Introduction to coding theory (CMU, Spr 2010)

April 22, 2010

List-decodability of random linear codes

Filed under: Announcements — Venkat Guruswami @ 9:46 am

In our discussion on random coding arguments to show the existence of list-decodable codes, we showed that a random q-ary code of rate 1-h_q(p)-1/L was (p,L)-list decodable w.h.p. For random linear codes over {\mathbb F}_q, the result (or rather proof) was weaker, and only guaranteed a rate of 1-h_q(p)-1/\log_q(L+1). I had mentioned that this discrepancy in list-size between linear and general codes was recently resolved, showing that a random linear code of rate 1-h_q(p) - O(1/L) is (p,L)-list decodable w.h.p as well.

I’ll speak about this result in the ACO seminar today. The paper can be downloaded here.

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