  Compute-and-forward (CF) harnesses interference in a wireless networkby
allowing relays to compute combinations of source messages. The computed
message combinations at relays are correlated, and so directly forwarding these
combinations to a destination generally incurs information redundancy and
spectrum inefficiency. To address this issue, we propose a novel relay
strategy, termed compute-compress-and-forward (CCF). In CCF, source messages
are encoded using nested lattice codes constructed on a chain of nested coding
and shaping lattices. A key difference of CCF from CF is an extra compressing
stage inserted in between the computing and forwarding stages of a relay, so as
to reduce the forwarding information rate of the relay. The compressing stage
at each relay consists of two operations: first to quantize the computed
message combination on an appropriately chosen lattice (referred to as a
quantization lattice), and then to take modulo on another lattice (referred to
as a modulo lattice). We study the design of the quantization and modulo
lattices and propose successive recovering algorithms to ensure the
recoverability of source messages at destination. Based on that, we formulate a
sum-rate maximization problem that is in general an NP-hard mixed integer
program. A low-complexity algorithm is proposed to give a suboptimal solution.
Numerical results are presented to demonstrate the superiority of CCF over the
existing CF schemes.
