Posted by: atri | October 2, 2007

Lecture 14: List Decoding Capacity

In first part of today’s lecture we saw the proof that 1-H_q(\rho) is the list decoding capacity for q-ary codes that can list decoded up to \rho fraction of errors.
In the class I mentioned that there exists linear codes with rate 1-H_q(\rho)-\epsilon that are \left(\rho, q^{O(1/\epsilon)}\right)-list decodable (and this results holds with high probability). I also mentioned that just for q=2, one can show the existence of \left(\rho,O(1/\epsilon)\right)-list decodable codes. This result (among other things) was proven in the paper titled Combinatorial Bounds for List Decoding by Guruswami, Håstad, Sudan and Zuckerman.

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