Perturbed Derivative Decoding Based on Ordered Statistics for Cyclic Codes

It has been shown that perturbations can improve the performance of ordered statistics decoding (OSD). In this paper, we focus on perturbations for derivative decoding based on OSD (DD-OSD) for cyclic codes, where the results of OSD in different derivative directions vote for the estimate of codewords. It reveals that the local maximum likelihood decoding (l-MLD) errors in derivative directions may trap DD-OSD. It proves that such traps can be detected by the null space of the derivative ascendants of cyclic codes, thereby guiding us to perform perturbations to avoid the traps. Simulation results show that perturbed DD-OSD with order-1 can achieve 1.3 dB gain over OSD with order-4 for extended BCH codes, and perform closely to maximum likelihood decoding with moderate complexity.