On error correction with feedback under list decoding

This work provides some preliminary results on the problem of error correction in the presence of noiseless feedback, where list-of-L decoding is allowed. The methods introduced by Berlekamp for the list-of-1 setting are generalized, and some basic finite-block constraints are described. These constraints are then combined to derive an upper bound on the asymptotically achievable rates for a large family of strategies, as a function of the maximal error fraction p and the list size L.