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Maximum Distance Separable Codes for Symbol-Pair Read Channels

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5 Author(s)
Yeow Meng Chee ; Division of Mathematical Sciences, School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore, Singapore ; Lijun Ji ; Han Mao Kiah ; Chengmin Wang
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We study (symbol-pair) codes for symbol-pair read channels introduced recently by Cassuto and Blaum (2010). A Singleton-type bound on symbol-pair codes is established and infinite families of optimal symbol-pair codes are constructed. These codes are maximum distance separable (MDS) in the sense that they meet the Singleton-type bound. In contrast to classical codes, where all known q-ary MDS codes have length O(q), we show that q-ary MDS symbol-pair codes can have length Ω(q2). In addition, we completely determine the existence of MDS symbol-pair codes for certain parameters.

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IEEE Transactions on Information Theory  (Volume:59 ,  Issue: 11 )