Study on Successive Cancellation Decoding of Polar Codes.

Harish Vangala, Emanuele Viterbo, Yi Hong

Abstract—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 in simulations that this can yield BER gains for high code rates. For lower rates we observe that the polar code matched to a given PSCD performs as well 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. Keywords—Successive cancellation decoder, permuted succes-sive cancellation decoder, decoding order, permuted polar code construction, permutation invariance of the polar encoder. I.

So‐Yeon Choi, Youngjoo Lee, Hoyoung Yoo

Ali Farsiabi, Hamid Ebrahimzad, Masoud Ardakani +1 more

Non-binary polar codes (NBPCs) decoded by successive cancellation (SC) algorithm have remarkable bit-error-rate performance compared to the binary polar codes (BPCs). Due to the serial nature, SC decoding suffers from large latency. The latency issue in BPCs has been the topic of extensive research and it has been notably resolved by the introduction of fast SC-based decoders. However, the vast majority of research on NBPCs is devoted to issues concerning design and efficient implementation. In this paper, we propose fast SC decoding for NBPCs constructed based on 2 x 2 kernels. In particular, we identify various non-binary special nodes in the SC decoding tree of NBPCs and propose their fast decoding. This way, we avoid traversing the full decoding tree and significantly reduce the decoding delay compared to symbol-by-symbol SC decoding. We also propose a simplified NBPC structure that facilitates the procedure of non-binary fast SC decoding. Using our proposed fast non-binary decoder, we observed an improvement of up to 95% in latency concerning the original SC decoding. This is while our proposed fast SC decoder for NBPCs incurs no error-rate loss.

So Yeon Choi, Ho Young Yoo

Moon-Ho Lee, Jun Li, Juyong M. Park

Ali Farsiabi, Hamid Ebrahimzad, Masoud Ardakani +1 more

Non-binary polar codes (NBPCs) decoded by successive cancellation (SC) algorithm have remarkable bit-error-rate performance compared to the binary polar codes (BPCs). Due to its serial nature, SC decoding suffers from long latency. The latency issue in BPCs has been the topic of extensive research and it has been notably resolved by the introduction of fast SC-based decoders. However, the latency problem of NBPCs is mainly untouched and the vast majority of research on NBPCs is devoted to issues concerning design and efficient implementation. In this paper, we propose fast SC decoding for NBPCs constructed based on$2\times 2$kernels. In particular, we extend the special nodes of BPCs to their non-binary counterpart and define various non-binary special nodes in the SC decoding tree of NBPCs and propose their fast decoding. This way, we avoid traversing the full decoding tree and significantly reduce the decoding delay compared to symbol-by-symbol SC decoding. We also propose a simplified NBPC structure that facilitates the procedure of non-binary fast SC decoding. Using our proposed fast non-binary decoder, we observe an improvement of more than 96% in latency concerning the original SC decoding. This is while our proposed fast SC decoder for NBPCs incurs no error-rate loss.