Decoding of cyclic codes over symbol-pair read channels
Decoding of cyclic codes over symbol-pair read channels
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DOI：
10.1109/isit.2012.6284053
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发表时间：
2012-07
期刊：
影响因子：
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通讯作者：
Eitan Yaakobi;Jehoshua Bruck;P. Siegel
中科院分区：
文献类型：
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作者：
Eitan Yaakobi;Jehoshua Bruck;P. Siegel
Cassuto和Blaum最近研究了符号对读取通道，其中读取过程的输出是成对的连续符号。这种新模式是由高密度数据存储系统中读取过程的局限性所激发的。他们研究了这种新范式下的纠错，特别是纠错码的最小汉明距离与最小对距离之间的关系，最小对距离是由码字导出的符号对向量之间的最小汉明距离。证明了对于最小汉明距离dH的线性循环码，其对应的最小对距离至少为dH + 3。我们的主要贡献是证明了对于一个给定的具有最小汉明距离dH的线性循环码，最小对距离至少为dH + [dH/2]。我们还描述了基于有限距离解码器的循环码解码算法，其对符号纠错能力反映了更大的最小对距离。此外，我们考虑读通道输出为规定数字b >的情况；2，连续符号，并提供一些推广我们的结果。我们注意到符号对读信道问题是Levenshtein提出的序列重构问题的一个特例。
Symbol-pair read channels, in which the outputs of the read process are pairs of consecutive symbols, were recently studied by Cassuto and Blaum. This new paradigm is motivated by the limitations of the reading process in high density data storage systems. They studied error correction in this new paradigm, specifically, the relationship between the minimum Hamming distance of an error correcting code and the minimum pair distance, which is the minimum Hamming distance between symbol-pair vectors derived from codewords of the code. It was proved that for a linear cyclic code with minimum Hamming distance dH, the corresponding minimum pair distance is at least dH + 3. Our main contribution is proving that, for a given linear cyclic code with a minimum Hamming distance dH, the minimum pair distance is at least dH + [dH/2]. We also describe decoding algorithms, based upon bounded distance decoders for the cyclic code, whose pair-symbol error correcting capabilities reflects the larger minimum pair distance. In addition, we consider the case where a read channel output is a prescribed number, b >; 2, of consecutive symbols and provide some generalizations of our results. We note that the symbol-pair read channel problem is a special case of the sequence reconstruction problem that was introduced by Levenshtein.