Construction of Network Error Correction Codes in Packet Networks
Xuan Guang, Fang-Wei Fu, Zhen Zhang

TL;DR
This paper advances network error correction coding by refining bounds, providing constructive algorithms for code design, and analyzing the performance of random linear network error correction codes.
Contribution
It offers a more explicit proof of the refined Singleton bound, reduces the required field size for MDS codes, and evaluates the failure probabilities of random coding schemes.
Findings
Refined Singleton bound for NEC proved explicitly.
Constructive algorithm for linear network error correction codes provided.
Failure probabilities of random codes approach zero as field size increases.
Abstract
Recently, network error correction coding (NEC) has been studied extensively. Several bounds in classical coding theory have been extended to network error correction coding, especially the Singleton bound. In this paper, following the research line using the extended global encoding kernels proposed in \cite{zhang-correction}, the refined Singleton bound of NEC can be proved more explicitly. Moreover, we give a constructive proof of the attainability of this bound and indicate that the required field size for the existence of network maximum distance separable (MDS) codes can become smaller further. By this proof, an algorithm is proposed to construct general linear network error correction codes including the linear network error correction MDS codes. Finally, we study the error correction capability of random linear network error correction coding. Motivated partly by the performance…
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsCooperative Communication and Network Coding · Advanced Wireless Communication Technologies · Full-Duplex Wireless Communications
