Coding Theory: A General Framework and Two Inverse Problems

作     者：Bortolussi, Luca Dinu, Liviu P. Franzoi, Laura Sgarro, Andrea 

作者机构：Univ Trieste Dept Math & Geosci I-34127 Trieste Italy Univ Bucharest Fac Math & Comp Sci Bucharest 010014 Romania 

出 版 物：《FUNDAMENTA INFORMATICAE》 (信息科学基础)

年 卷 期：2015年第141卷第4期

页      面：296-309页

核心收录：

学科分类：08[工学] 0835[工学-软件工程] 0701[理学-数学] 0812[工学-计算机科学与技术（可授工学、理学学位）] 

主　　题：Shannon theory coding theory decoding errors upper probabilities 

摘      要：We put forward an ample framework for coding based on upper probabilities, or more generally on normalized monotone set-measures, and model accordingly noisy transmission channels and decoding errors. Two inverse problems are considered. In the first case, a decoder is given and one looks for channels of a specified family over which that decoder would work properly. In the second and more ambitious case, it is codes which are given, and one looks for channels over which those codes would ensure the required error correction capabilities. Upper probabilities allow for a solution of the two inverse problems in the case of usual codes based on checking Hamming distances between codewords: one can equivalently check suitable upper probabilities of the decoding errors. This soon extends to odd codeword distances for DNA strings as used in DNA word design, where instead, as we prove, not even the first unassuming inverse problem admits of a solution if one insists on channel models based on usual probabilities.