-QAM)
at the source and symbol-by-symbol uniform scalar quantizers
(uSQs) at the relays is better than that achieved by DF and CF
relaying strategies when the system is in the low signal-to-noise
ratio (SNR) regime and the backhaul capacity is sufficient. This
behavior is due to the structure of coded modulation, as opposed
to Gaussian signaling, which leads to better EEs for simple
relaying strategies compared to its more complex counterparts.