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 an 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 on the likelihood, 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 $(128, 64)$ PAC 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 $\boldsymbol{G}_N$-陪集码，提出一种名为逐次消除有序搜索（SCOS）的树搜索算法，该算法在二进制输入加性白高斯噪声信道上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，因此也适用于经动态冻结比特修正的 $\boldsymbol{G}_N$-陪集码。对于速率范围广泛、长度达 $512$ 比特的码字，其平均复杂度接近逐次消除（SC）译码在实际误帧率（FER）下的复杂度，性能距离随机编码联合界不超过 $0.25$ dB，且比里德-穆勒码在ML译码下性能提升高达 $0.5$ dB。仿真表明，在不同信噪比条件下，SCOS在FER和平均复杂度方面同时优于SC-Fano、SC堆栈（SCS）和SC列表（SCL）译码。进一步扩展SCOS，通过强制寻找满足似然阈值条件的候选者，使其在复杂度约束下性能优于基本SCOS。修正的SCOS无需外码即可实现强检错能力。特别地，$(128, 64)$ PAC码在修正SCOS下，高信噪比时相比CRC辅助极化码在SCL/动态SC翻转译码下具有整体FER和未检测FER性能增益。