Polar Coding for Parallel Dirty Paper Channels

This paper proposes three coding techniques based on polar codes for transmission over parallel dirty paper channels, which models the effective channel of a particular user in a Gaussian MIMO broadcast channel. The proposed coding schemes exhibit a comparable frame error rate performance to multi-level shaped polar codes over parallel AWGN channels. For parallel dirty paper channels, it is shown that designing a single multi-level polar code with a structured interleaver provides about 0.24 dB gain in comparison to the transmission of separate multi-level polar codes when a successive cancellation (SC) decoder is used for shaping and an SC list decoder with a list size of 8 is used for channel decoding. To show the performance limits over parallel dirty paper channels in the finite block length regime, achievability and converse bounds are computed and a normal approximation is formulated under the assumption of perfect constellation shaping.