List decoding algorithms for certain concatenated codes
STOC '00 Proceedings of the thirty-second annual ACM symposium on Theory of computing
Introduction to Coding Theory
Computing From Partial Solutions
COCO '99 Proceedings of the Fourteenth Annual IEEE Conference on Computational Complexity
List decoding of error-correcting codes
List decoding of error-correcting codes
Improved decoding of Reed-Solomon and algebraic-geometry codes
IEEE Transactions on Information Theory
Efficient decoding of Reed-Solomon codes beyond half the minimum distance
IEEE Transactions on Information Theory
| Hi-index | 0.00 |
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)).