An Analytical Model for Sparse Network Codes: Field Size Considerations

One of the by-products of Sparse Network Coding (SNC) is the ability to perform partial decoding, i.e., decoding some original packets prior to collecting all needed coded packets to decode the entire coded data. Due to this ability, SNC has been recently used as a technique for reducing the Average...

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Veröffentlicht in:	IEEE communications letters Jg. 24; H. 4; S. 729 - 733
Hauptverfasser:	Zarei, Amir, Pahlevani, Peyman, Lucani, Daniel E.
Format:	Journal Article
Sprache:	Englisch
Veröffentlicht:	New York IEEE 01.04.2020 The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Schlagworte:	Analytical models average decoding delay per packet Computer simulation Decoding Delays Encoding Fields (mathematics) Lower bounds Markov chains Markov processes Mathematical models Multimedia Random linear network coding Receivers Sparse matrices sparse network coding
ISSN:	1089-7798, 1558-2558
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Abstract	One of the by-products of Sparse Network Coding (SNC) is the ability to perform partial decoding, i.e., decoding some original packets prior to collecting all needed coded packets to decode the entire coded data. Due to this ability, SNC has been recently used as a technique for reducing the Average Decoding Delay (ADD) per packet in real-time multimedia applications. This study focuses on characterizing the ADD per packet for SNC considering the impact of finite field size. We present a Markov Chain model that allows us to determine lower bounds on the mean number of transmissions required to decode a fraction of a generation and the ADD per packet of the generation. We validate our model using simulations and show that the smaller finite fields, e.g., <inline-formula> <tex-math notation="LaTeX">q = 2^{4} </tex-math></inline-formula>, outperform large finite fields, e.g., <inline-formula> <tex-math notation="LaTeX">q = 2^{32} </tex-math></inline-formula>, in regard to the ADD per packet and provide a better trade-off between the ADD per packet and the overall number of transmissions to decode a generation.
AbstractList	One of the by-products of Sparse Network Coding (SNC) is the ability to perform partial decoding, i.e., decoding some original packets prior to collecting all needed coded packets to decode the entire coded data. Due to this ability, SNC has been recently used as a technique for reducing the Average Decoding Delay (ADD) per packet in real-time multimedia applications. This study focuses on characterizing the ADD per packet for SNC considering the impact of finite field size. We present a Markov Chain model that allows us to determine lower bounds on the mean number of transmissions required to decode a fraction of a generation and the ADD per packet of the generation. We validate our model using simulations and show that the smaller finite fields, e.g., [Formula Omitted], outperform large finite fields, e.g., [Formula Omitted], in regard to the ADD per packet and provide a better trade-off between the ADD per packet and the overall number of transmissions to decode a generation. One of the by-products of Sparse Network Coding (SNC) is the ability to perform partial decoding, i.e., decoding some original packets prior to collecting all needed coded packets to decode the entire coded data. Due to this ability, SNC has been recently used as a technique for reducing the Average Decoding Delay (ADD) per packet in real-time multimedia applications. This study focuses on characterizing the ADD per packet for SNC considering the impact of finite field size. We present a Markov Chain model that allows us to determine lower bounds on the mean number of transmissions required to decode a fraction of a generation and the ADD per packet of the generation. We validate our model using simulations and show that the smaller finite fields, e.g., <inline-formula> <tex-math notation="LaTeX">q = 2^{4} </tex-math></inline-formula>, outperform large finite fields, e.g., <inline-formula> <tex-math notation="LaTeX">q = 2^{32} </tex-math></inline-formula>, in regard to the ADD per packet and provide a better trade-off between the ADD per packet and the overall number of transmissions to decode a generation.
Author	Zarei, Amir Lucani, Daniel E. Pahlevani, Peyman
Author_xml	– sequence: 1 givenname: Amir orcidid: 0000-0002-0287-513X surname: Zarei fullname: Zarei, Amir email: az.hldv@gmail.com organization: Institute for Advanced Studies in Basic Sciences (IASBS), Zanjan, Iran – sequence: 2 givenname: Peyman orcidid: 0000-0001-5918-7250 surname: Pahlevani fullname: Pahlevani, Peyman organization: Wireless Communication Laboratory, Institute for Advanced Studies in Basic Sciences (IASBS), Zanjan, Iran – sequence: 3 givenname: Daniel E. orcidid: 0000-0001-5325-8863 surname: Lucani fullname: Lucani, Daniel E. organization: Department of Engineering, Aarhus University, Aarhus, Denmark
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Cites_doi	10.1109/TCOMM.2017.2657621 10.1007/978-3-642-23041-7_13 10.1109/TIT.2006.881746 10.1109/LCOMM.2018.2840139 10.1109/icc.2011.5963013 10.1109/NETCOD.2009.5191397
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SubjectTerms	Analytical models average decoding delay per packet Computer simulation Decoding Delays Encoding Fields (mathematics) Lower bounds Markov chains Markov processes Mathematical models Multimedia Random linear network coding Receivers Sparse matrices sparse network coding
Title	An Analytical Model for Sparse Network Codes: Field Size Considerations
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