  Compute-and-forward (CF) harnesses interference in wireless communications by
exploiting structured coding. The key idea of CF is to compute integer
combinations of codewords from multiple source nodes, rather than to decode
individual codewords by treating others as noise. Compute-compress-and-forward
(CCF) can further enhance the network performance by introducing compression
operations at receivers. In this paper, we develop a more general compression
framework, termed generalized compute-compress-and-forward (GCCF), where the
compression function involves multiple quantization-and-modulo lattice
operations. We show that GCCF achieves a broader compression rate region than
CCF. We also compare our compression rate region with the fundamental
Slepian-Wolf (SW) region. We show that GCCF is optimal in the sense of
achieving the minimum total compression rate. We also establish the criteria
under which GCCF achieves the SW region. In addition, we consider a two-hop
relay network employing the GCCF scheme. We formulate a sum-rate maximization
problem and develop an approximate algorithm to solve the problem. Numerical
results are presented to demonstrate the performance superiority of GCCF over
CCF and other schemes.
