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In this paper, we propose an optimal scalar locally repairable code (LRC) with locality 1 in the sense of achieving the maximum possible minimum distance using the serial concatenation technique. A technique to construct an optimal vector LRC with locality 1 based on the proposed scalar LRC is also provided.
We propose a design criterion for serially concatenated LDGM codes which require single decoder. The inner LDGM code can be obtained by expanding the rows of the parity check matrix of the outer LDGM code. The resulting codes can be decoded using only the inner LDGM decoder with slight modification. Simulation results show that the performance of the proposed codes is almost the same as that of serially...
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