2,390 research outputs found
Erasure List-Decodable Codes from Random and Algebraic Geometry Codes
Erasure list decoding was introduced to correct a larger number of erasures
with output of a list of possible candidates. In the present paper, we consider
both random linear codes and algebraic geometry codes for list decoding erasure
errors. The contributions of this paper are two-fold. Firstly, we show that,
for arbitrary ( and are independent),
with high probability a random linear code is an erasure list decodable code
with constant list size that can correct a fraction
of erasures, i.e., a random linear code achieves the
information-theoretic optimal trade-off between information rate and fraction
of erasure errors. Secondly, we show that algebraic geometry codes are good
erasure list-decodable codes. Precisely speaking, for any and
, a -ary algebraic geometry code of rate from the
Garcia-Stichtenoth tower can correct
fraction of erasure errors with
list size . This improves the Johnson bound applied to algebraic
geometry codes. Furthermore, list decoding of these algebraic geometry codes
can be implemented in polynomial time
Improved error bounds for the erasure/list scheme: the binary and spherical cases
We derive improved bounds on the error and erasure rate for spherical codes
and for binary linear codes under Forney's erasure/list decoding scheme and
prove some related results.Comment: 18 pages, 3 figures. Submitted to IEEE Transactions on Informatin
Theory in May 2001, will appear in Oct. 2004 (tentative
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