Successive Cancellation Ordered Search Decoding of Modified $\G_N$-Coset Codes

A tree search algorithm called successive cancellation ordered search (SCOS) is proposed for $\boldsymbol{G}_N$-coset codes that implements maximum-likelihood (ML) decoding by using an adaptive search schedule. The average complexity is close to that of successive cancellation (SC) decoding for practical frame error rates (FERs) when applied to polar and Reed-Muller (RM) codes with block lengths up to 128. By modifying the algorithm to limit the worst-case complexity, one obtains near-ML performance for longer RM codes and their subcodes. Unlike other bit-flip decoders, no outer code is needed to terminate decoding so SCOS also applies to modified $\boldsymbol{G}_N$-coset codes with dynamic frozen bits. SCOS decoding is further extended by forcing it to look for candidates satisfying a threshold, thereby outperforming basic SCOS decoding under complexity constraints. Simulations with a (128,64) polarization-adjusted convolutional code show gains in overall and undetected FER as compared to polar codes concatenated with an outer cyclic redundancy check code under SC list decoding at high signal-to-noise ratio over binary-input additive white Gaussian noise channels.