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  • 天元讲堂(6.12)​上官冲:Combinatorial list-decoding of Reed-Solomon codes
  • 浏览量:10 发布人: 发布时间:2020-06-09
  • 题目:Combinatorial list-decoding of Reed-Solomon codes

    报告人:上官冲博士 (Tel Aviv University)

    时间:2020/6/12 14:00-15:00

    线上讲座,WeLink会议信息见下

     

    报告摘要:List-decoding of Reed-Solomon (RS) codes beyond the so called Johnson radius has been one of the main open questions in coding theory since the work of Guruswami and Sudan. It is now known by the work of Rudra and Wootters, using techniques from high dimensional probability, that over large enough alphabets there exist RS codes that are list-decodable beyond this radius.

     

    In this talk, we take a more combinatorial approach which allows us to determine the precise relation (up to the exact constant) between the decoding radius and the list size. We prove a generalized Singleton bound for a given list size, and show that the bound is tight for list size $L=2$. As a by-product we show that most RS codes with a rate of at least $1/4$ are list-decodable beyond the Johnson radius. We also give the first explicit construction of such RS codes.

     

    The main tool used in the proof is the polynomial method that captures a new type of linear dependency between codewords of a code that are contained in a small Hamming ball.

     

    欢迎参加!

     

    WeLink会议信息:

    会议时间:2020/6/12 14:00-15:0

    会议 ID:986 784 065

    密码:502935

    邀请人:汪

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