Precoded integer-forcing equalization is a low-complexity transmission and reception scheme, primarily designed for open-loop communication. The data is encoded into independent streams, all using the same linear code, after which linear precoding is applied, while integer-forcing equalization is applied at the receiver side. Previous works have established that this architecture achieves channel capacity up to a finite gap for general multiple-input multiple-output Gaussian channels, as well as obtained tighter bounds for the special case of diagonal (parallel) channels. The present work provides a precise performance characterization when integer-forcing equalization is applied to two parallel channels and where precoding is done using the full-diversity rotation matrix cyclo2. It is shown that this scheme achieves capacity up to a gap bounded by log2(9/5) bits per complex channel use when the standard integer-forcing receiver is used, and the gap is reduced to log2(5/4) bits per complex channel use when its successive decoding variant is applied. In addition, a full characterization of the basis transformation matrices used by the integer-forcing receiver is derived. These turn out to consist only of Fibonacci numbers and are explicitly determined as a function of the condition number. The results obtained are also highly relevant to lattice-reduction detection schemes.
- lattice reduction
- unitary precoding