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arXiv · 2103.14122

Private and Resource-Bounded Locally Decodable Codes for Insertions and Deletions

Alexander R. Block·Jeremiah Blocki
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Abstract

We construct locally decodable codes (LDCs) to correct insertion-deletion errors in the setting where the sender and receiver share a secret key or where the channel is resource-bounded. Our constructions rely on a so-called "Hamming-to-InsDel" compiler (Ostrovsky and Paskin-Cherniavsky, ITS '15 & Block et al., FSTTCS '20), which compiles any locally decodable Hamming code into a locally decodable code resilient to insertion-deletion (InsDel) errors. While the compilers were designed for the classical coding setting, we show that the compilers still work in a secret key or resource-bounded setting. Applying our results to the private key Hamming LDC of Ostrovsky, Pandey, and Sahai (ICALP '07), we obtain a private key InsDel LDC with constant rate and polylogarithmic locality. Applying our results to the construction of Blocki, Kulkarni, and Zhou (ITC '20), we obtain similar results for resource-bounded channels; i.e., a channel where computation is constrained by resources such as space or time.

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Alexander R. Block, Jeremiah Blocki. 2021-03-25. Private and Resource-Bounded Locally Decodable Codes for Insertions and Deletions. https://doi.org/10.1109/isit45174.2021.9518249

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