TY - GEN
T1 - Local list recovery of high-rate tensor codes & applications
AU - Hemenway, Brett
AU - Ron-Zewi, Noga
AU - Wootters, Mary
N1 - Publisher Copyright:
© 2017 IEEE.
PY - 2017/11/10
Y1 - 2017/11/10
N2 - In this work, we give the first construction of high-rate locally list-recoverable codes. List-recovery has been an extremely useful building block in coding theory, and our motivation is to use these codes as such a building block. In particular, our construction gives the first capacity-achieving locally list-decodable codes (over constant-sized alphabet); the first capacity achieving} globally list-decodable codes with nearly linear time list decoding algorithm (once more, over constant-sized alphabet); and a randomized construction of binary codes on the Gilbert-Varshamov bound that can be uniquely decoded in near-linear-time, with higher rate than was previously known.Our techniques are actually quite simple, and are inspired by an approach of Gopalan, Guruswami, and Raghavendra (Siam Journal on Computing, 2011) for list-decoding tensor codes. We show that tensor powers of (globally) list-recoverable codes are approximately locally list-recoverable, and that the approximately modifier may be removed by pre-encoding the message with a suitable locally decodable code. Instantiating this with known constructions of high-rate globally list-recoverable codes and high-rate locally decodable codes finishes the construction.
AB - In this work, we give the first construction of high-rate locally list-recoverable codes. List-recovery has been an extremely useful building block in coding theory, and our motivation is to use these codes as such a building block. In particular, our construction gives the first capacity-achieving locally list-decodable codes (over constant-sized alphabet); the first capacity achieving} globally list-decodable codes with nearly linear time list decoding algorithm (once more, over constant-sized alphabet); and a randomized construction of binary codes on the Gilbert-Varshamov bound that can be uniquely decoded in near-linear-time, with higher rate than was previously known.Our techniques are actually quite simple, and are inspired by an approach of Gopalan, Guruswami, and Raghavendra (Siam Journal on Computing, 2011) for list-decoding tensor codes. We show that tensor powers of (globally) list-recoverable codes are approximately locally list-recoverable, and that the approximately modifier may be removed by pre-encoding the message with a suitable locally decodable code. Instantiating this with known constructions of high-rate globally list-recoverable codes and high-rate locally decodable codes finishes the construction.
KW - coding theory
KW - error correcting codes
KW - list recovery
KW - local list recovery
KW - tensor codes
UR - http://www.scopus.com/inward/record.url?scp=85041139167&partnerID=8YFLogxK
U2 - 10.1109/FOCS.2017.27
DO - 10.1109/FOCS.2017.27
M3 - Conference contribution
AN - SCOPUS:85041139167
T3 - Annual Symposium on Foundations of Computer Science - Proceedings
SP - 204
EP - 215
BT - Proceedings - 58th Annual IEEE Symposium on Foundations of Computer Science, FOCS 2017
PB - IEEE Computer Society
T2 - 58th Annual IEEE Symposium on Foundations of Computer Science, FOCS 2017
Y2 - 15 October 2017 through 17 October 2017
ER -