2009
DOI: 10.1109/tit.2008.2009580
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Finite-Length Scaling for Iteratively Decoded LDPC Ensembles

Abstract: In this paper we investigate the behavior of iteratively decoded low-density paritycheck codes over the binary erasure channel in the so-called "waterfall region." We show that the performance curves in this region follow a very basic scaling law. We conjecture that essentially the same scaling behavior applies in a much more general setting and we provide some empirical evidence to support this conjecture. The scaling law, together with the error floor expressions developed previously, can be used for fast fi… Show more

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Cited by 125 publications
(262 citation statements)
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“…As shown in [16], the DD of the residual graph at any time converges (in the code length) to a multivariate Gaussian whose mean and covariance matrix is given by the solution of a coupled system of differential equations. Using these results, estimating the error probability consists in computing the probability that, during the decoding process, the random process representing the fraction of degree-one check nodes in the residual graph reaches zero before all variables have been determined.…”
Section: Csit] 25 May 2015mentioning
confidence: 99%
See 4 more Smart Citations
“…As shown in [16], the DD of the residual graph at any time converges (in the code length) to a multivariate Gaussian whose mean and covariance matrix is given by the solution of a coupled system of differential equations. Using these results, estimating the error probability consists in computing the probability that, during the decoding process, the random process representing the fraction of degree-one check nodes in the residual graph reaches zero before all variables have been determined.…”
Section: Csit] 25 May 2015mentioning
confidence: 99%
“…Under the assumption that the distribution of the number of degree-one check nodes in the graph is Gaussian [16], the statistics for the fraction of degree-one check nodes during the critical phase of the decoding process are those of an appropriately chosen Ornstein-Uhlenbeck (OU) process [22]. OU processes have been widely studied and used in diverse areas of applied mathematics like biological modeling [23], [24], mathematical finance [25], [26] and statistical physics [27].…”
Section: Csit] 25 May 2015mentioning
confidence: 99%
See 3 more Smart Citations