Coding with Constraints: Minimum Distance Bounds and Systematic Constructions
- Creators
- Halbawi, Wael
- Thill, Matthew
- Hassibi, Babak
Abstract
We examine an error-correcting coding framework in which each coded symbol is constrained to be a function of a fixed subset of the message symbols. With an eye toward distributed storage applications, we seek to design systematic codes with good minimum distance that can be decoded efficiently. On this note, we provide theoretical bounds on the minimum distance of such a code based on the coded symbol constraints. We refine these bounds in the case where we demand a systematic linear code. Finally, we provide conditions under which each of these bounds can be achieved by choosing our code to be a subcode of a Reed-Solomon code, allowing for efficient decoding. This problem has been considered in multisource multicast network error correction. The problem setup is also reminiscent of locally repairable codes.
Additional Information
© 2015 IEEE.Attached Files
Submitted - Coding_with_Constraints-_Minimum_Distance_Bounds_and_Systematic_Constructions.pdf
Files
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Additional details
- Eprint ID
- 55122
- DOI
- 10.1109/ISIT.2015.7282666
- Resolver ID
- CaltechAUTHORS:20150224-070606037
- Created
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2015-03-04Created from EPrint's datestamp field
- Updated
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2021-11-10Created from EPrint's last_modified field