Work

Gilbert–Varshamov Bound for Codes in L₁ Metric Using Multivariate Analytic Combinatorics

Year: 2024

Type: article

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 permutation channel, the repetition channel, the adjacent transposition (bit-shift) channel, the multilevel flash memory channel, etc.

Source: IEEE Transactions on Information Theory

DOI: 10.1109/tit.2024.3483303

Authors: Keshav Goyal, Duc Tu Dao, Mladen Kovačević, Han Mao Kiah

Institutions: Nanyang Technological University, Genome Institute of Singapore, University of Novi Sad

Language: English

Topic: Coding theory and cryptography

Subfield: Artificial Intelligence

Field: Computer Science

Domain: Physical Sciences

Open Access status: green

Funder: Provincial Secretariat for Higher Education and Scientific Research, Autonomous Province of Vojvodina

Award: G5340079750