Bounds of Codes over Symbol-Pair Read Channels
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Symbol-pair read channels are first introduced by Cassuto and Blaum, in which the outputs of the read process are pairs of consecutive symbols. This new paradigm is motivated by the limitations of the reading process in some high density data storage systems. Soon later, a Singleton type bound for symbol-pair codes are established by Chee et al. and symbol-pair codes achieving this code are called MDS symbol-pair codes. With the benchmark, a lot of optimal symbol-pair are constructed by the effort of several papers. It is well known that bounds play an important role in coding theory. Two more bounds of symbol-codes are presented by Elishco et al very recently. In this paper, we continue the investigation of bounds of symbol-pair codes and establish two types of bounds, one is called Plotkin type bound and the other is call restricted Johnson type bound. We also present some examples of optimal symbol-pair codes that achieve these two new bounds.
Symbol-pair code; Plotkin type bound; Johnson type Bound; Cauchy-Schwartz inequality