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