A generator matrix (GM)-based approach for adaptively deriving cut-inducing redundant parity checks (RPCs) during the adaptive linear programming decoding algorithm is presented. More precisely speaking, if the decoder gets stuck in a non-integral pseudocodeword, then the resulting RPCs are likely to provide violated forbidden-set inequalities that can separate this non-integral optimal solution from the feasible region. The described approach can be viewed as a GM-based counterpart of the approach proposed by Zhang and Siegel in 2012. For binary linear codes of low rate, while providing the same error-correcting performance, our approach requires much less computational time compared to its analogue.
Falsafain, H., & Mousavi, S. R. (2016). A Generator-Matrix-Based Approach for Adaptively Generating Cut-Inducing Redundant Parity Checks. IEEE Communications Letters, 20(4), 640-643. https://doi.org/10.1109/LCOMM.2016.2530706