New Constructions of Codes for Asymmetric Channels via Concatenation
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Author(s)
Grassl, Markus
Smith, Graeme
Smolin, John
Zeng, Bei
Shor, Peter Williston
Date Issued
April 2015
Journal
IEEE Transactions on Information Theory
Publisher
Institute of Electrical and Electronics Engineers (IEEE)
Citation
Grassl, Markus et al. “New Constructions of Codes for Asymmetric Channels via Concatenation.” IEEE Transactions on Information Theory 61, 4 (April 2015): 1879–1886 © 2015 IEEE
Version
Original manuscript
Abstract
We present new constructions of codes for asymmetric channels for both binary and nonbinary alphabets, based on methods of generalized code concatenation. For the binary asymmetric channel, our methods construct nonlinear single-error-correcting codes from ternary outer codes. We show that some of the Varshamov-Tenengol'ts-Constantin-Rao codes, a class of binary nonlinear codes for this channel, have a nice structure when viewed as ternary codes. In many cases, our ternary construction yields even better codes. For the nonbinary asymmetric channel, our methods construct linear codes for many lengths and distances which are superior to the linear codes of the same length capable of correcting the same number of symmetric errors.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
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Creative Commons Attribution-Noncommercial-Share Alike
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DOI of Published Version
https://doi.org/10.1109/TIT.2015.2401567
