Nonuniform Codes for Correcting Asymmetric Errors in Data Storage
Abstract
The construction of asymmetric error-correcting codes is a topic that was studied extensively, however; the existing approach for code construction assumes that every codeword should tolerate t asymmetric errors. Our main observation is that in contrast to symmetric errors, asymmetric errors are content dependent. For example, in Z-channels, the all-1 codeword is prone to have more errors than the all-0 codeword. This motivates us to develop nonuniform codes whose codewords can tolerate different numbers of asymmetric errors depending on their Hamming weights. The idea in a nonuniform codes' construction is to augment the redundancy in a content-dependent way and guarantee the worst case reliability while maximizing the code size. In this paper, we first study nonuniform codes for Z-channels, namely, they only suffer one type of errors, say 1→ 0. Specifically, we derive their upper bounds, analyze their asymptotic performances, and introduce two general constructions. Then, we extend the concept and results of nonuniform codes to general binary asymmetric channels, where the error probability for each bit from 0 to 1 is smaller than that from 1 to 0.
Additional Information
© 2013 IEEE. Manuscript received June 15, 2012; revised October 17, 2012; accepted December 29, 2012. Date of publication January 17, 2013; date of current version April 17, 2013. This work was supported in part by the National Science Foundation (NSF) CAREER Award CCF-0747415, in part by the NSF under Grants ECCS-0802107 and CCF-1217944, and in part by the NSF National Robotics Initiative Award. This paper was presented in part at the 2011 IEEE International Symposium on Information Theory. The authors would like to thank the anonymous reviewers for their valuable comments and suggestions to improve the quality of the paper.Attached Files
Submitted - 1209.0740.pdf
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Additional details
- Eprint ID
- 38959
- Resolver ID
- CaltechAUTHORS:20130617-115747407
- CCF-0747415
- NSF
- ECCS-0802107
- NSF
- CCF-1217944
- NSF
- Created
-
2013-06-18Created from EPrint's datestamp field
- Updated
-
2021-11-09Created from EPrint's last_modified field
- Other Numbering System Name
- INSPEC Accession Number
- Other Numbering System Identifier
- 13448800