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A Class of Array codes Correcting a Cluster of Unidirectional Errors for two-dimensional Matrix Symbols

IEICE TRANSACTIONS ON FUNDAMENTALS OF ELECTRONICS COMMUNICATIONS AND COMPUTER SCIENCES 2009年第6期E92A卷 1508-1519页

作者： Kaneko, Haruhiko Fujiwara, Eiji Tokyo Inst Technol Dept Comp Sci Tokyo 1528552 Japan

two-dimensional (2D) matrix symbols have higher storage capacity than conventional bar-codes, and hence have been used in various applications, including parts management in factories and Internet site addressing in camera-equipped mobile phones. These symbols generally utilize strong error control codes to protect data from errors caused by blots and scratches, and therefore require a large number of check bits. Because 2D matrix symbols are expressed in black and white dot patterns, blots and scratches often induce clusters of unidirectional errors (i.e., errors that affect black but not white dots, or vice versa). This paper proposes a new class of unidirectional l(m) x l(n)-clustered error correcting codes capable of correcting unidirectional errors confined to a rectangle with l(m) rows and l(n) columns. The proposed code employs 2D interleaved parity-checks, as well as vertical and horizontal arithmetic residue checks. Clustered error pattern is derived using the 2D interleaved parity-checks, while vertical and horizontal positions of the error are calculated using the vertical and horizontal arithmetic residue checks. This paper also derives an upper bound on the number of codewords based on Hamming bound. Evaluation shows that the proposed code provides high code rate close to the bound. For example, for correcting a cluster of unidirectional 40 x 40 errors in 150 x 150 codeword, the code rate of the proposed code is 0.9272, while the upper bound is 0.9284.

关键词： unidirectional error burst error clustered error array code two-dimensional bar-code arithmetic residue check QR code

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