  In this paper, we analyze the error performance of decode and forward (DF)
and amplify and forward (AF) multi-way relay networks (MWRN). We consider a
MWRN with pair-wise data exchange protocol using binary phase shift keying
(BPSK) modulation in both additive white Gaussian noise (AWGN) and Rayleigh
fading channels. We quantify the possible error events in an $L$-user DF or AF
MWRN and derive accurate asymptotic bounds on the probability for the general
case that a user incorrectly decodes the messages of exactly $k$
($k\in[1,L-1]$) users. We show that at high signal-to-noise ratio (SNR), the
higher order error events ($k\geq 3$) are less probable in AF MWRN, but all
error events are equally probable in a DF MWRN. We derive the average BER of a
user in a DF or AF MWRN in both AWGN and Rayleigh fading channels under high
SNR conditions. Simulation results validate the correctness of the derived
expressions. Our results show that at medium to high SNR, DF MWRN provides
better error performance than AF MWRN in AWGN channels even with a large number
of users (for example, L=100). Whereas, AF MWRN outperforms DF MWRN in Rayleigh
fading channels even for much smaller number of users (for example, $L > 10$).
