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Revision #1 to TR10-047 | 25th April 2010 17:02

Local list decoding with a constant number of queries

Revision #1
Authors: Avraham Ben-Aroya, Klim Efremenko, Amnon Ta-Shma
Accepted on: 25th April 2010 17:02
Keywords:

Abstract:

Recently Efremenko showed locally-decodable codes of sub-exponential
length. That result showed that these codes can handle up to
$\frac{1}{3}$ fraction of errors. In this paper we show that the
same codes can be locally unique-decoded from error rate
$\half-\alpha$ for any $\alpha>0$ and locally list-decoded from
error rate $1-\alpha$ for any $\alpha>0$, with only a constant
number of queries and a constant alphabet size. This gives the first
sub-exponential codes that can be locally list-decoded with a
constant number of queries.

Paper:

TR10-047 | 23rd March 2010 16:08

Local list decoding with a constant number of queries

TR10-047
Authors: Avraham Ben-Aroya, Klim Efremenko, Amnon Ta-Shma
Publication: 23rd March 2010 19:26
Keywords:

Abstract:

Recently Efremenko showed locally-decodable codes of sub-exponential
length. That result showed that these codes can handle up to
$\frac{1}{3}$ fraction of errors. In this paper we show that the
same codes can be locally unique-decoded from error rate
$\half-\alpha$ for any $\alpha>0$ and locally list-decoded from
error rate $1-\alpha$ for any $\alpha>0$, with only a constant
number of queries and a constant alphabet size. This gives the first
sub-exponential codes that can be locally list-decoded with a
constant number of queries.

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