
For FullText PDF, please login, if you are a member of IEICE,
or go to Pay Per View on menu list, if you are a nonmember of IEICE.

A Class of Array Codes Correcting a Cluster of Unidirectional Errors for TwoDimensional Matrix Symbols
Haruhiko KANEKO Eiji FUJIWARA
Publication
IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences
Vol.E92A
No.6
pp.15081519 Publication Date: 2009/06/01
Online ISSN: 17451337
DOI: 10.1587/transfun.E92.A.1508
Print ISSN: 09168508 Type of Manuscript: PAPER Category: Coding Theory Keyword: unidirectional error, burst error, clustered error, array code, twodimensional barcode, arithmetic residue check, QR code,
Full Text: PDF(1.3MB)>>
Summary:
Twodimensional (2D) matrix symbols have higher storage capacity than conventional barcodes, and hence have been used in various applications, including parts management in factories and Internet site addressing in cameraequipped 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} 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 paritychecks, as well as vertical and horizontal arithmetic residue checks. Clustered error pattern is derived using the 2D interleaved paritychecks, 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 40 errors in 150 150 codeword, the code rate of the proposed code is 0.9272, while the upper bound is 0.9284.

