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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| Published in: | IEEE communications letters Vol. 16; no. 5; pp. 720 - 721 |
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| Format: | Journal Article |
| Language: | English |
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New York, NY
IEEE
01.05.2012
Institute of Electrical and Electronics Engineers The Institute of Electrical and Electronics Engineers, Inc. (IEEE) |
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| ISSN: | 1089-7798, 1558-2558 |
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| Abstract | 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. |
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| AbstractList | 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. 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 greater than or equal to 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. |
| Author | Xubo Zhao |
| Author_xml | – sequence: 1 givenname: Xubo surname: Zhao fullname: Zhao, Xubo |
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| Cites_doi | 10.1017/CBO9780511987045 10.1007/978-3-540-69499-1_14 10.1109/LCOMM.2010.110310.101480 10.1109/TIT.2006.881746 |
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| Keywords | Finite field Linear coding Packet switching Linear combination Random linear coding Wireless telecommunication decoding probability Network coding Wireless network wireless networks Decoding Random coding |
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| Snippet | 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... 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... |
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| SubjectTerms | 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 |
| Title | Notes on "Exact Decoding Probability Under Random Linear Network Coding" |
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