  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 has
been analyzed for the perfect codes, BCH codes, and maximum distance separable
(MDS) codes. Through numerical analysis, it is shown that the proposed decoding
algorithm has good erasure decoding performance with lower decoding complexity
and delay than the conventional AGD. For some cyclic codes, it is shown that
the proposed TS-AGD achieves the perfect decoding in the erasure channel, that
is, the same decoding performance as the maximum likelihood (ML) decoder. For
MDS codes, TS-AGDs with the expanded parity check matrix and the submatrix
inversion are also proposed and analyzed.
