# 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 goodbinary linear codes of rate Ω(ɛ^{2}/ 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(ɛ^{3} lg(1/ɛ)).

## Keywords

Error-correcting codes Linear codes Decoding algorithms List decoding Erasure channel## Preview

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