Alternating direction method of multipliers (ADMM) is a popular technique for linear-programming decoding of low-density parity-check codes. The computational complexity of ADMM is dominated by the Euclidean projection of a real-valued vector onto a parity-check polytope. Existing algorithms for such a projection all require sorting operations, which happen to be the most complex part of the projection. In this letter, we propose an iterative algorithm, without sorting operation, for projection onto the parity-check polytope. The proposed algorithm has a worst case complexity linear in the input dimension compared with the super-linear complexity of existing algorithms.
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Wei et al. (2017) studied this question.
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