On Relaxed Locally Decodable Codes for Hamming and Insertion-Deletion Errors
Alex Block, Jeremiah Blocki, Kuan Cheng, Elena Grigorescu, Xin Li, Yu, Zheng, Minshen Zhu

TL;DR
This paper investigates relaxed locally decodable codes (RLDCs) in Hamming and insertion-deletion error settings, establishing exponential lower bounds and demonstrating fundamental differences between these variants, with implications for DNA data storage technologies.
Contribution
It provides the first exponential lower bounds for 2-query binary RLDCs in Hamming errors and introduces novel variants of RLDCs in the insdel error setting, highlighting their differences.
Findings
Exponential lower bounds for 2-query Hamming RLDCs over binary alphabet.
A phase-transition behavior in codeword length for constant-query Hamming RLDCs.
Strict separation between Hamming RLDCs and Insdel RLDCs.
Abstract
Locally Decodable Codes (LDCs) are error-correcting codes with super-fast decoding algorithms. They are important mathematical objects in many areas of theoretical computer science, yet the best constructions so far have codeword length that is super-polynomial in , for codes with constant query complexity and constant alphabet size. In a very surprising result, Ben-Sasson et al. showed how to construct a relaxed version of LDCs (RLDCs) with constant query complexity and almost linear codeword length over the binary alphabet, and used them to obtain significantly-improved constructions of Probabilistically Checkable Proofs. In this work, we study RLDCs in the standard Hamming-error setting, and introduce their variants in the insertion and deletion (Insdel) error setting. Insdel LDCs were first studied by Ostrovsky and Paskin-Cherniavsky, and are…
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
