  Orthogonal time frequency space (OTFS) modulation is a recently developed
multi-carrier multi-slot transmission scheme for wireless communications in
high-mobility environments. In this paper, the error performance of coded OTFS
modulation over high-mobility channels is investigated. We start from the study
of conditional pairwise-error probability (PEP) of the OTFS scheme, based on
which its performance upper bound of the coded OTFS system is derived. Then, we
show that the coding improvement for OTFS systems depends on the squared
Euclidean distance among codeword pairs and the number of independent
resolvable paths of the channel. More importantly, we show that there exists a
fundamental trade-off between the coding gain and the diversity gain for OTFS
systems, i.e., the diversity gain of OTFS systems improves with the number of
resolvable paths, while the coding gain declines. Furthermore, based on our
analysis, the impact of channel coding parameters on the performance of the
coded OTFS systems is unveiled. The error performance of various coded OTFS
systems over high-mobility channels is then evaluated. Simulation results
demonstrate a significant performance improvement for OTFS modulation over the
conventional orthogonal frequency division multiplexing (OFDM) modulation over
high-mobility channels. Analytical results and the effectiveness of the
proposed code design are also verified by simulations with the application of
both classical and modern codes for OTFS systems.
