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arXiv · 2402.14712

Gilbert-Varshamov Bound for Codes in $L_1$ Metric using Multivariate Analytic Combinatorics

Keshav Goyal·Duc Tu Dao·Mladen Kovačević·Han Mao Kiah
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Abstract

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.

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Keshav Goyal, Duc Tu Dao, Mladen Kovačević, Han Mao Kiah. 2024-02-22. Gilbert-Varshamov Bound for Codes in $L_1$ Metric using Multivariate Analytic Combinatorics. https://doi.org/10.1109/tit.2024.3483303

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