  Integer Forcing (IF) is a novel linear receiver architecture, where instead
of separating the codewords sent by each transmitter, and decoding them
individually, forces integer-valued linear combinations at each receive
antenna, and decodes the linear combinations. The original codewords are
obtained by inverting the integer-valued matrix. While demonstrating superior
performance, IF requires complex optimization in order to find the optimal
linear combinations, and demands either using multi-level nested lattice codes,
or reducing the rates of all transmitters to equal the weakest one. Finally,
the distribution of the resulting effective SNR is hard to evaluate.
  In this paper, we first give simple upper and lower bounds on the effective
SNR of a single linear combination in IF. These expressions allow us to easily
bound the distribution of the effective SNR for any given linear combination
used. We then suggest two simple block-based IF schemes. These schemes, while
sub-optimal, significantly reduce the complexity of the optimization process,
and, more importantly, do not require reducing the rates of all transmitters,
as decoding is done block-wise. Finally, we bound the distribution of the
effective SNR of the decoding schemes, and show via simulations the superiority
of block-wise schemes at low SNR.
