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arXiv · 0905.3733

Trapping Set Enumerators for Repeat Multiple Accumulate Code Ensembles

Christian Koller·Alexandre Graell i Amat·Joerg Kliewer·Daniel J. Costello Jr
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Abstract

The serial concatenation of a repetition code with two or more accumulators has the advantage of a simple encoder structure. Furthermore, the resulting ensemble is asymptotically good and exhibits minimum distance growing linearly with block length. However, in practice these codes cannot be decoded by a maximum likelihood decoder, and iterative decoding schemes must be employed. For low-density parity-check codes, the notion of trapping sets has been introduced to estimate the performance of these codes under iterative message passing decoding. In this paper, we present a closed form finite length ensemble trapping set enumerator for repeat multiple accumulate codes by creating a trellis representation of trapping sets. We also obtain the asymptotic expressions when the block length tends to infinity and evaluate them numerically.

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Christian Koller, Alexandre Graell i Amat, Joerg Kliewer, Daniel J. Costello Jr. 2009-05-22. Trapping Set Enumerators for Repeat Multiple Accumulate Code Ensembles. https://doi.org/10.1109/isit.2009.5205355

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