  A polar-coded transmission (PCT) scheme with joint channel estimation and
decoding is proposed for channels with unknown channel state information (CSI).
The CSI is estimated via successive cancellation (SC) decoding and the
constraints imposed by the frozen bits. SC list decoding with an outer code
improves performance, including resolving a phase ambiguity when using
quadrature phase-shift keying (QPSK) and Gray labeling. Simulations with 5G
polar codes and QPSK show gains of up to $2$~dB at a frame error rate (FER) of
$10^{-4}$ over pilot-assisted transmission for various non-coherent models.
Moreover, PCT performs within a few tenths of a dB to a coherent receiver with
perfect CSI. For Rayleigh block-fading channels, PCT outperforms an FER upper
bound based on random coding and within one dB of a lower bound.
