A Revisit of Linear Network Error Correction Coding

作     者：Guang, Xuan Yeung, Raymond W. 

作者机构：Nankai Univ Sch Math Sci Tianjin 300071 Peoples R China Nankai Univ Key Lab Pure Math & Combinator LPMC Tianjin 300071 Peoples R China Chinese Univ Hong Kong Inst Network Coding Hong Kong Peoples R China Chinese Univ Hong Kong Dept Informat Engn Hong Kong Peoples R China 

出 版 物：《IEEE JOURNAL ON SELECTED AREAS IN INFORMATION THEORY》 (IEEE. J. Sel. Area. Inf. Theory.)

年 卷 期：2023年第4卷

页      面：514-523页

核心收录：

基　　金：National Key Research and Development Program of China [2022YFA1005000] Natural Science Foundation of China Fundamental Research Funds for the Central Universities of China [NKU 050-63233070] Research Grants Council of the Hong Kong Special Administrative Region, China [CUHK SRFS2223-4S03] 

主　　题：Network coding network error detection and correction linear network error correction (LNEC) coding additive adversarial network for LNEC coding enhanced characterization of the error correction capability 

摘      要：We consider linear network erro correction (LNEC) coding when errors may occur on the edges of a communication network of which the topology is known. In this paper, we first present a framework of additive adversarial network for LNEC coding, and then prove the equivalence of two well-known LNEC coding approaches, which can be unified under this framework. Furthermore, by developing a graph-theoretic approach, we obtain a significantly enhanced characterization of the error correction capability of LNEC codes in terms of the minimum distances at the sink nodes. Specifically, in order to ensure that an LNEC code can correct up to r errors at a sink node t, it suffices to ensure that this code can correct every error vector in a reduced set of error vectors;and on the other hand, this LNEC code in fact can correct every error vector in an enlarged set of error vectors. In general, the size of this reduced set is considerably smaller than the number of error vectors with Hamming weight not larger than r, and the size of this enlarged set is considerably larger than the same number. This result has the important implication that the computational complexities for decoding and for code construction can be significantly reduced.