Achieving the gains promised by Integer-Forcing equalization with binary codes

We address the problem of constructing practical coding schemes for Integer-Forcing (IF) equalization. Previously proposed IF schemes suggested the use of nested lattice codes or linear block codes over Z_q. While such codes have good properties from a theoretic point of view, their implementation complexity may become significant when q is large. In this work we show that at high transmission rates, linear codes suitable for IF equalization may be constructed using binary codes, incurring only moderate losses compared to optimal capacity achieving nested lattice codes. The technique is based on Ungerboeck´s method of mapping by set partitioning.