  In this paper, we analyze the symbol error rate (SER) of space-time network
coding (STNC) in a distributed cooperative network over independent but not
necessarily identically distributed (i.n.i.d.) Nakagami-$m$ fading channels. In
this network, multiple sources communicate with a single destination with the
assistance of multiple decode-and-forward (DF) relays. We first derive new
exact closed-form expressions for the SER with $M$-ary phase shift-keying
modulation ($M$-PSK) and $M$-ary quadrature amplitude modulation ($M$-QAM). We
then derive new compact expressions for the asymptotic SER to offer valuable
insights into the network behavior in the high signal-to-noise ratio (SNR)
regime. Importantly, we demonstrate that STNC guarantees full diversity order,
which is determined by the Nakagami-$m$ fading parameters of all the channels
but independent of the number of sources. Based on the new expressions, we
examine the impact of the number of relays, relay location, Nakagami-$m$ fading
parameters, power allocation, and nonorthogonal codes on the SER.
