Locally Decodable Codes with Randomized Encoding
Kuan Cheng, Xin Li, and Yu Zheng

TL;DR
This paper explores the use of randomized encoding in locally decodable codes to improve the tradeoff between code rate and query complexity, applicable to both error models, with potential for more efficient data recovery.
Contribution
It introduces a novel approach using randomized encoding to enhance rate-query tradeoffs in locally decodable codes across various error models.
Findings
Achieves better rate-query tradeoff with randomized encoding.
Works for both Hamming and edit error models.
Improves efficiency of local decoding processes.
Abstract
We initiate a study of locally decodable codes with randomized encoding. Standard locally decodable codes are error correcting codes with a deterministic encoding function and a randomized decoding function, such that any desired message bit can be recovered with good probability by querying only a small number of positions in the corrupted codeword. This allows one to recover any message bit very efficiently in sub-linear or even logarithmic time. Besides this straightforward application, locally decodable codes have also found many other applications such as private information retrieval, secure multiparty computation, and average-case complexity. However, despite extensive research, the tradeoff between the rate of the code and the number of queries is somewhat disappointing. For example, the best known constructions still need super-polynomially long codeword length even with a…
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Taxonomy
TopicsCryptography and Data Security · Algorithms and Data Compression · Complexity and Algorithms in Graphs
