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A tree search algorithm called successive cancellation ordered search (SCOS)is proposed for $\boldsymbol{G}_N$-coset codes that implementsmaximum-likelihood (ML) decoding with an adaptive complexity for transmissionover binary-input AWGN channels. Unlike bit-flip decoders, no outer code isneeded to terminate decoding; therefore, SCOS also applies to$\boldsymbol{G}_N$-coset codes modified with dynamic frozen bits. The averagecomplexity is close to that of successive cancellation (SC) decoding atpractical frame error rates (FERs) for codes with wide ranges of rate andlengths up to $512$ bits, which perform within $0.25$ dB or less from therandom coding union bound and outperform Reed--Muller codes under ML decodingby up to $0.5$ dB. Simulations illustrate simultaneous gains for SCOS overSC-Fano, SC stack (SCS) and SC list (SCL) decoding in FER and the averagecomplexity at various SNR regimes. SCOS is further extended by forcing it tolook for candidates satisfying a threshold on the likelihood, therebyoutperforming basic SCOS under complexity constraints. The modified SCOSenables strong error-detection capability without the need for an outer code.In particular, the $(128, 64)$ PAC code under modified SCOS provides gains inoverall and undetected FER compared to CRC-aided polar codes under SCL/dynamicSC flip decoding at high SNR.

Successive Cancellation Ordered Search Decoding of Modified $\boldsymbol{G}_N$-Coset Codes