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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 problem of characterizing the error-floor domain in the Laplacian channel. An example of the (155,64,20) LDPC code with four iterations (each iteration consisting of two semi-steps: from bits-to-checks and from checks-to-bits) of the min-sum decoding is discussed. A generalized computational tree analysis is devised to explain the rational structure of the leading instantons. The asymptotic for the symbol Bit-Error-Rate in the error-floor domain is comprised of individual instanton contributions, each estimated as ~ exp(-l_{inst;L} s), where the effective distances, l_{inst;L}, of the the leading instantons are 7.6, 8.0 and 8.0 respectively. (The Hamming distance of the code is 20.) The analysis shows that the instantons are distinctly different from the ones found for the same coding/decoding scheme performing over the Gaussian channel. We validate instanton results against direct simulations and offer an explanation for remarkable performance of the instanton approximation not only in the extremal, s -> infty, limit but also at the moderate s values of practical interest.
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
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
It is proved in this work that exhaustively determining bad patterns in arbitrary, finite low-density parity-check (LDPC) codes, including stopping sets for binary erasure channels (BECs) and trapping sets (also known as near-codewords) for general m
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
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