A tree search algorithm called successive cancellation ordered search (SCOS) is proposed for $\boldsymbol{G}_N$-coset codes that implements maximum-likelihood (ML) decoding with adaptive complexity for transmission over binary-input AWGN channels. Unlike bit-flip decoders, no outer code is needed to terminate decoding; therefore, SCOS also applies to $\boldsymbol{G}_N$-coset codes modified with dynamic frozen bits. The average complexity is close to that of successive cancellation (SC) decoding at practical frame error rates (FERs) for codes with wide ranges of rate and lengths up to $512$ bits, which perform within $0.25$ dB or less from the random coding union bound and outperform Reed--Muller codes under ML decoding by up to $0.5$ dB. Simulations illustrate simultaneous gains for SCOS over SC-Fano, SC stack (SCS) and SC list (SCL) decoding in FER and the average complexity at various SNR regimes. SCOS is further extended by forcing it to look for candidates satisfying a threshold, thereby outperforming basic SCOS under complexity constraints. The modified SCOS enables strong error-detection capability without the need for an outer code. In particular, the $(128, 64)$ polarization-adjusted convolutional code under modified SCOS provides gains in overall and undetected FER compared to CRC-aided polar codes under SCL/dynamic SC flip decoding at high SNR.

翻译：针对二元输入加性高斯白噪声信道下的$\boldsymbol{G}_N$-陪集码，提出一种名为逐次消除有序搜索（SCOS）的树搜索算法，该算法能以自适应复杂度实现最大似然（ML）译码。与比特翻转译码器不同，SCOS无需外码即可终止译码；因此，该算法同样适用于采用动态冻结比特修正的$\boldsymbol{G}_N$-陪集码。对于码率范围广泛且码长不超过$512$比特的码字，SCOS的平均复杂度接近逐次消除（SC）译码在实际帧错误率（FER）下的表现，其译码性能与随机编码联合界相差$0.25$ dB以内，且比里德-穆勒码在ML译码下的性能高出$0.5$ dB。仿真结果表明，在不同信噪比（SNR）区间内，SCOS在FER和平均复杂度方面均优于SC-Fano译码、SC堆栈（SCS）译码和SC列表（SCL）译码。进一步通过强制SCOS搜索满足阈值的候选路径，扩展后的SCOS在复杂度受限条件下性能优于基础SCOS。修正后的SCOS无需外码即可实现强检错能力。特别地，使用修正SCOS的$(128, 64)$极化调整卷积码在高SNR环境下，其总体FER和未检测FER相比采用SCL/动态SC翻转译码的CRC辅助极化码均获得性能增益。