High Rate Efficient Local List Decoding from HDX
Yotam Dikstein, Max Hopkins, Russell Impagliazzo, Toniann Pitassi

TL;DR
This paper introduces highly efficient, locally decodable list codes based on high-dimensional expanders, achieving near-optimal rate, error tolerance, and computational efficiency, with applications in complexity theory and cryptography.
Contribution
It presents the first locally list decodable codes with near-theoretic limits, utilizing a novel belief propagation framework and explicit local routing on HDX.
Findings
Codes run in polylogarithmic time and sub-logarithmic depth.
Achieves near-optimally input-preserving hardness amplification.
Resolves several longstanding problems in coding and complexity theory.
Abstract
We construct the first (locally computable, approximately) locally list decodable codes with rate, efficiency, and error tolerance approaching the information theoretic limit, a core regime of interest for the complexity theoretic task of hardness amplification. Our algorithms run in polylogarithmic time and sub-logarithmic depth, which together with classic constructions in the unique decoding (low-noise) regime leads to the resolution of several long-standing problems in coding and complexity theory: 1. Near-optimally input-preserving hardness amplification (and corresponding fast PRGs) 2. Constant rate codes with -depth list decoding (RNC) 3. Complexity-preserving distance amplification Our codes are built on the powerful theory of (local-spectral) high dimensional expanders (HDX). At a technical level, we make two key contributions. First, we introduce a new…
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Taxonomy
TopicsComplexity and Algorithms in Graphs · Advanced Data Storage Technologies · Error Correcting Code Techniques
