Exact free distance and trapping set growth rates for LDPC convolutional codes

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.

DOI: 10.1109/ISIT.2011.6033700

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Cite this paper

@article{Mitchell2011ExactFD, title={Exact free distance and trapping set growth rates for LDPC convolutional codes}, author={David G. M. Mitchell and Ali Emre Pusane and Michael Lentmaier and Daniel J. Costello}, journal={2011 IEEE International Symposium on Information Theory Proceedings}, year={2011}, pages={1096-1100} }