Permuted successive cancellation decoder for polar codes

We study a new variant of Arikan´s successive cancellation decoder (SCD) for polar codes. We first propose a new decoding algorithm on a new decoder graph, where the various stages of the graph are permuted. We then observe that, even though the usage of the permuted graph doesn´t affect the encoder, it can significantly affect the decoding performance of a given polar code. The new permuted successive cancellation decoder (PSCD) typically exhibits a performance degradation, since the polar code is optimized for the standard SCD. We then present a new polar code construction rule matched to the PSCD and show their performance in simulations. For all rates we observe that the polar code matched to a given PSCD performs the same as the original polar code with the standard SCD. We also see that a PSCD with a reversal permutation can lead to a natural decoding order, avoiding the standard bit-reversal decoding order in SCD without any loss in performance.