Error Exponents of Expander Codes under Linear-Complexity Decoding
SIAM Journal on Discrete Mathematics
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
Good error-correcting codes based on very sparse matrices
IEEE Transactions on Information Theory
Factor graphs and the sum-product algorithm
IEEE Transactions on Information Theory
Improved low-density parity-check codes using irregular graphs
IEEE Transactions on Information Theory
The capacity of low-density parity-check codes under message-passing decoding
IEEE Transactions on Information Theory
Analysis of sum-product decoding of low-density parity-check codes using a Gaussian approximation
IEEE Transactions on Information Theory
Improved bounds on the word error probability of RA(2) codes with linear-programming-based decoding
IEEE Transactions on Information Theory
Using linear programming to Decode Binary linear codes
IEEE Transactions on Information Theory
MAP estimation via agreement on trees: message-passing and linear programming
IEEE Transactions on Information Theory
Guessing facets: polytope structure and improved LP decoder
IEEE Transactions on Information Theory
A separation algorithm for improved LP-decoding of linear block codes
IEEE Transactions on Information Theory
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We initiate the probabilistic analysis of linear programming (LP) decoding of low-density parity-check (LDPC) codes. Specifically, we show that for a random LDPC code ensemble, the linear programming decoder of Feld-man et al. succeeds in correcting a constant fraction of errors with high probability. The fraction of correctable errors guaranteed by our analysis surpasses all prior non-asymptotic results for LDPC codes, and in particular exceeds the best previous finite-length result on LP decoding by a factor greater than ten. This improvement stems in part from our analysis of probabilistic bit-flipping channels, as opposed to adversarial channels. At the core of our analysis is a novel combinatorial characterization of LP decoding success, based on the notion of a generalized matching. An interesting by-product of our analysis is to establish the existence of "almost expansion" in random bipartite graphs, in which one requires only that almost every (as opposed to every) set of a certain size expands, with expansion coefficients much larger than the classical case.