A Matroidal Framework for Network-Error Correcting Codes
K. Prasad, B. Sundar Rajan

TL;DR
This paper introduces a matroidal framework linking network-error correcting codes to representable matroids, providing algorithms for constructing such networks and demonstrating the limitations of linear coding.
Contribution
It establishes a novel matroidal approach to characterize and construct network-error correcting codes, including algorithms and complexity analysis.
Findings
Network-error correcting codes correspond to representable matroids.
Algorithms enable construction of networks with arbitrary parameters.
Linear coding is insufficient for some network-error detection problems.
Abstract
We abstract the essential aspects of network-error detecting and correcting codes to arrive at the definitions of matroidal error detecting networks and matroidal error correcting networks. An acyclic network (with arbitrary sink demands) is then shown to possess a scalar linear error detecting (correcting) network code if and only if it is a matroidal error detecting (correcting) network associated with a representable matroid. Therefore, constructing such network-error correcting and detecting codes implies the construction of certain representable matroids that satisfy some special conditions, and vice versa. We then present algorithms which enable the construction of matroidal error detecting and correcting networks with a specified capability of network-error correction. Using these construction algorithms, a large class of hitherto unknown scalar linearly solvable networks with…
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Taxonomy
TopicsCooperative Communication and Network Coding · Full-Duplex Wireless Communications · Advanced Wireless Communication Technologies
