  In this paper we design network coding schemes for Differential Chaos Shift
Keying (DCSK) modulation. In this work, non-coherent chaos-based communication
system is used due to its simplicity and robustness to multipath propagation
effects, while dispensing with any channel state information knowledge at the
receiver. We propose a relay network using network coding and DCSK, where we
first present a Physical layer Network Coding (PNC) scheme with two users,
$\mathcal{A}$ and $\mathcal{B}$, sharing the same spreading code and bandwidth,
while synchronously transmitting their signals to the relay node $\mathcal{R}$.
We show that the main drawback of this design in multipath channels is the high
level of interference in the resultant signal, which severely degrades the
system performance. Hence, in order to address this problem, we propose two
coding schemes, which separate the users' signals in the frequency or the time
domains. We show also in this paper that the performance of the Analog Network
Coding (ANC) with DCSK modulation suffers from the same interference problem as
the PNC scheme. We present the analytical bit error rate performance for
multipath Rayleigh fading channel for the different scenarios and we analyse
these schemes in terms of complexity, throughput and link spectral efficiency.
