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.

In this letter, we address the design of fractionally spaced adaptive equalizers when the input signal is sampled with noninteger, subsymbol sampling. We consider the problem of joint equalization and sample rate conversion and derive a stochastic gradient-based weight update algorithm for the equalizer. This enables us to decouple the equalization of channel impairments from that of fixed (periodic) distortion arising from noninteger, subsymbol sampling. This decoupling leads to a novel low-complexity architecture for the equalizer that shows superior or equal performance as compared to the existing architectures with higher complexity.