Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2401.16540 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866911622024396800 |
|---|---|
| author | Goshkoder, Daniil Polyanskii, Nikita Vorobyev, Ilya |
| author_facet | Goshkoder, Daniil Polyanskii, Nikita Vorobyev, Ilya |
| contents | This work focuses on non-adaptive combinatorial group testing, with a primary goal of efficiently identifying a set of at most $d$ defective elements among a given set of $n$ elements using the fewest possible tests. Non-adaptive combinatorial group testing often employs disjunctive matrices (DM) and separable matrices (SM). This paper discusses separable matrices and recently introduced list-decoding separable matrices (LDSM) with list size $n^{1/d}$, which allow for non-adaptive identification of defectives with the decoding complexity linear in the number of tests and the number of elements. In our study, we distinguish two subclasses of these matrices: matrices which can be used when the number of defectives $d$ is a priori known ($d$-SM and $(d, n^{1/d})$-LDSM), and matrices which can be used for any subset of at most $d$ defectives ($\bar{d}$-SM and $(\bar{d}, n^{1/d})$-LDSM). Our contribution lies in deriving new lower bounds on the rates of $d$-SM, $\bar{d}$-SM, $(d, n^{1/d})$-LDSM and $(\bar{d}, n^{1/d})$-LDSM for an arbitrary number $d \ge 3$ of defectives. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_16540 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Improved Probabilistic Lower Bounds for Separable Matrices Goshkoder, Daniil Polyanskii, Nikita Vorobyev, Ilya Information Theory This work focuses on non-adaptive combinatorial group testing, with a primary goal of efficiently identifying a set of at most $d$ defective elements among a given set of $n$ elements using the fewest possible tests. Non-adaptive combinatorial group testing often employs disjunctive matrices (DM) and separable matrices (SM). This paper discusses separable matrices and recently introduced list-decoding separable matrices (LDSM) with list size $n^{1/d}$, which allow for non-adaptive identification of defectives with the decoding complexity linear in the number of tests and the number of elements. In our study, we distinguish two subclasses of these matrices: matrices which can be used when the number of defectives $d$ is a priori known ($d$-SM and $(d, n^{1/d})$-LDSM), and matrices which can be used for any subset of at most $d$ defectives ($\bar{d}$-SM and $(\bar{d}, n^{1/d})$-LDSM). Our contribution lies in deriving new lower bounds on the rates of $d$-SM, $\bar{d}$-SM, $(d, n^{1/d})$-LDSM and $(\bar{d}, n^{1/d})$-LDSM for an arbitrary number $d \ge 3$ of defectives. |
| title | Improved Probabilistic Lower Bounds for Separable Matrices |
| topic | Information Theory |
| url | https://arxiv.org/abs/2401.16540 |