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Integer-forcing receivers generalize traditional linear receivers for themultiple-input multiple-output channel by decoding integer-linear combinationsof the transmitted streams, rather then the streams themselves. Previous workshave shown that the additional degree of freedom in choosing the integercoefficients enables this receiver to approach the performance ofmaximum-likelihood decoding in various scenarios. Nonetheless, even for theoptimal choice of integer coefficients, the additive noise at the equalizer'soutput is still correlated. In this work we study a variant of integer-forcing,termed successive integer-forcing, that exploits these noise correlations toimprove performance. This scheme is the integer-forcing counterpart ofsuccessive interference cancellation for traditional linear receivers.Similarly to the latter, we show that successive integer-forcing is capacityachieving when it is possible to optimize the rate allocation to the differentstreams. In comparison to standard successive interference cancellationreceivers, the successive integer-forcing receiver offers more possibilitiesfor capacity achieving rate tuples, and in particular, ones that are morebalanced.

Successive Integer-Forcing and its Sum-Rate Optimality