Notes on "Exact Decoding Probability Under Random Linear Network Coding"

In a recent letter, Trullols-Cruces et al. derived the exact decoding probability P ns (K,N) that a receiver node obtained N linearly independent coded packets among K (K≥ N) received coded packets, when the source node uses a random linear coding scheme over a Galois Field GF(q). They discussed P n...

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Bibliographic Details
Published in:	IEEE communications letters Vol. 16; no. 5; pp. 720 - 721
Main Author:	Zhao, Xubo
Format:	Journal Article
Language:	English
Published:	New York, NY IEEE 01.05.2012 Institute of Electrical and Electronics Engineers The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects:	Applied sciences Coding Coding, codes Decoding decoding probability Derivation Educational institutions Encoding Exact sciences and technology Information, signal and communications theory Matrices Network coding Networks Random linear coding Receivers Signal and communications theory Switching and signalling Systems, networks and services of telecommunications Telecommunications Telecommunications and information theory Vectors wireless networks Finite field Linear coding Packet switching Linear combination Random linear coding Wireless telecommunication decoding probability Network coding Wireless network wireless networks Decoding Random coding
ISSN:	1089-7798, 1558-2558
Online Access:	Get full text
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Summary:	In a recent letter, Trullols-Cruces et al. derived the exact decoding probability P ns (K,N) that a receiver node obtained N linearly independent coded packets among K (K≥ N) received coded packets, when the source node uses a random linear coding scheme over a Galois Field GF(q). They discussed P ns (K,N) both in the case of the source node sending the random linear combination of the original packets, including all-zero combinations, as well as the case of excluding all-zero combinations. However, their derivations are a bit complicated. In this note, we demonstrate simple derivations of the exact decoding probability P ns (K,N) in both cases. Furthermore, we point out that there is a more succinct expression of P ns (K,N) for the latter case.
Bibliography:	ObjectType-Article-2 SourceType-Scholarly Journals-1 ObjectType-Feature-1 content type line 14 content type line 23
ISSN:	1089-7798 1558-2558
DOI:	10.1109/LCOMM.2012.041112.112564