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.

翻译：多变量解析组合学是指一套为某些组合量提供精确渐近估计的工具。本文应用这些工具确定了L1度量下最优码率的Gilbert-Varshamov下界。本文分析了多种码空间，包括Z^n中的单纯形和超立方体，这些空间均受具体数据存储与传输模型启发，例如粘性插入信道、置换信道、相邻换位（比特位移）信道、多级闪存信道等。