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A Linear Time Erasure-Resilient Code With Nearly Optimal Recovery

Summary: A Linear Time Erasure-Resilient Code
With Nearly Optimal Recovery
Noga Alon
Michael Luby
We develop an efficient scheme that produces an encoding of a
given message such that the message can be decoded from any por-
tion of the encoding that is approximately equal to the length of the
message. More precisely, an (n, c, , r)-erasure-resilient code consists
of an encoding algorithm and a decoding algorithm with the following
properties. The encoding algorithm produces a set of -bit packets of
total length cn from an n-bit message. The decoding algorithm is able
to recover the message from any set of packets whose total length is
r, i.e., from any set of r/ packets. We describe erasure-resilient codes
where both the encoding and decoding algorithms run in linear time
and where r is only slightly larger than n.
1 Introduction
Most existing and proposed networks are packet based, where a packet is
fixed length indivisible unit of information that either arrives intact upon
transmission or is completely lost. This model accurately reflects properties


Source: Alon, Noga - School of Mathematical Sciences, Tel Aviv University


Collections: Mathematics