DocumentCode :
51136
Title :
LDPC Codes for 2D Arrays
Author :
Cassuto, Yuval ; Shokrollahi, A.
Author_Institution :
Dept. of Electr. Eng., Technion - Israel Inst. of Technol., Haifa, Israel
Volume :
60
Issue :
6
fYear :
2014
fDate :
Jun-14
Firstpage :
3279
Lastpage :
3291
Abstract :
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 combinatorial-probabilistic model of limiting the number of column failures, and assuming a binary erasure channel in each failing column. For this model, we give 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 parity-check codes.
Keywords :
binary codes; combinatorial mathematics; iterative decoding; parity check codes; probability; 1D low-density parity-check codes; 2D arrays; 2D codes; LDPC codes; MDS array codes; array column; binary codes; code constructions; code design parameters; combinatorial erasure model; combinatorial-probabilistic model; data storage; decoding graphs; decoding performance; failure parameters; low-complexity iterative decoding; maximum distance separable array codes; probabilistic codes construction; storage device; Arrays; Decoding; Encoding; Iterative decoding; Probabilistic logic; Sockets; Array codes; LDPC codes; data storage; iterative decoding; two-dimensional codes;
fLanguage :
English
Journal_Title :
Information Theory, IEEE Transactions on
Publisher :
ieee
ISSN :
0018-9448
Type :
jour
DOI :
10.1109/TIT.2014.2313720
Filename :
6778036
Link To Document :
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