TY - GEN

T1 - Lower bounds for approximate LDCs

AU - Briët, Jop

AU - Dvir, Zeev

AU - Hu, Guangda

AU - Saraf, Shubhangi

PY - 2014

Y1 - 2014

N2 - 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 ℝd so that, for each i ∈ [d] there are Ω(δn) disjoint q-tuples (u1,...,uq) in V so that span(u 1,...,uq) contains a unit vector whose i'th coordinate is at least α. We prove exponential lower bounds of the form n ≥ 2 Ω(αδ√d) for the case q = 2 and, in some cases, stronger bounds (exponential in d).

AB - 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 ℝd so that, for each i ∈ [d] there are Ω(δn) disjoint q-tuples (u1,...,uq) in V so that span(u 1,...,uq) contains a unit vector whose i'th coordinate is at least α. We prove exponential lower bounds of the form n ≥ 2 Ω(αδ√d) for the case q = 2 and, in some cases, stronger bounds (exponential in d).

UR - http://www.scopus.com/inward/record.url?scp=84904204077&partnerID=8YFLogxK

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U2 - 10.1007/978-3-662-43948-7_22

DO - 10.1007/978-3-662-43948-7_22

M3 - Conference contribution

AN - SCOPUS:84904204077

SN - 9783662439470

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 259

EP - 270

BT - Automata, Languages, and Programming - 41st International Colloquium, ICALP 2014, Proceedings

PB - Springer Verlag

T2 - 41st International Colloquium on Automata, Languages, and Programming, ICALP 2014

Y2 - 8 July 2014 through 11 July 2014

ER -