Gilbert-Varshamov Bound for Codes in $L_1$ Metric using Multivariate Analytic Combinatorics
<|reference_start|>Gilbert-Varshamov Bound for Codes in $L_1$ Metric using Multivariate Analytic 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.<|reference_end|>
@article{goyal2024gilbert-varshamov,
    title={Gilbert-Varshamov Bound for Codes in $L_1$ Metric using Multivariate
  Analytic Combinatorics},
    author={Keshav Goyal, Duc Tu Dao, Mladen Kovav{c}evi'c, and Han Mao Kiah},
    journal={arXiv preprint arXiv:2402.14712},
    year={2024},
    archivePrefix={arXiv},
    eprint={2402.14712},
    primaryClass={cs.IT cs.DM math.CO math.IT}
}