Interference is usually viewed as an obstacle to communication in wireless networks, so we developed a new methodology to quantize the channel coefficients in order to realize interference alignment onto a lattice. Our channel model is the same from the compute-and-forward strategy. In this work, we are going to explicit one example of channel quantization, which is related to the dimension 4 (real) or 2 (complex), and we will make use of the binary cyclotomic field Q(ξ8), where ξ8 is the 8-th root of unity.
In this work, we propose an innovative methodology to extend the construction of minimum and non-minimum delay perfect codes as a subset of cyclic division algebras over Q(ζ 3), where the signal constellations are isomorphic to the hexagonal A n 2-rotated lattice, for any channel of any dimension n such that gcd(n, 3) = 1.
Through algebraic number theory and Construction $A$ we extend an algebraic procedure which generates complex lattice codes from the polynomial ring \mathbb{F}_{2}[x]/(x^{n}-1), where \mathbb{F}_{2}=\{0,1\}, by using ideals from the generalized polynomial ring \frac{\mathbb{F}_{2}[x,\frac{1}{2}\mathbb{Z}_{0}]}{((x^{\frac{1}{2}})^{n}-1)} through the ring of integers $\mathcal{O}_{\mathbb{L}}$ of the cyclotomic field \mathbb{L}=\mathbb{Q}(\zeta_{2^{s}}), where \zeta_{2^{s}} is a 2^{s}-th root of the unit, with s2.
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