LDPC Codes for 2D Arrays

Yuval Cassuto, Amin Shokrollahi
<span title="">2014</span> <i title="Institute of Electrical and Electronics Engineers (IEEE)"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/niovmjummbcwdg4qshgzykkpfu" style="color: black;">IEEE Transactions on Information Theory</a> </i> &nbsp;
Binary codes over 2D arrays are very useful in data storage, where each array column represents a storage device or unit that may suffer failure. In this paper, we propose a new framework for probabilistic construction of codes on 2D arrays. Instead of a pure combinatorial erasure model used in traditional array codes, we propose a mixed combinatorialprobabilistic model of limiting the number of column failures, and assuming a binary erasure channel in each failing column. For this model, we
more &raquo; ... e code constructions and detailed analysis that allow sustaining a large number of column failures with graceful degradation in the fraction of erasures correctable in failing columns. Another advantage of the new framework is that it uses low-complexity iterative decoding. The key component in the analysis of the new codes is to analyze the decoding graphs induced by the failed columns, and infer the decoding performance as a function of the code design parameters, as well as the array size and failure parameters. A particularly interesting class of codes, called probabilistically maximum distance separable (MDS) array codes, gives fault-tolerance that is equivalent to traditional MDS array codes. The results also include a proof that the 2D codes outperform standard 1D low-density paritycheck codes.
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1109/tit.2014.2313720">doi:10.1109/tit.2014.2313720</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/527v5jryybcnxd7s3ajltjslhy">fatcat:527v5jryybcnxd7s3ajltjslhy</a> </span>
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