Fast Successive-Cancellation Decoding of 2 x 2 Kernel Non-Binary Polar Codes: Identification, Decoding and Simplification

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

Ordered Reliability Direct Error Pattern Testing Decoding Algorithm

We introduce a novel universal soft-decision decoding algorithm for binary block codes called ordered reliability direct error pattern testing (ORDEPT). Our results, obtained for a variety of popular short high-rate codes, demonstrate that ORDEPT outperforms state-of-the-art decoding algorithms of comparable complexity such as ordered reliability bits guessing random additive noise decoding (ORBGRAND) in terms of the decoding error probability and latency. The improvements carry on to the iterative decoding of product codes and convolutional product-like codes, where we present a new adaptive decoding algorithm and demonstrate the ability of ORDEPT to efficiently find multiple candidate codewords to produce soft output