Abstract
Cassuto and Blaum recently studied the symbol-pair channel, a model where every two consecutive symbols are read together. This special structure of channels is motivated by the limitations of the reading process in high density data storage systems, where it is no longer possible to read individual symbols. In this new paradigm, the errors are no longer individual symbol errors, but rather symbol-pair errors, where at least one of the symbols is erroneous. In this work, we study bounds and construction of codes over the symbol-pair channels. We extend the Johnson bound and the linear programming bound for this channel and show that they improve upon existing bounds. We then propose new code constructions that improve upon existing results that use linear cyclic codes when the pair distance is between four and ten.
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