  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.
