freedom that we achieve for a symmetric three user Gaussian IC using the layered lattice coding approach.

\[fig : dof symmetric\] ![Plot of Achievable Degrees of Freedom versus $a^2$](dof_symmetric1 "fig:"){width="3.5"}

From (\[eqn : Theorem 1\]), we can see that the achievable total degrees of freedom tends to $3/2$ as the channel gain $a \rightarrow \infty$, and when $a \rightarrow 0$. We should also see that when the channel gain $a = 0$, then we can achieve $3$ degrees of freedom.

Comparing Lattice Coding and Han Kobayashi Coding
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In this section, we compare our layer lattice coding approach with the extension of Han-Kobayashi scheme for the three user symmetric Gaussian IC. In the Han-Kobayashi coding scheme for the two user IC [@HanKobayashi1981], each transmitter splits its message into two parts, a private part and a common part. For decoding, each receiver decodes its message and the common message transmitted by the interfering transmitter. In the extension of this scheme to the three user IC, each transmitter splits its message into four parts - one private part and three common parts. For instance, transmitter $1$ splits its message $m_1$ into four parts - 1) $m_{11}$, the private part, 2) $m_{12}$, the 