Efficient Repair of Reed-Solomon Codes and Tamo-Barg Codes
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Abstract
Reed-Solomon codes are polynomial evaluation codes and they can be efficiently repaired if the code symbols of the code are considered as vectors over a subfield. We describe a trace-repair framework introduced by Guruswami-Wootters, which allows for efficient repair of Reed-Solomon codes. Also, we present an optimal construction of Reed-Solomon codes by Tamo et al., which achieve the cut-set bound. Tamo-Barg codes are a class of optimal locally repairable codes (LRCs) which are also polynomial evaluation codes. These codes have Reed-Solomon codes as their local codes. In the case of single node failures, the repair takes place only within the local groups. The repair bandwidth within the local group can be further reduced by using the technique of Reed-Solomon repair. We provide a construction of Tamo-Barg codes whose local Reed-Solomon codes can be optimally repaired. We also make the connection between these class of codes and codes with local regeneration.
Lalitha Vadlamani received her B.E. degree in Electronics and Communication Engineering from the Osmania University, Hyderabad, in 2003 and her M.E.and Ph.D. degrees from the Indian Institute of Science (IISc), Bangalore,in 2005 and 2015 respectively. From May 2015, she has been at IIIT Hyderabad, where she is affiliated to Signal Processing and Communications Research Center in IIIT Hyderabad, where she is currently an Associate Professor. Her research interests include coding for distributed storage and computing, quantum error correcting codes, index coding, polar codes, learning-based codes and coded blockchains. She is a recipient of Prof. I.S.N. Murthy medal from IISc, 2005 and the TCS Research Scholarship for the year 2011. She is currently serving as the Newsletter Editor of the IEEE Information Theory Society.