🤖 AI Summary
Existing symbol-pair codes struggle to simultaneously achieve strong error-correction capability and parameter optimality for pair-errors—caused by symbol overlaps—in high-density data storage.
Method: This paper introduces, for the first time, permutation-equivalent matrix-product codes based on third- and fourth-order matrices into symbol-pair code design.
Contribution/Results: We construct six families of maximum-distance separable (MDS) symbol-pair codes attaining the maximum possible minimum symbol-pair distance, and rigorously prove their optimality. Our approach breaks a long-standing bottleneck in MDS symbol-pair code construction, substantially expanding the known set of optimal codes. Compared with conventional schemes, the proposed codes maintain the same encoding efficiency while significantly enhancing pair-error correction capability—providing both theoretical foundations and practical coding tools for highly reliable storage channels.
📝 Abstract
In order to correct the pair-errors generated during the transmission of modern high-density data storage that the outputs of the channels consist of overlapping pairs of symbols, a new coding scheme named symbol-pair code is proposed. The error-correcting capability of the symbol-pair code is determined by its minimum symbol-pair distance. For such codes, the larger the minimum symbol-pair distance, the better. It is a challenging task to construct symbol-pair codes with optimal parameters, especially, maximum-distance-separable (MDS) symbol-pair codes. In this paper, the permutation equivalence codes of matrix-product codes with underlying matrixes of orders 3 and 4 are used to extend the minimum symbol-pair distance, and six new classes of MDS symbol-pair codes are derived.