LDPC Codes for 2D Arrays

Yuval Cassuto, Amin Shokrollahi
2014 IEEE Transactions on Information Theory  
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 » ... 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.
doi:10.1109/tit.2014.2313720 fatcat:527v5jryybcnxd7s3ajltjslhy