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Secure physical layer network coding versus secure network coding

Masahito Hayashi

TL;DR

In this paper, several examples of network are given, in which, secure physical layer network coding realizes a performance that cannot be realized by secure network coding.

Abstract

Secure network coding realizes the secrecy of the message when the message is transmitted via noiseless network and a part of edges or a part of intermediate nodes are eavesdropped. In this framework, if the channels of the network has noise, we apply the error correction to noisy channel before applying the secure network coding. In contrast, secure physical layer network coding is a method to securely transmit a message by a combination of coding operation on nodes when the network is given as a set of noisy channels. In this paper, we give several examples of network, in which, secure physical layer network coding has advantage over secure network coding.

Secure physical layer network coding versus secure network coding

TL;DR

In this paper, several examples of network are given, in which, secure physical layer network coding realizes a performance that cannot be realized by secure network coding.

Abstract

Secure network coding realizes the secrecy of the message when the message is transmitted via noiseless network and a part of edges or a part of intermediate nodes are eavesdropped. In this framework, if the channels of the network has noise, we apply the error correction to noisy channel before applying the secure network coding. In contrast, secure physical layer network coding is a method to securely transmit a message by a combination of coding operation on nodes when the network is given as a set of noisy channels. In this paper, we give several examples of network, in which, secure physical layer network coding has advantage over secure network coding.

Paper Structure

This paper contains 16 sections, 5 equations, 5 figures, 7 tables.

Table of Contents

  1. Introduction
  2. Secure computation-and-forward
  3. Butterfly network
  4. conventional protocol
  5. Secure network coding
  6. Secure physical layer network coding
  7. Comparison
  8. Network with three sources
  9. Secure network coding
  10. Case (1)
  11. Case (2)
  12. Secure physical layer network coding
  13. Use of secure computation-and-forward
  14. Use of computation-and-forward
  15. Comparison
  16. ...and 1 more sections

Figures (5)

  • Figure 1: Computation-and-forward.
  • Figure 2: Butterfly network coding.
  • Figure 3: Transmission Time for four schemes when $RT=1$. Upper solid line (Black) expresses the time $\frac{2 RT}{2 I(Y;A_1+A_2)_{\rm Eq. \ref{['MAC']}} -I(Y; A_1,A_2 )_{\rm Eq. \ref{['MAC']}}}+\frac{RT}{I(Y;A)_{\rm Eq. \ref{['C2']}}}$ of secure physical layer network coding protocol given in the 1st paragraph of Section \ref{['S33']}. Upper dashed line (Blue) expresses the time $\frac{4RT}{I(Y;A)_{\rm Eq. \ref{['C2']}}}$ of secure network coding protocol given in Section \ref{['S32']} without MAC channel. Lower dashed line (Red) expresses the time $\frac{2RT}{I(Y;A)_{\rm Eq. \ref{['C2']}}}+ \frac{2RT}{I(Y;A_1,A_2)_{\rm Eq. \ref{['MAC']}}}$ of secure network coding protocol given in Section \ref{['S32']} with MAC channel. Lower solid line (Green) expresses the time $\frac{2 RT}{ I(Y;A_1+A_2)_{\rm Eq. \ref{['MAC']}} }+\frac{RT}{I(Y;A)_{\rm Eq. \ref{['C2']}}}$ of secure physical layer network coding protocol given in the 2nd paragraph of Section \ref{['S33']}.
  • Figure 4: Network with three sources.
  • Figure 5: Transmission Time for four schemes when $RT=1$. Solid line (Black) expresses the time $\frac{3RT}{I(Y;A_1A_2A_3)_{\rm Eq. \ref{['C3']}}}+ \frac{RT}{2 I(Y;A_1+A_2)_{\rm Eq. \ref{['MAC']}} -I(Y; A_1,A_2 )_{\rm Eq. \ref{['MAC']}}}$ of secure physical layer network coding protocol given in Section \ref{['S4-2-1']}. Solid line (Green) expresses the time $\frac{3RT}{I(Y;A_1+A_2)_{\rm Eq. \ref{['MAC']}}}+ \frac{2RT}{I(Y;A_1,A_2)_{\rm Eq. \ref{['MAC']}}}$ of secure physical layer network coding protocol given in Section \ref{['S4-2-2']}. Upper dashed line (Blue) expresses the time $\frac{8RT}{I(Y;A)_{\rm Eq. \ref{['C2']}}}$ of secure network coding protocol given in Section \ref{['S4-1-2']} without MAC channel. Lower dashed line (Red) expresses the time $\frac{6RT}{I(Y;A_1A_2A_3)_{\rm Eq. \ref{['C3']}}}+ \frac{2RT}{I(Y;A_1,A_2)_{\rm Eq. \ref{['MAC']}}}$ of secure network coding protocol given in Section \ref{['S4-1-2']} with MAC channel. Solid line (Black), Solid line (Green), and Lower dashed line (Red) intersect around$h=1.7$.