Paper Info
Title
Average-radius list-recovery of random linear codes: it really ties the room together.
Abstract
We analyze the list-decodability, and related notions, of random linear codes. This has been studied extensively before: there are many different parameter regimes and many different variants. Previous works have used complementary styles of arguments---which each work in their own parameter regimes but not in others---and moreover have left some gaps in our understanding of the list-decodability of random linear codes. particular, none of these arguments work well for list-recovery, a generalization of list-decoding that has been useful in a variety of settings. In this work, we present a new approach, which works across parameter regimes and further generalizes to list-recovery. Our main theorem can establish better list-decoding and list-recovery results for low-rate random linear codes over large fields; list-recovery of high-rate random linear codes; and it can recover the rate bounds of Guruswami, Hastad, and Kopparty for constant-rate random linear codes (although with large list sizes).
Year
Venue
Field
2017
arXiv: Information Theory
Discrete mathematics,Mathematics
DocType
Volume
Citations 
Journal
abs/1704.02420
0
PageRank 
References 
Authors
0.34
0
2
Name
Order
Citations
PageRank
Atri Rudra160162.87
Mary Wootters217225.99