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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Vydáno v:IEEE communications letters Ročník 24; číslo 4; s. 729 - 733
Hlavní autoři: Zarei, Amir, Pahlevani, Peyman, Lucani, Daniel E.
Médium: Journal Article
Jazyk:angličtina
Vydáno: New York IEEE 01.04.2020
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Témata:
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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Shrnutí: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.
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ISSN:1089-7798
1558-2558
DOI:10.1109/LCOMM.2020.2965928