Reweighted LP Decoding for LDPC Codes

Abstract

Abstract-We introduce a novel algorithm for decoding binary linear codes by linear programming. We build on the LP decoding algorithm of Feldman et al. and introduce a post-processing step that solves a second linear program that reweights the objective function based on the outcome of the original LP decoder output. Our analysis shows that for some LDPC ensembles we can improve the provable threshold guarantees compared to standard LP decoding. We also show significant empirical performance gains for the reweighted LP decoding algorithm with very small additional computational complexity.

The ADMM Penalized Decoder for LDPC Codes

“…i − 0.5) and α > 0 is a constant. Using lemmas introduced in [26], we show that this scheme corrects more errors than LP decoding.…”

“…We use L1PD (ℓ 1 penalized decoding) to denote ADMM-PD with an ℓ 1 penalty and RLPD (reweighted LP decoding) to denote our reweighted LP algorithm. Note that this reweighted LP is different from that in [26] (cf. (2.2)).…”

“…a a The set T is chosen using the both the pseudocodeword and the channel output. See details in [26].…”

“…We refer interested readers to [25] for a more comprehensive review on methods to improve LP decoding. In an inspiring paper [26], Khajehnejad et al propose solving a second, reweighted LP, if LP decoding fails. This reweighted LP is constructed using the fractional output of the LP decoder, i.e., the pseudocodeword solution.…”

“…In the BSC, error performance of LP decoding can be improved when a second (reweighted) LP is used whenever LP decoding fails [26]. We denote this reweighted LP as RLPD-KDHVB (Reweighted LP decoding by Khajehnejad-Dimakis-Hassibi-Vigoda-Bradley).…”