New Two-Stage Automorphism Group Decoders for Cyclic Codes

Recently, error correcting codes in the erasure channel have drawn great attention for various applications such as distributed storage systems and wireless sensor networks, but many of their decoding algorithms are not practical because they have higher decoding complexity and longer delay. Thus, the automorphism group decoder (AGD) for cyclic codes in the erasure channel was introduced, which has good erasure decoding performance with low decoding complexity. In this paper, we propose new two-stage AGDs (TS-AGDs) for cyclic codes in the erasure channel by modifying the parity-check matrix and introducing the preprocessing stage to the AGD scheme. The proposed TS-AGD is analyzed for binary extended Golay and BCH codes. Also, TS-AGD can be used in the error channel using ordered statistics. Through numerical analysis, it is shown that the proposed decoding algorithm has good erasure decoding performance with lower decoding complexity than the conventional AGD. For some cyclic codes, it is shown that the proposed TS-AGD achieves the performance nearly identical to the maximum likelihood (ML) decoder in the erasure channel and the ordered statistics decoder (OSD) in the error channel.