Abstract
A Maximum Distance Separable code over an alphabet F is defined via an encoding function C : Fk → Fn that allows to retrieve a message m Fk from the codeword C(m) even after erasing any n - k of its symbols. The minimum possible alphabet size of general (non-linear) MDS codes for given parameters n and k is unknown and forms one of the central open problems in coding theory. The paper initiates the study of the alphabet size of codes in a generalized setting where the coding scheme is required to handle a pre-specified subset of all possible erasure patterns, naturally represented by an n-vertex k-uniform hypergraph. We relate the minimum possible alphabet size of such codes to the strong chromatic number of the hypergraph and analyze the tightness of the obtained bounds for both the linear and non-linear settings. We further consider variations of the problem which allow a small probability of decoding error.
Original language | English |
---|---|
Title of host publication | 2020 IEEE International Symposium on Information Theory, ISIT 2020 - Proceedings |
Publisher | Institute of Electrical and Electronics Engineers Inc. |
Pages | 144-149 |
Number of pages | 6 |
ISBN (Electronic) | 9781728164328 |
DOIs | |
State | Published - Jun 2020 |
Externally published | Yes |
Event | 2020 IEEE International Symposium on Information Theory, ISIT 2020 - Los Angeles, United States Duration: 21 Jul 2020 → 26 Jul 2020 |
Publication series
Name | IEEE International Symposium on Information Theory - Proceedings |
---|---|
Volume | 2020-June |
ISSN (Print) | 2157-8095 |
Conference
Conference | 2020 IEEE International Symposium on Information Theory, ISIT 2020 |
---|---|
Country/Territory | United States |
City | Los Angeles |
Period | 21/07/20 → 26/07/20 |
Bibliographical note
Publisher Copyright:© 2020 IEEE.