The Birthday Problem and Zero-Error List Codes

A key result of classical information theory states that if the rate a randomly generated codebook is less than mutual between channel's input and output, then probability has negligible error goes to one as blocklength infinity. In an attempt bridge gap probabilistic world combinatorial zero-error theory, this work derives necessary sufficient conditions on so operated under list decoding (for any fixed size) zero Furthermore, extends birthday problem information-theoretic setting, which results in definition “noisy” counterpart Rényi entropy, analogous how can be considered noisy Shannon entropy.