Performance of precoded integer-forcing for parallel Gaussian channels

Recently, an open-loop transmission scheme for multiple-input multiple-output Gaussian channels based on precoded integer-forcing was proposed. The transmitter encodes the data into independent streams, all taken from the same linear code. The coded streams are then linearly precoded using a unitary matrix. At the receiver side, integer-forcing equalization is applied, followed by single-stream decoding. It was shown that this communication architecture achieves capacity up to a finite gap. In the present work we consider precoded integer-forcing for parallel Gaussian channels. We derive tighter bounds for this class of channels, which are related to the minimum product distance figure of merit. We further suggest a practical scheme that is applicable for all transmission rates, where the precoding matrix is capacity-dependent, chosen so as to maximize the achievable rate for a given value of capacity. For example, it is shown that for the case of two and three parallel channels, the scheme universally (for any value of capacity) achieves 94% and 82% of capacity, respectively.