Symbol-Likelihood Based Successive-Cancellation List Polar Decoding for Short-Packet Non-Coherent Communications

Motivated by using non-coherent transmission for coverage enhancement of 5G uplink control channel, this paper proposes a symbol-likelihood based successive cancellation list (SCL) polar decoder that takes into account the impact of constellation modulation. The conventional SCL polar decoding is based on likelihoods of individual coded bits, implicitly assuming independence among them. To circumvent the issue that in practice bit-dependency may occur for bits transmitted in the same constellation symbol, an interleaver is typically inserted before bit-to-symbol mapping. However, interleaving cannot be effective if the transmission is made of only few symbols, as in short packet non-coherent communications typically using highorder multi-dimensional constellations. The proposed decoder is shown to effectively solve this problem and improves the block error rate in a short packet regime, without needs for changing the encoder. Moreover, this symbol-based decoding can still be efficiently performed in a recursive manner by using a data flow graph with butterfly structure as in conventional polar decoding.