A Note on Amplifying the Error-Tolerance of Locally Decodable Codes

Trevisan [Tre03] suggested a transformation that allows amplifying the error rate a code can handle. We observe that this transformation, that was suggested in the non-local setting, works also in the local setting and thus gives a generic, simple way to amplify the error-tolerance of locally decodable codes. Specifically, this shows how to transform a locally decodable code that can tolerate a constant fraction of errors to a locally decodable code that can recover from a much higher error-rate, and how to transform such locally decodable codes to locally list-decodable codes. The transformation of [Tre03] involves a simple composition with an approximately locally (list) decodable code. Using a construction of such codes by Impagliazzo et al. [IJKW10], the transformation incurs only a negligible growth in the length of the code and in the query complexity.

• Type: Journal
• Year: 2010
• Where: ECCC
• Authors: Avraham Ben-Aroya, Klim Efremenko, Amnon Ta-Shma
• Keywords: Code, Decodable Code, ECCC 2010, ECommerce, Locally Decodable Codes