Delay-Complexity Trade-Off of Random Linear Network Coding in Wireless Broadcast

In wireless broadcast, random linear network coding (RLNC) over GF(<inline-formula> <tex-math notation="LaTeX">2^{L} </tex-math></inline-formula>) is known to asymptotically achieve the optimal completion delay with increasing <inline-formula> <tex-math not...

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Bibliographic Details
Published in:IEEE transactions on communications Vol. 68; no. 9; pp. 5606 - 5618
Main Authors: Su, Rina, Sun, Qifu Tyler, Zhang, Zhongshan
Format: Journal Article
Language:English
Published: New York IEEE 01.09.2020
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects:
Asymptotic properties
Binary system
circular-shift
Coding
completion delay
Complexity
Complexity theory
Decoding
decoding complexity
Delay
Delays
Encoding
Network coding
random linear network coding
Receivers
Tradeoffs
Wireless broadcast
Wireless communication
ISSN:0090-6778, 1558-0857
Online Access:Get full text
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Summary:In wireless broadcast, random linear network coding (RLNC) over GF(<inline-formula> <tex-math notation="LaTeX">2^{L} </tex-math></inline-formula>) is known to asymptotically achieve the optimal completion delay with increasing <inline-formula> <tex-math notation="LaTeX">L </tex-math></inline-formula>. However, the high decoding complexity hinders the potential applicability of RLNC schemes over large GF(<inline-formula> <tex-math notation="LaTeX">2^{L} </tex-math></inline-formula>). In this paper, a comprehensive analysis of completion delay and decoding complexity is conducted for field-based systematic RLNC schemes in wireless broadcast. In particular, we prove that the RLNC scheme over GF(2) can also asymptotically approach the optimal completion delay per packet when the packet number goes to infinity. Moreover, we introduce a new method, based on circular-shift operations, to design RLNC schemes which avoid multiplications over large GF(<inline-formula> <tex-math notation="LaTeX">2^{L} </tex-math></inline-formula>). Based on both theoretical and numerical analyses, the new RLNC schemes turn out to have a much better trade-off between completion delay and decoding complexity. In particular, numerical results demonstrate that the proposed schemes can attain average completion delay just within 5% higher than the optimal one, while the decoding complexity is only about 3 times the one of the RLNC scheme over GF(2).
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ISSN:0090-6778
1558-0857
DOI:10.1109/TCOMM.2020.3001133