It has been shown that perturbations can improve the performance ofordered statistics decoding(OSD). In this paper, we focus on perturbations forderivative 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 thelocal 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.

It shows in [1], [2] that the performance of ordered statistics decoding (OSD) can be improved by derivative decoding (DD) for cyclic codes. Since error bits with high reliabilities may result in erroneous re-encoding, this paper proposes to further enhance DD-OSD by introducing perturbations on control band. Aided by the detection capability of cyclic codes on voted estimates of DD, the output decision is chosen sequentially from estimates given by different perturbations. Simulation results show that it can achieve 1.1 dB gain over DD-OSD for extended Bose-Chaudhuri-Hocquenghem codes, and performs closely to maximum likelihood decoding with moderate complexity.

This paper introduces theordered statistics decoding(OSD) without Gaussian elimination for affine-invariant codes based on theirderivative descendants(DDs). Based on the affine-invariant property, the reliable bits can be permuted into the information positions for re-encoding by an affine permutation. Moreover, it makes the information bits more reliable to perform the re-encoding process on not the original codes, but their DDs. Thanks to the much smaller dimension of our defined affine DDs, OSD can be carried out more efficiently. Simulation results show that the proposed ordered statistics derivative decoding can provide good performance without Gaussian elimination, even better than the conventional OSD with higher order.