Motivated by the need for channel codes with low-complexity soft-decision decoding algorithms, we consider the recursive Plotkin concatenation of optimal low-rate and high-rate codes based on simplex codes and their duals. These component codes come with low-complexity maximum likelihood (ML) decoding which, in turn, enables efficient successive cancellation (SC)-based decoding. As a result, the proposed optimally recursively concatenated simplex (ORCAS) codes achieve a performance that is at least as good as that of polar codes. For practical parameters, the proposed construction significantly outperforms polar codes in terms of block error rate by up to 0.5 dB while maintaining similar decoding complexity. Furthermore, the codes offer greater flexibility in codeword length than conventional polar codes.

翻译：受低复杂度软判决译码算法信道码需求的驱动，本文研究了基于单纯形码及其对偶码的最优低码率与高码率码的递归普洛特金级联。这些分量码具备低复杂度的最大似然译码特性，从而支持高效的连续消除译码。因此，所提出的最优递归级联单纯形码在性能上至少与极化码相当。对于实际参数，所提构造在保持相近译码复杂度的同时，其分组误码率性能显著优于极化码达0.5 dB。此外，该码型在码长设计上较传统极化码具有更高的灵活性。