List decoding from erasures: bounds and code constructions

Abstract

We consider the problem of list decoding from erasures. We establish lower and upper bounds on the rate of a (linear) code that can be list decoded with list size L when up to a fraction p of its symbols are adversarially erased. Our results show that in the limit of large L, the rate of such a code approaches the capacity (1 - p) of the erasure channel. Such nicely list decodable codes are then used as inner codes in a suitable concatenation scheme to give a uniformly constructive family of asymptotically good binary linear codes of rate Ω(Ɛ2/ lg(1/Ɛ)) that can be efficiently list decoded using lists of size O(1/Ɛ) from up to a fraction (1-Ɛ) of erasures. This improves previous results from [14] in this vein, which achieveda rate of Ω(Ɛ3 lg(1/Ɛ)).