Small-bias Probability Spaces: efficient constructions and Applications

Noga Alon    Shuki Bruck    Joseph Naor    Moni Naor    Ronny Roth


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.

The paper: Postscript, gzipped Postscript.


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