Polar codes for partial response channels

We describe an error-correcting system that combines polar codes with turbo equalization for partial response channels. The successive cancellation decoder, originally proposed by Arikan for polar codes, does not produce the soft outputs needed for turbo processing. The belief propagation decoder, on the other hand, requires many iterations and has high computational complexity. In this paper, we propose a soft-input soft-output variant of the successive cancellation decoder that produces the soft information required for turbo architectures, while keeping the computational complexity low. Numerical results show that the proposed decoder performs better than the hard-output successive cancellation decoder and the belief propagation decoder in the context of turbo equalization. The proposed decoder achieves this performance gain with lower complexity compared to belief propagation and maximum-likelihood decoders. Additionally, we prove that Arikan's successive cancellation decoder is a fast-polarizing instance of our soft-input soft-output successive cancellation decoder.