The Birthday Problem and Zero-Error List Codes
Abstract
As an attempt to bridge the gap between the probabilistic world of classical information theory and the combinatorial world of zero-error information theory, this paper studies the performance of randomly generated codebooks over discrete memoryless channels under a zero-error list-decoding constraint. This study allows the application of tools from one area to the other. Furthermore, it leads to an information-theoretic formulation of the birthday problem, which is concerned with the probability that in a given population, a fixed number of people have the same birthday. Due to the lack of a closed-form expression for this probability when the distribution of birthdays is not uniform, the resulting expression is not simple to analyze; in the information-theoretic formulation, however, the asymptotic behavior of this probability can be characterized exactly for all distributions.
Cite
@article{arxiv.1802.04719,
title = {The Birthday Problem and Zero-Error List Codes},
author = {Parham Noorzad and Michelle Effros and Michael Langberg and Victoria Kostina},
journal= {arXiv preprint arXiv:1802.04719},
year = {2018}
}
Comments
Extended version of paper presented at ISIT 2017 in Aachen