Convolutional Polar Codes on Channels with Memory
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Arikan's recursive code construction was designed for memoryless channels, but was recently shown to also polarize channels with finite-state memory. The resulting successive cancellation decoder has a complexity that scales like the third power of the channel's memory size. Furthermore, the polar code construction was extended by replacing the block polarization kernel by a convoluted kernel. Here, we extend the polar code efficient decoding algorithm for channels with memory to the family of convolutional polar code. We use numerical simulations to study the performance of these algorithms for practically relevant code sizes and find that the convolutional structure outperforms the standard polar codes on a variety of channels with memory.
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