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

TL;DR

This paper develops locally decodable codes (LDCs) that correct insertion and deletion errors in resource-limited or secret key settings, extending existing compilers to new practical scenarios with constant rate and polylogarithmic locality.

Contribution

It demonstrates that Hamming-to-InsDel compilers remain effective in secret key and resource-bounded environments, enabling new private and resource-efficient LDC constructions.

Findings

Achieved private key InsDel LDC with constant rate and polylogarithmic locality.

Extended compiler applicability to resource-bounded channels.

Provided constructions for both secret key and resource-constrained settings.

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.