A Low-Complexity Projection Algorithm for ADMM-Based LP Decoding

In this paper, we present a new low-complexity algorithm for computing the projection onto the parity polytope in the context of ADMM-based LP decoding. This projection is the heart of the ADMM algorithm, that usually involves a sorting operation, which is the main effort of the projection. Our proposed algorithm relies on new findings in the recursive structure of the parity polytope and works by fixing selected components in an iterative manner. The absence of the sorting operation makes it preferable for efficient hard-and software implementations. In addition, we can show that this new projection algorithm requires up to 37% less arithmetic operations compared to state-of-the-art projections.