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Lower Bounds for Approximate LDCs

Author(s): Briët, Jop; Dvir, Zeev; Hu, Guangda; Saraf, Shubhangi

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Abstract: We study an approximate version of q-query LDCs (Locally Decodable Codes) over the real numbers and prove lower bounds on the encoding length of such codes. A q-query (α,δ)-approximate LDC is a set V of n points in ℝ d so that, for each i ∈ [d] there are Ω(δn) disjoint q-tuples (u 1,…,u q ) in V so that span(u 1,…,u q ) contains a unit vector whose i’th coordinate is at least α. We prove exponential lower bounds of the form 𝑛≥2Ω(𝛼𝛿𝑑√) for the case q = 2 and, in some cases, stronger bounds (exponential in d).
Publication Date: 2014
Citation: Briët, Jop, Zeev Dvir, Guangda Hu, and Shubhangi Saraf. "Lower Bounds for Approximate LDCs." International Colloquium on Automata, Languages, and Programming (2014): pp. 259-270. doi:10.1007/978-3-662-43948-7_22
DOI: 10.1007/978-3-662-43948-7_22
ISSN: 0302-9743
EISSN: 1611-3349
Pages: 259 - 270
Type of Material: Conference Article
Journal/Proceeding Title: International Colloquium on Automata, Languages, and Programming
Version: Author's manuscript

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