Codes for Data Entry Systems in .NET

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Codes for Data Entry Systems
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Nonbinary M-ary words processed by data entry systems often suffer from asymmetric errors. In character recognition systems, for example, two symbols ai and aj with similar shapes have a high probability of being mistaken for one another. Among the many types of data processed by data entry systems, M-ary words selected from a speci ed codebook, such as postal codes and product numbers, should be strongly protected from asymmetric errors because these words are often used for indexing a database. This chapter presents two types of M-ary asymmetric error correcting codes, that is, systematic codes and nonsystematic codes, that can be utilized to generate these codebooks. In the data entry systems such as keyboard input systems and character recognition systems, some types of human-made errors may add to the asymmetric errors. These errors are, for example, symbol deletion / insertion errors in the keyboard input systems, or adjacent-symbol-transposition errors in the keyboard input systems or the handwritten character recognition systems. This chapter also presents another class of M-ary asymmetric error correcting codes capable of correcting single deletion / insertion / adjacent-symbol-transposition errors as well as correcting single asymmetric errors. As another data entry systems, new types of bar codes (i.e., two-dimensional matrix symbols) have been popularly used in various sales items and products. This chapter discusses quick response codes (i.e., QR codes) and two-dimensional unidirectional clustered error correcting codes for high-density two-dimensional matrix symbols.
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M-ARY ASYMMETRIC ERRORS IN DATA ENTRY SYSTEMS
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Improved reliability is strongly required for data entry systems, for example, keyboard input systems and character recognition systems, because they often suffer from errors such as mis-typing and mis-identi cation. Among the many types of data processed by
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Code Design for Dependable Systems: Theory and Practical Applications, by Eiji Fujiwara Copyright # 2006 John Wiley & Sons, Inc.
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CODES FOR DATA ENTRY SYSTEMS
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data entry systems, M-ary words selected from a speci ed codebook, such as postal codes, product numbers, bank account numbers, and driver s license numbers, should be strongly protected from errors because these words are often used for indexing a database. Errors in these M-ary words can be corrected or detected by applying M-ary error control codes [GALL96, TANG70]. Generally, the number M of symbols used in data entry systems is neither prime nor the power of a prime, for instance, M 10 for numerals and M 10 26 26 62 for alphanumeric symbols using upper-case and lower-case letters as well as numerals. Therefore conventional error control codes de ned over a Galois eld cannot be directly applied to M-ary words in most cases. To overcome this problem, systematic M-ary error correcting codes have been designed based on the prime factorization of M-ary symbols [BROW73]. Recently a class of systematic M-ary single-symbol error correcting codes has been designed using a prime eld and an integer residue ring [NAMB01]. As an extension to this class of codes, systematic M-ary single-symbol error correcting codes capable of correcting adjacent-symbol transposition errors have been proposed [SUZU98]. The aforementioned M-ary error control codes are designed based on the assumption that the error is symmetric, which means that each symbol in a codeword may be erroneously changed to another symbol with equal probability. In data entry systems, however, errors are generally asymmetric; that is to say, the probability of a symbol ai being mistaken for another symbol aj , denoted by p aj jai , is generally not equal to p ak jai , where aj 6 ak . For example, in character recognition systems, the probability of a 7 being mistaken for a 9 is much higher than that of a 7 being mistaken for a 4, or p 9j7 ) p 4j7 , because the numerals 7 and 9 are similar in shape whereas 7 and 4 are dissimilar in shape. Likewise, in keyboard input systems, symbols located on adjacent keys are mistaken for one another with high probability. Based on this observation, systematic M-ary asymmetric single-symbol error locating codes [SAOW01] have been designed. Several classes of asymmetric symbol error control codes for M-ary channels have been proposed in [VARS73], [SAIT90a]. These codes correct either additive errors, where transmitted integer u u 2 f0; 1; ; M 1g is changed to u e e > 0; u e M 1 , or subtractive errors, where u is changed to u e e > 0; u e ! 0 . On the other hand, errors in data entry systems cannot be expressed as additive or subtractive errors. Therefore the codes for M-ary channels are not applicable to these systems. An asymmetric symbol error correction scheme for character recognition systems have been proposed in [INAB94]. This scheme employs concatenated codes to correct asymmetric symbol errors.
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