报告题目：List Decoding of Rank-Metric Codes with Row-to-Column Ratio Bigger Than 1/2

报告专家：刘姝 电子科技大学 副教授

报告时间：2023年11月04日（周六）上午09:15-10:00

报告地点：南教1-120报告厅

线上平台：腾讯会议 会议ID：153 622 933

报告摘要：This paper is to explicitly construct a class of rank-metric codes C of rate R with the column-to-row ratio up to 2/3 and efficiently list decode these codes with decoding radius beyond the decoding radius (1-R)/2 (note that (1-R)/2 is at least half of relative minimum distance δ). In literature, the largest column-to-row ratio of rank-metric codes that can be efficiently list decoded beyond half of minimum distance is 1/2. Thus, it is greatly desired to efficiently design list decoding algorithms for rank-metric codes with the column-to-row ratio bigger than 1/2 or even close to 1. Our key idea is to compress an element of the field F_qn into a smaller  F_q-subspace via a linearized polynomial. Thus, the column-to-row ratio gets increased at the price of reducing the code rate. Our result shows that the compression technique is powerful and it has not been employed in the topic of list decoding of both the Hamming and rank metrics. Apart from the above algebraic technique, we follow some standard techniques to prune down the list. The algebraic idea enables us to pin down the message into a structured subspace of dimension linear in the number n of columns. This “periodic” structure allows us to pre-encode the message to prune down the list.

专家简介：刘姝目前是电子科技大学通信抗干扰全国重点实验室副教授。2018年在新加坡南洋理工大学获得博士学位，2018-2019年在南洋理工大学从事research fellow工作，2018年加入电子科技大学，入选2020年度四川省高层次人才引进“青年千人计划”。从事代数编码及其应用方面的基础研究，尤其致力于非经典纠错码的构造与列表译码机理研究。近五年在信息论与编码领域国际学术期刊上发表论文二十余篇，含IEEE TIT期刊论文9篇，IEEE TCOM 2篇。主持国家重点研发计划课题1项、国家自然科学基金面上项目1项、国家自然科学青年科学基金项目1项及国防重点实验室基金项目3项等；在国际重要编码理论学术会议上作邀请报告15余次；申请发明专利8项，授权发明专利3项；担任多个国际学术期刊IEEE TIT、FFA等的审稿人。