Locally Decodable Codes
Sergey Yekhanin
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Locally Decodable Codes

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Over 60 years of research in coding theory, that started with the works of Shannon and Hamming, have given us nearly optimal ways to add redundancy to messages, encoding bit strings representing messages into longer bit strings called codewords, in a way that the message can still be recovered even if a certain fraction of the codeword bits are corrupted. Classical error-correcting codes, however, do not work well when messages are modern massive datasets, because their decoding time increases (at least) linearly with the length of the message. As a result in typical applications large dataset...