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 ε ) were known only for codes of rate exp(1/ε), where k is the length of the message. Furthermore, for codes of rate > 1/2, no nontrivial locality has been achieved.

Authors

• Swastik Kopparty
• Shubhangi Saraf
• Sergey Yekhanin

Keywords

• derivatives
• error-correcting codes
• locally decodable codes
• multiplicity codes
• polynomials
• sublinear-time algorithms