Exact Decoding Probability Under Random Linear Network Coding

• Published in: IEEE communications letters Vol. 15; no. 1; pp. 67 - 69
• Main Authors: Trullols-Cruces, O, Barcelo-Ordinas, J M, Fiore, M
• Format: Journal Article Publication
• Language: English
• Published: New York, NY IEEE 01.01.2011; Institute of Electrical and Electronics Engineers; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Applied sciences; Coding; Coding, codes; Computer networks; Computer Science; Computer simulation; Decoding; Encoding; Enginyeria de la telecomunicació; error control; Exact sciences and technology; Galois fields; Implementació; Information, signal and communications theory; Mathematical analysis; Mathematical models; Network coding; Networking and Internet Architecture; Networks; Random linear network coding; Receivers; Signal and communications theory; Telecommunications and information theory; Telemàtica i xarxes d'ordinadors; Upper bound; Vectors; Wireless communication systems; wireless networks; Xarxes sense fils; Àrees temàtiques de la UPC; Finite field; Upper bound; Linear coding; Grounding; Wireless telecommunication; error control; Wireless network; wireless networks; Decoding; Random coding; Random linear network coding
• ISSN: 1089-7798; 1558-2558
• DOI: 10.1109/LCOMM.2010.110310.101480

In this letter, we compute the exact probability that a receiver obtains N linearly independent packets among K ≥ N received packets, when the sender/s use/s random linear network coding over a Galois Field of size q. Such condition maps to the receiver's capability to decode the original information, and its mathematical characterization helps to design the coding so to guarantee the correctness of the transmission. Our formulation represents an improvement over the current upper bound for the decoding probability, and provides theoretical grounding to simulative results in the literature.