Randomized Scheduling of ADMM-LP Decoding Based on Geometric Priors

We present a randomized schedule for alternating direction method of multipliers with linear programming (ADMM-LP) decoding of low-density parity check (LDPC) codes. The randomized schedule is based on horizontal layered decoding, where nodes are updated sequentially. Unlike existing layered decoding frameworks where all check nodes are updated exactly once per iteration, we propose a randomized schedule where more problematic nodes are updated more frequently. To do so, we sample from a probability mass function (PMF) over all check nodes and the check with sampled index is updated. The probability of each check to be updated is determined by its state. The PMF is constructed based on the distribution of replica (check) vectors inside or on the parity polytope. The randomized decoder usually converges faster than both standard and horizontal layered decoders, making it suitable for limited-iteration decoding in high-throughput applications.