  Integer-forcing receivers generalize traditional linear receivers for the
multiple-input multiple-output channel by decoding integer-linear combinations
of the transmitted streams, rather then the streams themselves. Previous works
have shown that the additional degree of freedom in choosing the integer
coefficients enables this receiver to approach the performance of
maximum-likelihood decoding in various scenarios. Nonetheless, even for the
optimal choice of integer coefficients, the additive noise at the equalizer's
output is still correlated. In this work we study a variant of integer-forcing,
termed successive integer-forcing, that exploits these noise correlations to
improve performance. This scheme is the integer-forcing counterpart of
successive interference cancellation for traditional linear receivers.
Similarly to the latter, we show that successive integer-forcing is capacity
achieving when it is possible to optimize the rate allocation to the different
streams. In comparison to standard successive interference cancellation
receivers, the successive integer-forcing receiver offers more possibilities
for capacity achieving rate tuples, and in particular, ones that are more
balanced.
