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Summary: Construction of Asymptotically Good
Low-Rate Error-Correcting Codes through
Pseudo-Random Graphs
Noga Alon
Jehoshua Bruck
Joseph Naor
Moni Naor
Ron M. Roth§
Abstract
A new technique, based on the pseudo-random properties of certain graphs, known
as expanders, is used to obtain new simple explicit constructions of asymptotically good
codes. In one of the constructions, the expanders are used to enhance Justesen codes by
replicating, shuffling and then regrouping the code coordinates. For any fixed (small)
rate, and for sufficiently large alphabet, the codes thus obtained lie above the Zyablov
bound. Using these codes as outer codes in a concatenated scheme, a second asymptotic
good construction is obtained which applies to small alphabets (say, GF(2)) as well.
Although these concatenated codes lie below Zyablov bound, they are still superior to
previously-known explicit constructions in the zero-rate neighborhood.
Key words: Expanders; Justesen codes; Zyablov bound; Independent sets.
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