Separable Codes for the Symmetric Multiple-Access Channel

A binary matrix is called an <inline-formula> <tex-math notation="LaTeX">{s} </tex-math></inline-formula>- separable code for the disjunctive multiple-access channel ( disj-MAC ) if Boolean sums of sets of <inline-formula> <tex-math notation="LaTeX&quo...

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Bibliographic Details
Published in:IEEE transactions on information theory Vol. 65; no. 6; pp. 3738 - 3750
Main Authors: D'yachkov, Arkadii, Polyanskii, Nikita, Shchukin, Vladislav, Vorobyev, Ilya
Format: Journal Article
Language:English
Published: New York IEEE 01.06.2019
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects:
Boolean algebra
Channel coding
Combinatorial analysis
Communication channels
Cryptography
list-decoding
Lower bounds
Mathematical analysis
Matrix methods
Multiple-access channel (MAC)
random coding method
separable codes
Terminology
Upper bound
ISSN:0018-9448, 1557-9654
Online Access:Get full text
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Summary:A binary matrix is called an <inline-formula> <tex-math notation="LaTeX">{s} </tex-math></inline-formula>- separable code for the disjunctive multiple-access channel ( disj-MAC ) if Boolean sums of sets of <inline-formula> <tex-math notation="LaTeX">{s} </tex-math></inline-formula> columns are all distinct. The well-known issue of the combinatorial coding theory is to obtain upper and lower bounds on the rate of <inline-formula> <tex-math notation="LaTeX">{s} </tex-math></inline-formula>-separable codes for the <inline-formula> <tex-math notation="LaTeX">{disj} </tex-math></inline-formula>-MAC. In our paper, we generalize the problem and discuss upper and lower bounds on the rate of <inline-formula> <tex-math notation="LaTeX">{q} </tex-math></inline-formula>-ary <inline-formula> <tex-math notation="LaTeX">{s} </tex-math></inline-formula>-separable codes for the models of noiseless symmetric MAC, i.e., at each time instant the output signal of MAC is a symmetric function of its <inline-formula> <tex-math notation="LaTeX">{s} </tex-math></inline-formula> input signals.
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ISSN:0018-9448
1557-9654
DOI:10.1109/TIT.2019.2893234