  Due to 5G deployment, there is significant interest in LDPC decoding. While
much research is devoted on efficient hardwiring of algorithms based on Belief
Propagation (BP), it has been shown that LDPC decoding can be formulated as a
combinatorial optimization problem, which could benefit from significant
acceleration of physical computation mechanisms such as Ising machines. This
approach has so far resulted in poor performance. This paper shows that the
reason is not fundamental but suboptimal hardware and formulation. A
co-designed Ising machine-based system can improve speed by 3 orders of
magnitude. As a result, a physical computation approach can outperform
hardwiring state-of-the-art algorithms. In this paper, we show such an
augmented Ising machine that is 4.4$\times$ more energy efficient than the
state of the art in the literature.
