TY - GEN
T1 - Minimizing the alphabet size of erasure codes with restricted decoding sets
AU - Gonen, Mira
AU - Haviv, Ishay
AU - Langberg, Michael
AU - Sprintson, Alex
N1 - Publisher Copyright:
© 2020 IEEE.
PY - 2020/6
Y1 - 2020/6
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=85090416477&partnerID=8YFLogxK
U2 - 10.1109/ISIT44484.2020.9174012
DO - 10.1109/ISIT44484.2020.9174012
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AN - SCOPUS:85090416477
T3 - IEEE International Symposium on Information Theory - Proceedings
SP - 144
EP - 149
BT - 2020 IEEE International Symposium on Information Theory, ISIT 2020 - Proceedings
PB - Institute of Electrical and Electronics Engineers Inc.
T2 - 2020 IEEE International Symposium on Information Theory, ISIT 2020
Y2 - 21 July 2020 through 26 July 2020
ER -