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arXiv · 1106.1414

Exact Free Distance and Trapping Set Growth Rates for LDPC Convolutional Codes

David G. M. Mitchell·Ali E. Pusane·Michael Lentmaier·Daniel J. Costello Jr
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Abstract

Ensembles of (J,K)-regular low-density parity-check convolutional (LDPCC) codes are known to be asymptotically good, in the sense that the minimum free distance grows linearly with the constraint length. In this paper, we use a protograph-based analysis of terminated LDPCC codes to obtain an upper bound on the free distance growth rate of ensembles of periodically time-varying LDPCC codes. This bound is compared to a lower bound and evaluated numerically. It is found that, for a sufficiently large period, the bounds coincide. This approach is then extended to obtain bounds on the trapping set numbers, which define the size of the smallest, non-empty trapping sets, for these asymptotically good, periodically time-varying LDPCC code ensembles.

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David G. M. Mitchell, Ali E. Pusane, Michael Lentmaier, Daniel J. Costello Jr. 2011-06-07. Exact Free Distance and Trapping Set Growth Rates for LDPC Convolutional Codes. https://doi.org/10.1109/isit.2011.6033700

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