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We discuss how the loop calculus approach of [Chertkov, Chernyak 06], enhanced by the pseudo-codeword search algorithm of [Chertkov, Stepanov 06] and the facet-guessing idea from [Dimakis, Wainwright 06], improves decoding of graph based codes in the error-floor domain. The utility of the new, Linear Programming based, decoding is demonstrated via analysis and simulations of the model $[155,64,20]$ code.
Cyclic liftings are proposed to lower the error floor of low-density parity-check (LDPC) codes. The liftings are designed to eliminate dominant trapping sets of the base code by removing the short cycles which form the trapping sets. We derive a nece
Staircase codes play an important role as error-correcting codes in optical communications. In this paper, a low-complexity method for resolving stall patterns when decoding staircase codes is described. Stall patterns are the dominating contributor
Spatially coupled turbo-like codes (SC-TCs) have been shown to have excellent decoding thresholds due to the threshold saturation effect. Furthermore, even for moderate block lengths, simulation results demonstrate very good bit error rate performanc
We analyze the performance of Low-Density-Parity-Check codes in the error-floor domain where the Signal-to-Noise-Ratio, s, is large, s >> 1. We describe how the instanton method of theoretical physics, recently adapted to coding theory, solves the pr
In this paper we develop instanton method introduced in [1], [2], [3] to analyze quantitatively performance of Low-Density-Parity-Check (LDPC) codes decoded iteratively in the so-called error-floor regime. We discuss statistical properties of the num