Gilbert-Varshamov Bound for Codes in $L_1$ Metric using Multivariate Analytic Combinatorics
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arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866917879163650048 |
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| author | Goyal, Keshav Dao, Duc Tu Kovačević, Mladen Kiah, Han Mao |
| author_facet | Goyal, Keshav Dao, Duc Tu Kovačević, Mladen Kiah, Han Mao |
| contents | Analytic combinatorics in several variables refers to a suite of tools that provide sharp asymptotic estimates for certain combinatorial quantities. In this paper, we apply these tools to determine the Gilbert--Varshamov lower bound on the rate of optimal codes in $L_1$ metric. Several different code spaces are analyzed, including the simplex and the hypercube in $\mathbb{Z^n}$, all of which are inspired by concrete data storage and transmission models such as the sticky insertion channel, the permutation channel, the adjacent transposition (bit-shift) channel, the multilevel flash memory channel, etc. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_14712 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Gilbert-Varshamov Bound for Codes in $L_1$ Metric using Multivariate Analytic Combinatorics Goyal, Keshav Dao, Duc Tu Kovačević, Mladen Kiah, Han Mao Information Theory Discrete Mathematics Combinatorics Analytic combinatorics in several variables refers to a suite of tools that provide sharp asymptotic estimates for certain combinatorial quantities. In this paper, we apply these tools to determine the Gilbert--Varshamov lower bound on the rate of optimal codes in $L_1$ metric. Several different code spaces are analyzed, including the simplex and the hypercube in $\mathbb{Z^n}$, all of which are inspired by concrete data storage and transmission models such as the sticky insertion channel, the permutation channel, the adjacent transposition (bit-shift) channel, the multilevel flash memory channel, etc. |
| title | Gilbert-Varshamov Bound for Codes in $L_1$ Metric using Multivariate Analytic Combinatorics |
| topic | Information Theory Discrete Mathematics Combinatorics |
| url | https://arxiv.org/abs/2402.14712 |