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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| Vydané v: | IEEE transactions on information theory Ročník 65; číslo 6; s. 3738 - 3750 |
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| Médium: | Journal Article |
| Jazyk: | English |
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01.06.2019
The Institute of Electrical and Electronics Engineers, Inc. (IEEE) |
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| ISSN: | 0018-9448, 1557-9654 |
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| Abstract | 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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| AbstractList | 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. A binary matrix is called an [Formula Omitted]- separable code for the disjunctive multiple-access channel ( disj-MAC ) if Boolean sums of sets of [Formula Omitted] columns are all distinct. The well-known issue of the combinatorial coding theory is to obtain upper and lower bounds on the rate of [Formula Omitted]-separable codes for the [Formula Omitted]-MAC. In our paper, we generalize the problem and discuss upper and lower bounds on the rate of [Formula Omitted]-ary [Formula Omitted]-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 [Formula Omitted] input signals. |
| Author | Vorobyev, Ilya Shchukin, Vladislav Polyanskii, Nikita D'yachkov, Arkadii |
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| Snippet | A binary matrix is called an <inline-formula> <tex-math notation="LaTeX">{s} </tex-math></inline-formula>- separable code for the disjunctive multiple-access... A binary matrix is called an [Formula Omitted]- separable code for the disjunctive multiple-access channel ( disj-MAC ) if Boolean sums of sets of [Formula... |
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| SubjectTerms | 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 |
| Title | Separable Codes for the Symmetric Multiple-Access Channel |
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