Polar code design for intersymbol interference channels

We analyze the general form of the extrinsic information transfer curve of polar codes viewed as multilevel codes with multistage decoding. Based on this analysis, we propose a graphical design methodology to construct polar codes for intersymbol interference channels. The method matches the extrinsic information transfer curve of the code to that of the intersymbol interference channels, so that there is an open convergence tunnel between the two. We show that polar codes can provide such a matching to the channel curve under soft-cancellation decoding and propose one such method to achieve it. Example code designs are presented to demonstrate that polar codes that are optimized for an ISI channel can significantly outperform polar codes that are designed for an AWGN channel.