High-rate codes with sublinear-time decoding

Locally decodable codes are error-correcting codes that admit efficient decoding algorithms; any bit of the original message can be recovered by looking at only a small number of locations of a corrupted codeword. The tradeoff between the rate of a code and the locality/efficiency of its decoding algorithms has been well studied, and it has widely been suspected that nontrivial locality must come at the price of low rate. A particular setting of potential interest in practice is codes of constant rate. For such codes, decoding algorithms with locality O(k ) were known only for codes of rate (1/ ) , where k is the length of the message. Furthermore, for codes of rate > 1/2, no nontrivial locality has been achieved. In this paper we construct a new family of locally decodable codes that have very efficient

• Type: Journal
• Year: 2010
• Where: ECCC
• Authors: Swastik Kopparty, Shubhangi Saraf, Sergey Yekhanin
• Keywords: Algorithms, Decodable Codes, ECCC 2010, Locally Decodable