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Decoding of binary quadratic residue codes with hash table

机译:用哈希表解码二进制二次残数代码

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摘要

An efficient decoding of quadratic residue (QR) codes utilising hashing search to find error patterns is presented in this study. The key idea behind the proposed decoding method is theoretically based on the existence of a one-to-one mapping between the single primary known syndrome and correctable error patterns. Compared with the binary search time approach, one of the advantages of utilising this method presented in this study is that the hashing search time can be reduced by a factor of two. This method would help reduce the binary search time for finding error patterns when decoding the (23, 12, 7), (41, 21, 9), and (47, 24, 11) QR codes. Furthermore, it would reduce the decoding time by 45% using the fast lookup table decoding method to decode the (71, 36, 11) QR code. Ultimately, the proposed decoding algorithm for QR codes can be made regular, simple, and suitable for software implementations.
机译:在这项研究中提出了一种有效的对二次残差(QR)码进行解码的方法,该算法利用哈希搜索来查找错误模式。所提出的解码方法背后的关键思想理论上是基于单个主要已知校正子与可纠正错误模式之间的一对一映射。与二元搜索时间方法相比,本研究中使用该方法的优点之一是可以将哈希搜索时间减少两倍。此方法将有助于减少解码(23、12、7),(41、21、9)和(47、24、11)QR码时用于查找错误模式的二进制搜索时间。此外,使用快速查找表解码方法解码(71、36、11)QR码将使解码时间减少45%。最终,所提出的QR码解码算法可以变得规则,简单并适合于软件实现。

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