Coding for the Gaussian Interference Channel

Abstract

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.

Construction of Nested Real Ideal Lattices for Interference Channel Coding

“…In [17], for the two-complex dimensional case and L = 2, we have the corresponding complex-valued channel quantization and the construction of complex nested ideal lattices from such a channel quantization. By (40) the functional related to such a minimization is given by…”

Construction of Complex Nested Ideal Lattices for Complex-Valued Channel Quantization

“…In [9] and [10] we have two examples of channel quantization. For the corresponding quantizations, we make use of the binary cyclotomic fields Q(ξ 8 ) and Q(ξ 16 ), respectively.…”

“…In [9] and [10] we have that the lattice partition chains related to r = 3 (n = 2) and r = 4 (n = 4) are given by…”

“…In [9], for the two-complex dimensional case and L = 2, we have the corresponding complex-valued channel quantization and the construction of complex nested ideal lattices from such a channel quantization. By (5.5) the functional related to such a minimization is given by…”