An LEK-Based Design Algorithm for MDS Linear Network Error Correction Codes on Cyclic Multicast Networks

• Published in: IEEE transactions on communications Vol. 67; no. 11; pp. 7392 - 7404
• Main Authors: Esmaeili, Morteza, Rekab-Eslami, Morteza, Samadi-Khaftari, Vahid, Gulliver, T. Aaron
• Format: Journal Article
• Language: English
• Published: New York IEEE 01.11.2019; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Algorithms; Codes; Convolutional codes; Encoding; Erroneous cyclic network; Error correction; Error correction & detection; Error correction codes; global encoding kernel (GEK); Image edge detection; Kernel; Kernels; linear network error correction (LNEC) code; local encoding kernel (LEK); Manufacturing cells; maximum distance separable (MDS); Multicast; Multicast algorithms; Network coding; Networks
• ISSN: 0090-6778; 1558-0857
• DOI: 10.1109/TCOMM.2019.2931571

A linear network (LN) code can be described by either global encoding kernels (GEKs) or local encoding kernels (LEKs). In the literature, the multicast property of an LN code is described using GEKs, so the design algorithms for multicast LN codes employ GEKs to check this property. In this paper, a criterion is developed so that LEKs rather than GEKs can be used to check the multicast maximum distance separable (MDS) property of linear network error correction (LNEC) codes on erroneous networks. Further, it is used to develop a design algorithm for multicast MDS LNEC codes on erroneous cyclic networks. This algorithm is more efficient than the algorithm that uses GEKs when the number of edges is high and the interconnection of these edges is low.