Skip to main content

Table 1 Encoding and decoding at nodes

From: Lattice-coded cooperation protocol for the half-duplex Gaussian two-way relay channel

 

Phase 1

Phase 2

Phase 3

Phase 4

(a) Encoding at nodes

    

Node 1

\(\boldsymbol {X}_{1}=\frac {1}{g_{1}}\left [\boldsymbol {V}_{1}+\boldsymbol {D}_{1}\right ]\textrm {mod }\Lambda _{s1}^{(n_{1})}\)

−

−

\(\boldsymbol {X}_{1}^{(4)}\left (\boldsymbol {L}_{b,1}\right)\)

Node 2

\(\boldsymbol {X}_{2}=\frac {1}{g_{2}}\left [\boldsymbol {V}_{2}+\boldsymbol {D}_{2}\right ]\textrm {mod }\Lambda _{s2}^{(n_{1})}\)

−

\(\boldsymbol {X}_{2}^{(3)}\left (\boldsymbol {L}_{2}^{(3)}\right)\)

−

Relay

−

\(\boldsymbol {X}_{r}^{(2)}\left (\boldsymbol {L}_{a,1}\right)\)

\(\boldsymbol {X}_{r}^{(3)}\left (\boldsymbol {L}_{r}^{(3)}\right)\)

\(\boldsymbol {X}_{r}^{(4)}\left (\boldsymbol {L}_{b,1}\right)\)

(b) Decoding at nodes

    

Node 1

−

V a,2

V b,2

−

Node 2

−

V a,1

−

V b,1

Relay

\(\begin {array}{lcl} \boldsymbol {V}_{r,1} & = & \left [\boldsymbol {V}_{1}+\boldsymbol {V}_{2}\right.\\ & & \left.-\mathcal {Q}_{\Lambda _{s2}}\left (\boldsymbol {V}_{2}+\boldsymbol {D}_{2}\right)\right ]\textrm {mod }\Lambda _{s1}^{(n_{1})}\\ \boldsymbol {V}_{r,2} & = & \left [\boldsymbol {V}_{1}+\boldsymbol {V}_{2}\right ]\textrm {mod }\Lambda _{s2}^{(n_{1})} \end {array}\)

−

−

−