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