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 finite-length optimization.

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SUMMARYWe explain how to optimise finite-length LDPC codes for transmission over the binary erasure channel. Our approach relies on an analytic approximation of the erasure probability. This is in turn based on a finite-length scaling result to model large scale erasures and a union bound involving minimal stopping sets to take into account small error events. We show that the performance of optimised ensembles as observed in simulations is well described by our approximation. Although we only address the case of transmission over the binary erasure channel, our method should be applicable to a more general setting.

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