The birthday problem and zero-error list codes

Parham Noorzad, Michelle Effros, Michael Langberg, Victoria Kostina

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review


As an attempt to bridge the gap between 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 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 computation is not feasible in some applications; the information-theoretic formulation, however, can be analyzed for all distributions.

Original languageEnglish
Title of host publication2017 IEEE International Symposium on Information Theory, ISIT 2017
PublisherInstitute of Electrical and Electronics Engineers Inc.
Number of pages5
ISBN (Electronic)9781509040964
StatePublished - 9 Aug 2017
Externally publishedYes
Event2017 IEEE International Symposium on Information Theory, ISIT 2017 - Aachen, Germany
Duration: 25 Jun 201730 Jun 2017

Publication series

NameIEEE International Symposium on Information Theory - Proceedings
ISSN (Print)2157-8095


Conference2017 IEEE International Symposium on Information Theory, ISIT 2017

Bibliographical note

Funding Information:
ACKNOWLEDGMENTS This material is based upon work supported by the National Science Foundation under Grant Numbers 1321129, 1527524, and 1526771. The first author thanks Ming Fai Wong for helpful discussions regarding an earlier version of Theorem 2.

Publisher Copyright:
© 2017 IEEE.


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