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Constructions and Decoding of Cyclic Codes Over <tex-math notation='LaTeX'>$b$ </tex-math> -Symbol Read Channels
- Source :
- IEEE Transactions on Information Theory. 62:1541-1551
- Publication Year :
- 2016
- Publisher :
- Institute of Electrical and Electronics Engineers (IEEE), 2016.
-
Abstract
- 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 $d_{H}$ , the corresponding minimum pair distance is at least $d_{H}+3$ . In this paper, we show that, for a given linear cyclic code with a minimum Hamming distance $d_{H}$ , the minimum pair distance is at least $d_{H} +\left \lceil{ {d_{H}/{2}}}\right \rceil $ . We then describe a decoding algorithm, based upon a bounded distance decoder for the cyclic code, whose symbol-pair error correcting capabilities reflect the larger minimum pair distance. Finally, we consider the case where the read channel output is a larger number, $b \geqslant 3$ , of consecutive symbols, and we provide extensions of several concepts, results, and code constructions to this setting.
- Subjects :
- Discrete mathematics
Hamming bound
020206 networking & telecommunications
Hamming distance
0102 computer and information sciences
02 engineering and technology
Library and Information Sciences
01 natural sciences
Linear code
Computer Science Applications
Hamming graph
010201 computation theory & mathematics
Cyclic code
0202 electrical engineering, electronic engineering, information engineering
Hamming(7,4)
Constant-weight code
Hamming code
Information Systems
Mathematics
Subjects
Details
- ISSN :
- 15579654 and 00189448
- Volume :
- 62
- Database :
- OpenAIRE
- Journal :
- IEEE Transactions on Information Theory
- Accession number :
- edsair.doi...........5562c61ed2d01444958a62a2e6058230