Dirty Paper Coding Based on Polar Codes and Probabilistic Shaping

A precoding technique based on polar codes and probabilistic shaping is introduced for dirty paper coding. Two variants of the precoding use multi-level shaping and sign-bit shaping in one dimension. The decoder uses multi-stage successive-cancellation list decoding with list-passing across the bit levels. The approach achieves approximately the same frame error rates as polar codes with multi-level shaping over standard additive white Gaussian noise channels at a block length of 256 symbols and with different amplitude shift keying (ASK) constellations.