Reweighted LP Decoding for LDPC Codes

Creators: Khajehnejad, Amin; Dimakis, Alexandros G.; Hassibi, Babak; Vigoda, Benjamin; Bradley, William

Abstract

We introduce a novel algorithm for decoding binary linear codes by linear programming (LP). We build on the LP decoding algorithm of Feldman and introduce a postprocessing 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.

Additional Information

© 2012 IEEE. Manuscript received March 14, 2011; revised September 27, 2011; accepted May 11, 2012. Date of publication June 01, 2012; date of current version August 14, 2012. This work was supported in part by the National Science Foundation under Grants CCF-0729203, CNS-0932428, and CCF-1018927, in part by the Office of Naval Research under the MURI Grant N00014-08-1-0747, in part by Caltech's Lee Center for Advanced Networking, and in part by DARPA FA8750-07-C-0231. The material in this paper was presented in part at the Allerton Conference on Communication, Control, and Computing, Monticello, IL, 2010.

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