  Polar codes are a class of capacity-achieving codes for the binary-input
discrete memoryless channels (B-DMCs). However, when applied in channels with
intersymbol interference (ISI), the codes may perform poorly with BCJR
equalization and conventional decoding methods. To deal with the ISI problem,
in this paper a new joint successive cancellation (SC) decoding algorithm is
proposed for polar codes in ISI channels, which combines the equalization and
conventional decoding. The initialization information of the decoding method is
the likelihood functions of ISI codeword symbols rather than the codeword
symbols. The decoding adopts recursion formulas like conventional SC decoding
and is without iterations. This is in contrast to the conventional iterative
algorithm which performs iterations between the equalizer and decoder. In
addition, the proposed SC trellis decoding can be easily extended to list
decoding which can further improve the performance. Simulation shows that the
proposed scheme significantly outperforms the conventional decoding schemes in
ISI channels.
